PKIigg+Principles Of Heat Transfer/Chapter_1.ipynb{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 1: Basic Modes of Heat Transfer"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.1: Page 8"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.1 \"\n",
"\n",
"#Temperature Inside in F\n",
"Ti = 55;\n",
"#Temperature outside in F\n",
"To = 45;\n",
"#Thickness of the wall in ft\n",
"t = 1;\n",
"#Heat loss through the wall in Btu/h-ft2\n",
"q = 3.4;\n",
"\n",
"#Converting Btu/h-ft2 to W/m2\n",
"print \"Heat loss through the wall in W/m2 is\"\n",
"#Heat loss through the wall in W/m2 \n",
"print \"qdash = \",(q*0.2931)/0.0929\n",
"\n",
"#Heat loss for a 100ft2 surface over a 24-h period\n",
"print \"Heat loss for a 100ft2 surface over a 24-h period in Btu is\"\n",
"#Heat loss for a 100ft2 surface over a 24-h period in Btu \n",
"print \"Q = (q*100)*24\n",
"\n",
"#Q in SI units i.e. kWh\n",
"print \"Q = \",(Q*0.2931)/1000;\n",
"\n",
"#At price of 10c/kWh, the total price shall be\n",
"print \"So, the total price in c are\"\n",
"#Total price in c\n",
"print \"Price = \",round(10*Q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.1 \n",
"Heat loss through the wall in W/m2 is\n",
"Heat loss for a 100ft2 surface over a 24-h period in Btu is\n",
"So, the total price in c are\n",
"Price = 24.0 c\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.2: Page 13"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.2 \"\n",
"\n",
"#Thermal conductivity of window glass in W/m-K\n",
"k = 0.81;\n",
"#Height of the glass in m\n",
"h = 1;\n",
"#Width of the glass in m\n",
"w = 0.5;\n",
"#Thickness of the glass in m\n",
"t = 0.005;\n",
"#Outside temperature in C\n",
"T2 = 24;\n",
"#Inside temperature in C\n",
"T1 = 24.5;\n",
"\n",
"#Assume that steady state exists and that the temperature is uniform over the inner and outer surfaces\n",
"\n",
"#Cross sectional area in m2\n",
"A = h*w;\n",
"\n",
"print \"Thermal resistance to conduction in K/W is\"\n",
"#Thermal resistance to conduction in K/W\n",
"R=t/(k*A)\n",
"print \"R = \",round(R,4)\n",
"\n",
"#The rate of heat loss from the interior to the exterior surface is\n",
"#obtained by dividing temperature difference from the thermal resistence\n",
"\n",
"print \"Heat loss in W from the window glass is\"\n",
"#Heat loss in W\n",
"print \"q = \",int((T1-T2)/R)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.2 \n",
"Thermal resistance to conduction in K/W is\n",
"R = 0.0123\n",
"Heat loss in W from the window glass is\n",
"q = 40\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.3: Page 20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.3 \"\n",
"\n",
"#Area of room in m2 is given as\n",
"A = 20*20;\n",
"#Air temperature in C\n",
"Tair = -3;\n",
"#Roof temperature in C\n",
"Troof = 27;\n",
"#Heat transfer coefficient in W/m2-K\n",
"h = 10;\n",
"\n",
"#Assume that steady state exists and the direction of heat flow is from the\n",
"#roof to the air i.e higher to lower temperature (as it should be).\n",
"\n",
"print \" The rate of heat transfer by convection from the roof to the air in W\"\n",
"#The rate of heat transfer by convection from the roof to the air in W\n",
"print \"q = \",(-h*A)*(Troof-Tair)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.3 \n",
" The rate of heat transfer by convection from the roof to the air in W\n",
"q = -120000\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.4: Page 22"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.4 \"\n",
"\n",
"#Diameter of rod in m\n",
"d = 0.02;\n",
"# Emissivity and temperautre of rod in K\n",
"epsilon = 0.9;\n",
"T1 = 1000;\n",
"#Temperature of walls of furnace\n",
"T2 = 800;\n",
"\n",
"#Assuming steady state has been reached.\n",
"#Since the walls of the furnace completely enclose the heating rod, all the radiant energy emitted by the surface of the rod is intercepted by the furnace walls\n",
"\n",
"#From eq. 1.17, net heat loss can be given\n",
"\n",
"print \"Net heat loss per unit length considering 1m length in W\"\n",
"#Area in m2\n",
"A =(math.pi*d)*1;\n",
"#Constant sigma in W/m2-K4\n",
"sigma = 0.0000000567;\n",
"#Net heat loss per unit length considering 1m length in W\n",
"q=((A*sigma)*epsilon)*(T1**4-T2**4)\n",
"print\" q = \",round(q)\n",
"#From eq. 1.21 radiation heat transfer coefficient in W/m2-K is\n",
"print \"Radiation heat transfer coefficient in W/m2-K is\"\n",
"#Radiation heat transfer coefficient in W/m2-K \n",
"print \"hr = \",round(((epsilon*sigma)*(T1**4-T2**4))/(T1-T2))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.4 \n",
"Net heat loss per unit length considering 1m length in W\n",
" q = 1893.0\n",
"Radiation heat transfer coefficient in W/m2-K is\n",
"hr = 151.0\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.5: Page 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.5 \"\n",
"\n",
"#Thickness of inside steel in m and thermal conductivity in W/m-k\n",
"t1 = 0.005;\n",
"k1 = 40;\n",
"#Thickness of outside brick in m and thermal conductivity in W/m-k\n",
"t2 = 0.1;\n",
"k2 = 2.5;\n",
"\n",
"#Inside temperature in C\n",
"T1 = 900;\n",
"#Outside temperature in C\n",
"To = 460;\n",
"\n",
"#Assuming the condition of steady state and umath.sing Eq. 1.24\n",
"print \"The rate of heat loss per unit area in W/m2 is\"\n",
"#The rate of heat loss per unit area in W/m2 \n",
"qk = (T1-To)/(t1/k1+t2/k2)\n",
"print int(qk)\n",
"\n",
"print \"Temperature at the interface in K is given as\"\n",
"#Temperature at the interface in K\n",
"T2 = T1-(qk*t1)/k1\n",
"print round(T2,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.5 \n",
"The rate of heat loss per unit area in W/m2 is\n",
"10965\n",
"Temperature at the interface in K is given as\n",
"898.6\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.6: Page 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.6 \"\n",
"\n",
"#Thermal conductivity of aluminium in W/m-K\n",
"k = 240.0;\n",
"#Thickness of each plate in m\n",
"t = 0.01;\n",
"#Temperature at the surfaces of plates in C is given as\n",
"Ts1 = 395.0;\n",
"Ts3 = 405.0;\n",
"#From Table 1.6 the contact resistance at the interface in K/W is\n",
"R2 = 0.000275;\n",
"#Thermal resistance of the plates in K/W is\n",
"R1 = t/k;\n",
"R3 = t/k;\n",
"\n",
"print \"Heat flux in W/m2-K is\"\n",
"#Heat flux in W/m2-K\n",
"q = (Ts3-Ts1)/(R1+R2+R3)\n",
"print \"{:.2e}\".format(q)\n",
"#Since the temperature drop in each section of this one-dimensional system is propor-tional to the resistance.\n",
"\n",
"print \"Temperature drop due to contact resistance in degree C is\"\n",
"#Temperature drop due to contact resistance in degree C\n",
"deltaT = (R2/(R1+R2+R3))*(Ts3-Ts1)\n",
"print round(deltaT,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.6 \n",
"Heat flux in W/m2-K is\n",
"2.79e+04\n",
"Temperature drop due to contact resistance in degree C is\n",
"7.67\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.7: Page 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.7 \"\n",
"\n",
"#Because of symmetry, we need to calculate for only one half of the system\n",
"\n",
"#Thickness of firebrick in inches\n",
"L1 = 1.0;\n",
"#Thermal conductivity of firebrick in Btu/h-ft-F\n",
"kb = 1.0;\n",
"#Thickness of steel plate in inches\n",
"L3 = 1/4.0;\n",
"#Thermal conductivity of steel in Btu/h-ft-F\n",
"ks = 30;\n",
"#Average height of asperities in inches is given as\n",
"L2 = 1/32.0;\n",
"#Temperature difference between the steel plates in F is\n",
"deltaT = 600.0;\n",
"\n",
"\n",
"#The thermal resistance of the steel plate is, on the basis of a unit wall area, equal to\n",
"R3 = L3/(12*ks);#12 is added to convert ft to in\n",
"\n",
"#The thermal resistance of the brick asperities is, on the basis of a unit wall area, equal to\n",
"R4 = L2/((0.3*12)*kb);#Considering the 30 percent area\n",
"\n",
"#At temperature of 300F, thermal conductivity of air in Btu/h-ft-F is\n",
"ka = 0.02;\n",
"\n",
"# Thermal resistance of the air trapped between the asperities, is, on the basis of a unit area, equal to\n",
"R5 = L2/((0.7*12)*ka);#Considering the other 70 percent area\n",
"\n",
"#Since R4 and R5 are in parallel, so there combined resistance is\n",
"R2 = (R4*R5)/(R4+R5);\n",
"\n",
"#The thermal resistance of half of the solid brick is\n",
"R1 = L1/(12*kb);\n",
"\n",
"#The overall unit conductance for half the composite wall in Btu/h-ft2-F is then\n",
"kk = 0.5/(R1+R2+R3);\n",
"\n",
"print \"The rate of heat flow per unit area in Btu/h-ft2 is\"\n",
"#The rate of heat flow per unit area in Btu/h-ft2\n",
"q = kk*deltaT\n",
"print round(q,2)\n",
"\n",
"# the answer is slightly different in textbook due to approximation\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.7 \n",
"The rate of heat flow per unit area in Btu/h-ft2 is\n",
"3249.52088923\n"
]
}
],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.8: Page 35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.8 \"\n",
"\n",
"#Length for heat transfer for stainless steel in m\n",
"Lss = 0.1;\n",
"\n",
"#Area for heat transfer for stainless steel in m2\n",
"A = 0.01;\n",
"\n",
"#Thermal conductivity for stainless steel in W/m-K\n",
"kss = 144;\n",
"\n",
"#Length for heat transfer for Duralumin in m\n",
"La1 = 0.02;\n",
"\n",
"#Area for heat transfer for Duralumin in m2\n",
"A = 0.01;\n",
"\n",
"#Thermal conductivity for Duralumin in W/m-K\n",
"ka1 = 164;\n",
"\n",
"#Resistance in case of steel in K/W\n",
"Rk1 = Lss/(A*kss);\n",
"\n",
"#Resistance in case of Duralumin in K/W\n",
"Rk2 = La1/(A*ka1);\n",
"\n",
"#From Fig. 1.20, contact resistance in K/W\n",
"Ri = 0.05;\n",
"\n",
"#Total resistance to heat transfer in K/W\n",
"Rtotal = Rk1+Rk2+Ri;\n",
"\n",
"#Temperature diff. is given in K\n",
"deltaT = 40;\n",
"\n",
"print \"Maximum allowable rate of heat dissipation in W is\"\n",
"#Maximum allowable rate of heat dissipation in W\n",
"q = deltaT/Rtotal\n",
"\n",
"print int(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.8 \n",
"Maximum allowable rate of heat dissipation in W is\n",
"303\n"
]
}
],
"prompt_number": 34
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.9: Page 37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.9 \"\n",
"\n",
"#Cross sectional area in m2\n",
"A = 1.0;\n",
"#Heat transfer coefficient on hot side in W/m2-K\n",
"hchot = 10.0;\n",
"#Heat transfer coefficient on cold side in W/m2-K\n",
"hccold = 40.0;\n",
"\n",
"#Length for heat transfer in m\n",
"L = 0.1;\n",
"#Thermal conductivity in W/m-K\n",
"k = 0.7;\n",
"\n",
"#Resistances in K/w\n",
"R1 = 1/(hchot*A);\n",
"R2 = L/(k*A);\n",
"R3 = 1/(hccold*A);\n",
"\n",
"#Total resistance\n",
"Rtotal = R1+R2+R3;\n",
"\n",
"#Temperature on hot side in K\n",
"T1 = 330.0;\n",
"#Temperature on cold side in K\n",
"T2 = 270.0;\n",
"\n",
"print \"Rate of heat transfer per unit area in W is\"\n",
"#Rate of heat transfer per unit area in W\n",
"q = (T1-T2)/(R1+R2+R3)\n",
"print round(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.9 \n",
"Rate of heat transfer per unit area in W is\n",
"224.0\n"
]
}
],
"prompt_number": 42
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.10: Page 40"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.10 \"\n",
"\n",
"#diameter of pipe in m\n",
"d = 0.5;\n",
"#Epsilon is given as\n",
"epsilon = 0.9;\n",
"#sigma(constant) in SI units is\n",
"sigma = 0.0000000567;\n",
"#Temperatures in K are given as\n",
"T1 = 500;\n",
"T2 = 300;\n",
"\n",
"#Radiation heat transfer coefficient in W/m2K\n",
"hr = ((sigma*epsilon)*(T1*T1+T2*T2))*(T1+T2);\n",
"\n",
"#Convection heat transfer coefficient in W/m2K\n",
"hc = 20;\n",
"\n",
"#total heat transfer coefficient in W/m2K\n",
"h = hc+hr;\n",
"\n",
"print \"Rate of heat loss per meter in W/m is\"\n",
"#Rate of heat loss per meter in W/m\n",
"q = ((math.pi*d)*h)*(T1-T2)\n",
"\n",
"print round(q,2)\n",
"\n",
"# the answer is slightly different due to approximation\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.10 \n",
"Rate of heat loss per meter in W/m is\n",
"10643.77\n"
]
}
],
"prompt_number": 46
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.11: Page 43"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.11 \"\n",
"\n",
"#Hot-gas temperature in K\n",
"Tgh = 1300.0;\n",
"#Heat transfer coefficient on hot side in W/m2K\n",
"h1 = 200.0;\n",
"#Heat transfer coefficient on cold side in W/m2K\n",
"h3 = 400.0;\n",
"#Coolant temperature in K\n",
"Tgc = 300.0;\n",
"#Max temp. in C\n",
"Tsg = 800.0;\n",
"#Maximum permissible unit thermal resistance per square meter of the metal wall in K/W\n",
"R2 = ((Tgh-Tgc)*(1/h1)/(Tgh-Tsg))-1/h1-1/h3;\n",
"print \"Maximum permissible unit thermal resistance per square meter of the metal wall in m2.K/W is\"\n",
"print R2\n",
"\n",
"# The answer is wrong in the textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.11 \n",
"Maximum permissible unit thermal resistance per square meter of the metal wall in m2.K/W is\n",
"0.0025\n"
]
}
],
"prompt_number": 54
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.12: Page 49"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.12 \"\n",
"\n",
"# total length of metal sheet in m\n",
"L = 0.625/39.4;\n",
"# we estimate the thermal conductivity of the metal sheets to be approximately 43 W/m K\n",
"k = 43;\n",
"# therefore the resistance in K/W offered by metal sheey\n",
"R = L/k;\n",
"\n",
"#heat loss in W/m2 is given as\n",
"q = 1200;\n",
"# overall heat transfer coefficient between the gas and the door is given\n",
"# in W/m2K\n",
"U = 20;\n",
"#The temperature drop between the gas and the interior surface of the door at the specified heat flux is\n",
"deltaT1 = q/U;\n",
"#Hence, the temperature of the Inconel will be in degree C\n",
"T = 1200-deltaT1;\n",
"\n",
"#The heat transfer coefficient between the outer surface of the door and\n",
"#the surroundings at 20\u00b0C in W/m2K\n",
"h = 5;\n",
"#The temperature drop at the outer surface in degree C is\n",
"deltaT2 = q/h;\n",
"#Selecting milled alumina-silica chips as insulator (Fig 1.31 on page 48)\n",
"\n",
"# Hence, temperature difference across the insulation is\n",
"deltaT3 = T-deltaT1-deltaT2;\n",
"\n",
"#thermal conductivity for milled alumina-silica chips in W/mK is\n",
"k = 0.27;\n",
"\n",
"print \"The insulation thickness in m is\"\n",
"#The insulation thickness in m\n",
"L = (k*deltaT3)/q\n",
"\n",
"print round(L,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.12 \n",
"The insulation thickness in m is\n",
"0.2\n"
]
}
],
"prompt_number": 57
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.13: Page 53"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.13 \"\n",
"\n",
"#Temperature of air in degree K\n",
"Tair = 300;\n",
"#Heat transfer coefficient in W/m2K\n",
"h = 10.0;\n",
"\n",
"print \"Part a\"\n",
"#Radiation solar flux in W/m2\n",
"q = 500.0;\n",
"#Ambient temperature in K\n",
"Tsurr = 50.0;\n",
"\n",
"print \"Solving energy balance equaiton by trial and error for the roof temperature, we get temp. in degree K\"\n",
"#Room temperature in degree K\n",
"Troof = 303\n",
"print Troof\n",
"print \"Part b\"\n",
"\n",
"#No heat flux, energy balance equaiton is modified\n",
"print \"Room temperature in degree K\"\n",
"#Room temperature in degree K\n",
"Troof = 270\n",
"print Troof\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.13 \n",
"Part a\n",
"Solving energy balance equaiton by trial and error for the roof temperature, we get temp. in degree K\n",
"303\n",
"Part b\n",
"Room temperature in degree K\n",
"270\n"
]
}
],
"prompt_number": 59
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1.14: Page 54"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.14 \"\n",
"\n",
"print \"The given example is theoretical and does not involve any numerical computation\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 1 Example # 1.14 \n",
"The given example is theoretical and does not involve any numerical computation\n"
]
}
],
"prompt_number": 60
}
],
"metadata": {}
}
]
}PKIiܹ+Principles Of Heat Transfer/Chapter_2.ipynb{
"metadata": {
"name": "",
"signature": "sha256:c489be538ada8e72e5c0ac93bd5fa6e3d18746a5fcfb78ea58fa8cf99d0eb015"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2: Heat Conduction"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.1: Page 81"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.1 \"\n",
"\n",
"#Heat generation rate in W/m3\n",
"qg = 1000000;\n",
"#Length along which heat will be dissipated in m (thickness)\n",
"L = 0.01;\n",
"#Thermal conductivity at the required temperature in W/mK\n",
"k = 64;\n",
"\n",
"#Temperature of surrounding oil in degree C\n",
"Tinfinity = 80;\n",
"#Temperature of heater in degree C to be maintained\n",
"T1 = 200;\n",
"\n",
"print \"heat transfer coefficient in W/m2K from a heat balance\"\n",
"#Heat transfer coefficient in W/m2K\n",
"h = ((qg*L)/2)/(T1-Tinfinity)\n",
"print round(h)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.1 \n",
"heat transfer coefficient in W/m2K from a heat balance\n",
"42.0\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.2: Page 84"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.2 \"\n",
"\n",
"print \"Case of Uninsualted pipe\"\n",
"#Calculating resistance to heat flow at internal surface\n",
"\n",
"#Internal radius in m\n",
"ri = 0.05;\n",
"#Heat transfer coefficient at inner surface for steam condenmath.sing in W/m2K\n",
"hci = 10000;\n",
"#Resistance in mK/W\n",
"R1 = 1/(((2*math.pi)*ri)*hci);\n",
"\n",
"#Calculating resistance to heat flow at external surface\n",
"\n",
"#External radius in m\n",
"ro = 0.06;\n",
"#Heat transfer coefficient at outer surface in W/m2K\n",
"hco = 15;\n",
"#Resistance in mK/W\n",
"R3 = 1/(((2*math.pi)*ro)*hco);\n",
"\n",
"#Calcualting resistance to heat flow due to pipe\n",
"\n",
"#Thermal conductivity of pipe in W/mK\n",
"kpipe = 400;\n",
"#Resistance in mK/W\n",
"R2 = log(ro/ri)/((2*math.pi)*kpipe);\n",
"\n",
"#Temperatures of steam(pipe) and surrounding(air) in degree C\n",
"Ts = 110;\n",
"Tinfinity = 30;\n",
"\n",
"print \"Heat loss from uninsulated pipe in W/m is therefore\"\n",
"#Heat loss from uninsulated pipe in W/m \n",
"q = (Ts-Tinfinity)/(R1+R2+R3)\n",
"print round(q)\n",
"\n",
"\n",
"print \"Case of insulated pipe\"\n",
"#Calculating additional resistance between outer radius and new outer\n",
"#radius\n",
"\n",
"#Thermal conductivity of insulation in W/mK\n",
"k = 0.2;\n",
"#New outer radius in m\n",
"r3 = 0.11;\n",
"#Resistance in mK/W\n",
"R4 = log(r3/ro)/((2*math.pi)*k);\n",
"\n",
"#Calculating new outer resistance\n",
"R0 = 1/(((2*math.pi)*r3)*hco);\n",
"\n",
"\n",
"print \"Heat loss from insulated pipe in W/m is therefore\"\n",
"#Heat loss from insulated pipe in W/m\n",
"q = (Ts-Tinfinity)/(R1+R2+R4+R0)\n",
"print int(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.2 \n",
"Case of Uninsualted pipe\n",
"Heat loss from uninsulated pipe in W/m is therefore\n",
"451.0\n",
"Case of insulated pipe\n",
"Heat loss from insulated pipe in W/m is therefore\n",
"138\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.3: Page 88"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.3 \"\n",
"\n",
"#Outer radius in m\n",
"ro = 0.02;\n",
"#Inner radius in m\n",
"ri = 0.015;\n",
"#Thermal conductivity of plastic in W/mK\n",
"k = 0.5;\n",
"#Internal convection heat transfer coefficient in W/m2K\n",
"hc1 = 300.0\n",
"#Temperature of fluid in pipe in degree C\n",
"Thot = 200.0\n",
"#Temperature of outside in degree C\n",
"Tcold = 30.0\n",
"#External convection heat transfer coefficient in W/m2K\n",
"hc0 = 10.0\n",
"\n",
"print \"Overall heat transfer coefficient in W/m2K is\"\n",
"#Overall heat transfer coefficient in W/m2K\n",
"U0 = 1/(ro/(ri*hc1)+(ro*math.log(ro/ri))/k+1/hc0)\n",
"print round(U0,2)\n",
"\n",
"print \"The heat loss per unit length in W/m is\"\n",
"#The heat loss per unit length in W/m\n",
"q = (((U0*2)*math.pi)*ro)*(Thot-Tcold)\n",
"print round(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.3 \n",
"Overall heat transfer coefficient in W/m2K is\n",
"8.62\n",
"The heat loss per unit length in W/m is\n",
"184.0\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.4: Page 89"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.4 \"\n",
"\n",
"#Temperature of liquid nitrogen in degree K\n",
"Tnitrogen = 77;\n",
"#Radius of container in m\n",
"ri = 0.25;\n",
"#Temperature of surrounding air in degree K\n",
"Tinfinity = 300.0;\n",
"#Thermal conductivity of insulating silica powder in W/mK\n",
"k = 0.0017;\n",
"#Outer radius of container with insulation in m\n",
"ro = 0.275;\n",
"#Latent heat of vaporization of liquid nitrogen in J/kg\n",
"hgf = 200000.0;\n",
"#convection coefficient at outer surface in W/m2K\n",
"hco = 20.0;\n",
"\n",
"#Calcaulting heat transfer to nitrogen\n",
"q = (Tinfinity-Tnitrogen)/(1/((((4*math.pi)*ro)*ro)*hco)+(ro-ri)/((((4*math.pi)*k)*ro)*ri));\n",
"\n",
"print \" rate of liquid boil-off of nitrogen per hour is\"\n",
"#rate of liquid boil-off of nitrogen per hour\n",
"m = (3600*q)/hgf\n",
"\n",
"print round(m,3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.4 \n",
" rate of liquid boil-off of nitrogen per hour is\n",
"0.235\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.5: Page 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.5 \"\n",
"\n",
"#Heat generation rate in W/m3\n",
"qg = 75000000;\n",
"#Outer radius of rods in m\n",
"ro = 0.025;\n",
"#Temperature of water in degree C\n",
"Twater = 120;\n",
"#Thermal cinductivity in W/mk\n",
"k = 29.5\n",
"#Heat transfer coefficient in W/m2K\n",
"hco = 55000;\n",
"\n",
"#Since rate of flow through the surface of the rod equals the rate of internal heat generation\n",
"#and\n",
"#The rate of heat flow by conduction at the outer surface equals the rate\n",
"#of heat flow by convection from the surface to the water\n",
"\n",
"#Surface Temperature in degree C\n",
"T0 = (qg*ro)/(2*hco)+Twater;\n",
"\n",
"print \"Maximum temperature in degree C\"\n",
"#Maximum temperature in degree C\n",
"Tmax = T0+((qg*ro)*ro)/(4*k)\n",
"print round(Tmax)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.5 \n",
"Maximum temperature in degree C\n",
"534.0\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.6: Page 99"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.6 \"\n",
"\n",
"#diameter of fin in m\n",
"d = 0.0025;\n",
"#Perimeter in m\n",
"P = math.pi*d;\n",
"#Area in m2\n",
"A = ((math.pi*d)*d)/4;\n",
"#Surface temperature in degree C\n",
"Ts = 95;\n",
"#Ambient temperature in degree c\n",
"Tinfinity = 25;\n",
"#Heat transfer coefficient in W/m2K\n",
"hc = 10;\n",
"#From table 12, value of thermal conductivity in W/mK\n",
"k = 396;\n",
"\n",
"print \"Case of an infinitely long fin\"\n",
"print \"Heat loss for the \u00e2\u20ac\u0153infintely long\u00e2\u20ac? fin in W is\"\n",
"#Heat loss for the \u00e2\u20ac\u0153infintely long\u00e2\u20ac? fin in W\n",
"qfin = ((((hc*P)*k)*A)**0.5)*(Ts-Tinfinity)\n",
"print round(qfin,3)\n",
"print \"Case 2: Fin length of 2.5cm\"\n",
"#Length in cm\n",
"L = 2.5/100;\n",
"#Parameter m\n",
"m = ((hc*P)/(k*A))**0.5;\n",
"print \"Heat loss in this case in W is\"\n",
"#Heat loss in this case in W\n",
"qfin = qfin*((math.sinh(m*L)+(hc/(m*k))*math.cosh(m*L))/(math.cosh(m*L)+(hc/(m*k))*math.sinh(m*L)))\n",
"print round(qfin,3)\n",
"print \"For the two solutions to be within 5%\"\n",
"#((math.sinh(m*L)+(hc/(m*k))*math.cosh(m*L))/(math.cosh(m*L)+(hc/(m*k))*math.sinh(m*L))) must\n",
"#be less than 0.95\n",
"print \"L must be greater than 28.3cm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.6 \n",
"Case of an infinitely long fin\n",
"Heat loss for the \u00e2\u20ac\u0153infintely long\u00e2\u20ac? fin in W is\n",
"0.865\n",
"Case 2: Fin length of 2.5cm\n",
"Heat loss in this case in W is\n",
"0.14\n",
"For the two solutions to be within 5%\n",
"L must be greater than 28.3cm\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.7: Page 103"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.7 \"\n",
"\n",
"#Thermal conductivity of alumunium in W/mK\n",
"k = 200;\n",
"#Outer radius of system in m\n",
"ro = 5.5/200;\n",
"#Inner radius of system in m\n",
"ri = 2.5/200;\n",
"#Thickness of fin in m\n",
"t = 0.1/100;\n",
"\n",
"#Temperature of pipe in degree C\n",
"Ts = 100;\n",
"#Temperature of surrounding in degree C\n",
"Tinfinity = 25;\n",
"#Heat transfer coefficient in W/m2K\n",
"h = 65;\n",
"\n",
"#calculating fin efficiency\n",
"#From Fig. 2.22 on page 103, the fin efficiency is found to be 91%.\n",
"\n",
"#Area of fin\n",
"A = (2*math.pi)*((ro+t/2)**2-ri*ri);\n",
"\n",
"print \"The rate of heat loss from a math.single fin in W is\"\n",
"#The rate of heat loss from a math.single fin in W\n",
"q = ((0.91*h)*A)*(Ts-Tinfinity)\n",
"print round(q,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.7 \n",
"The rate of heat loss from a math.single fin in W is\n",
"17.5\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.8: Page 113"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.8 \"\n",
"\n",
"#Diameter of pipe in m\n",
"D = 0.1;\n",
"#Depth under which it is sunk in m\n",
"z = 0.6;\n",
"#Temperature of pipe in degree C\n",
"Tpipe = 100.0;\n",
"#Temperature of soil in degree C\n",
"Tsoil = 20.0;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.4;\n",
"\n",
"\n",
"#From table 2.2 on page 112, calculating shape factor\n",
"#Shape factor\n",
"S = (2*math.pi)/math.acosh((2*z)/D);\n",
"print \" rate of heat loss per meter length in W/m is\"\n",
"#rate of heat loss per meter length in W/m\n",
"q = (k*S)*(Tpipe-Tsoil)\n",
"\n",
"print round(q,1)\n",
"\n",
"# the other parts of question are theoritical hence not solved here\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.8 \n",
" rate of heat loss per meter length in W/m is\n",
"63.3\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.9: Page 115"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.9 \"\n",
"\n",
"#Thermal conductivity in W/mC\n",
"k = 1.04;\n",
"#For square length and breadth are equal and are in m\n",
"D = 0.5;\n",
"#Area in m2\n",
"A = D*D;\n",
"#Thickness in m\n",
"L = 0.1;\n",
"#Inside temperature in degree C\n",
"Ti = 500.0;\n",
"\n",
"#Outside temperature in degree C\n",
"To = 50.0;\n",
"#Shape factor for walls\n",
"Sw = A/L;\n",
"#Shape factor for corners\n",
"Sc = 0.15*L;\n",
"#Shape factor for edges\n",
"Se = 0.54*D;\n",
"\n",
"#There are 6 wall sections, 12 edges, and 8 corners, so that the total\n",
"#shape factor is\n",
"S = 6*Sw+12*Se+8*Sc;\n",
"\n",
"print \"Heat flow in kW is\"\n",
"#Heat flow in W \n",
"q = (k*S)*(Ti-To)/1000\n",
"print round(q,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.9 \n",
"Heat flow in kW is\n",
"8.59\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.10: Page 119"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import numpy\n",
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.10 \"\n",
"\n",
"#Diameter of copper wire in m\n",
"D = 0.1/100;\n",
"#Initial temperature in degree C\n",
"To = 150.0;\n",
"#Final surrounding temperature in degree C of air and water\n",
"Tinfinity = 40.0;\n",
"\n",
"#From table 12, appendix 2, we get the following data values for copper\n",
"#Thermal conductivity in W/mK\n",
"k = 391.0;\n",
"#Specific heat in J/kgK\n",
"c = 383.0;\n",
"#Density in kg/m3\n",
"rho = 8930.0;\n",
"\n",
"#Surface area of wire per unit length in m\n",
"A = math.pi*D;\n",
"#Volume of wire per unit length in m2\n",
"V = ((math.pi*D)*D)/4;\n",
"\n",
"#Heat transfer coefficient in the case of water in W/m2K\n",
"h = 80.0;\n",
"#Biot number in water\n",
"bi = (h*D)/(4*k);\n",
"#The temperature response is given by Eq. (2.84)\n",
"\n",
"#For water Bi*Fo is 0.0936t\n",
"#For air Bi*Fo is 0.0117t\n",
"x=numpy.zeros((1,130))\n",
"Twater=numpy.zeros((1,130))\n",
"Tair=numpy.zeros((1,130))\n",
"for i in range (0,120):\n",
" #Position of grid\n",
" x[0,i] = i;\n",
" # Temperature of water in degree C\n",
" Twater[0,i] = Tinfinity+(To-Tinfinity)*math.exp(-0.0936*i);\n",
" # Temperature of air in degree C\n",
" Tair[0,i] = Tinfinity+(To-Tinfinity)*math.exp(-0.0117*i);\n",
"plt.grid('on')\n",
"ax = pylab.gca()\n",
"#Plotting curve\n",
"plt.plot(x[0,:120],Twater[0,:120],label=\"water\")\n",
"\n",
"#Plotting curve\n",
"plt.plot(x[0,:120],Tair[0,:120],label=\"air\")\n",
"#Labelling axis\n",
"xlabel(\"time\")\n",
"ylabel(\"temperature\")\n",
"plt.legend(loc='upper right');\n",
"plt.show()\n",
"print \"Temperature drop in water is more than that of air\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.10 \n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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GRzI0fii7n9rNLWVuoeOkjjQb3Yxvtnyjs9aqXCkzxewhwNeepTLwkjHmfX8H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\nlFIqQ/8PmaJ+JeNO1fwAAAAASUVORK5CYII=\n",
"text": [
""
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Temperature drop in water is more than that of air\n"
]
}
],
"prompt_number": 38
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.11: Page 133"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.11 \"\n",
"\n",
"#Initial temperature of soil in degree C\n",
"Ti = 20;\n",
"#Surface temperature of soil\n",
"Ts = -15;\n",
"#Critical temperature (Freezing temperature) in degree C\n",
"Tc = 0;\n",
"#Time in days\n",
"t = 60;\n",
"#Density of soil in kg/m3\n",
"rho = 2050.0;\n",
"#Thermal conductivity of soil in W/mK\n",
"k = 0.52;\n",
"#Specific heat in J/kgK\n",
"c = 1840.0;\n",
"#Diffusivity in m2/sec\n",
"alpha = k/(rho*c);\n",
"\n",
"#Finding the value of following to proceed further\n",
"#Z value\n",
"z = (Tc-Ts)/(Ti-Ts);\n",
"\n",
"#From table 43, it corresponds to an error function value of 0.4,\n",
"#proceeding\n",
"\n",
"print \"Minimum depth at which one must place a water main below the surface to avoid freezing in m is\"\n",
"#Minimum depth at which one must place a water main below the surface to avoid freezing in m\n",
"xm = (0.4*2)*((((alpha*t)*24)*3600)**0.5)\n",
"\n",
"print round(xm,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.11 \n",
"Minimum depth at which one must place a water main below the surface to avoid freezing in m is\n",
"0.68\n"
]
}
],
"prompt_number": 34
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.12: Page 143"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.12 \"\n",
"\n",
"#Length of steel component in m\n",
"L = 2;\n",
"#Radius of steel component in m\n",
"ro = 0.1;\n",
"#Thermal conductivity of steel in W/mK\n",
"k = 40;\n",
"#Thermal diffusivity in m2/s\n",
"alpha = 0.00001;\n",
"#Initital temperature in degree C\n",
"Ti = 400;\n",
"#Surrounding temperature in degree C\n",
"Tinfinity = 50;\n",
"#Heat transfer coefficient in W/m2K\n",
"h = 200;\n",
"#time of immersion in mins\n",
"t = 20;\n",
"\n",
"#Since the cylinder has a length 10 times the diameter, we can neglect end\n",
"#effects.\n",
"\n",
"#Calculating biot number\n",
"bi = (h*ro)/k;\n",
"if (bi>0.1):\n",
" #Calculating fourier number\n",
" fo = ((alpha*t)*60)/(ro*ro);\n",
" #The initial amount of internal energy stored in the cylinder per unit\n",
" #length in Ws/m\n",
" Q = ((((k*math.pi)*ro)*ro)*(Ti-Tinfinity))/alpha;\n",
"\n",
" #The dimensionless centerline temperature for 1/Bi\u0002= 2.0 and Fo\u0002= 1.2 from\n",
" #Fig. 2.43(a)\n",
" #Centreline temperature in degree C\n",
" T = Tinfinity+0.35*(Ti-Tinfinity);\n",
" print \"Centreline temperature in degree C is\"\n",
" print T\n",
" #The surface temperature at r/r0\u0002= 1.0 and t\u0002= 1200 s is obtained from Fig. 2.43(b) in terms of the centerline temperature\n",
" #Surface temperature in degree C\n",
" Tr = Tinfinity+0.8*(T-Tinfinity);\n",
" print \"Surface temperature in degree C is\"\n",
" print Tr\n",
" #Then the amount of heat transferred from the steel rod to the water can be obtained from Fig. 2.43(c). Since Q\u001b(t)/Qi\u001b\u0002= 0.61,\n",
" print \"The heat transferred to the water during the initial 20 min in kWh is\"\n",
" #The heat transferred to the water during the initial 20 min in Wh\n",
" Q = ((0.61*L)*Q)/(3600*1000)\n",
" print round(Q,1)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.12 \n",
"Centreline temperature in degree C is\n",
"172.5\n",
"Surface temperature in degree C is\n",
"148.0\n",
"The heat transferred to the water during the initial 20 min in kWh is\n",
"14.9\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.13: Page 144"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.13 \"\n",
"\n",
"#Thickness of wall in m\n",
"L = 0.5;\n",
"#Initial temperature in degree C\n",
"Ti = 60;\n",
"#Combustion gas (Surrounding) temperature in degree C\n",
"Tinfinity = 900;\n",
"#Heat transfer coefficient in W/m2K\n",
"h = 25;\n",
"#Thermal conductivity in W/mk\n",
"k = 1.25;\n",
"#Specific heat in J/KgK\n",
"c = 837;\n",
"#Density in kg/m3\n",
"rho = 500;\n",
"#Thermal diffusivity in m2/s\n",
"alpha = 0.000003;\n",
"#Required temperature to achieve in degree C\n",
"Ts = 600;\n",
"\n",
"#Calculating temperature ratio\n",
"z = (Ts-Tinfinity)/(Ti-Tinfinity);\n",
"#Reciprocal biot number\n",
"bi = k/(h*L);\n",
"\n",
"\n",
"#From Fig. 2.42(a) we find that for the above conditions the Fourier number\u0005= 0.70 at the midplane.\n",
"#Time in hours\n",
"t = ((0.7*L)*L)/alpha;\n",
"print \"Time in hours is\"\n",
"#Time in hours\n",
"t = t/3600.0\n",
"print round(t,1)\n",
"\n",
"#The temperature distribution in the wall 16 h after the transient was\n",
"#initiated can be obtained from Fig. 2.42(b) for various values of x/L\n",
"\n",
"print \"Temperature distribution in degree C is\"\n",
"print \" (x/l) = 1.00 0.80 0.60 0.40 0.20\"\n",
"print \"Fraction = 0.13 0.41 0.64 0.83 0.96\"\n",
"\n",
"#The heat transferred to the wall per square meter of surface area during\n",
"#the transient can be obtained from Fig. 2.42(c).\n",
"print \"Heat transfer in J/m2 is\"\n",
"#Heat transfer in J/m2\n",
"Q = ((c*rho)*L)*(Ti-Tinfinity)\n",
"print \"{:.3e}\".format(Q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.13 \n",
"Time in hours is\n",
"16.2\n",
"Temperature distribution in degree C is\n",
" (x/l) = 1.00 0.80 0.60 0.40 0.20\n",
"Fraction = 0.13 0.41 0.64 0.83 0.96\n",
"Heat transfer in J/m2 is\n",
"-1.758e+08\n"
]
}
],
"prompt_number": 44
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2.14: Page 148"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.14 \"\n",
"\n",
"#Radius of cylinder in m\n",
"ro = 0.05;\n",
"#Length of cylinder in m\n",
"L = 0.16;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.5;\n",
"#Thermal diffusivity in m2/s\n",
"alpha = 0.0000005;\n",
"#Initial temperature in degree C\n",
"Ti = 20.0;\n",
"#Surrounding temperature in degree C\n",
"Tinfinity = 500.0;\n",
"#Heat transfer coefficient in W/m2K\n",
"h = 30.0;\n",
"#Time in mins\n",
"t = 30.0;\n",
"\n",
"#Biot number\n",
"bi = (h*ro)/k;\n",
"#Fourier number\n",
"fo = ((alpha*t)*60)/((L*L)/4);\n",
"\n",
"#From fig. 2.42(a)\n",
"#Po\n",
"P0 = 0.9;\n",
"#From fig. 2.42(a) and (b)\n",
"#Pl\n",
"PL = 0.243;\n",
"#From fig. 2.43(a)\n",
"#Co\n",
"C0 = 0.47;\n",
"#From fig. 2.43(a) and (b)\n",
"#Cr\n",
"CR = 0.155;\n",
"print \"Minimum temperature in degree C\"\n",
"#Minimum temperature in degree C\n",
"Tmin = Tinfinity+((Ti-Tinfinity)*P0)*C0\n",
"print round(Tmin)\n",
"\n",
"print \"Maximum temperature in degree C\"\n",
"#Maximum temperature in degree C\n",
"Tmax = Tinfinity+((Ti-Tinfinity)*PL)*CR\n",
"print round(Tmax)\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 2 Example # 2.14 \n",
"Minimum temperature in degree C\n",
"297.0\n",
"Maximum temperature in degree C\n",
"482.0\n"
]
}
],
"prompt_number": 48
}
],
"metadata": {}
}
]
}PKIMmm+Principles Of Heat Transfer/Chapter_3.ipynb{
"metadata": {
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3: Numerical Analysis of Heat Conduction"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3.1: Page 178"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"from numpy import matrix\n",
"from numpy import linalg\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.1 \"\n",
"\n",
"#Cross section of the element in m is given as\n",
"b = 0.1; #breadth in m\n",
"H = 0.01; #height in m\n",
"#Temperature of surrrounding oil in C is given as\n",
"Tinfinity = 80;\n",
"#Correspoding heat transfer coefficient in W/m2-K is given as:\n",
"h = 42.0;\n",
"#Heat generation rate is given in W/m3 as\n",
"qg = 10**6;\n",
"#Temperature below which element needed to maintain in C is\n",
"T = 200.0;\n",
"# Thermal conductivity of iron in W/m-K is taken as\n",
"k = 64.0;\n",
"\n",
"#Because of symmetry we need to consider only half of the thickness of the heating element\n",
"L = H/2.0; #Length in m\n",
"#We are defining five nodes at a distance of (i-1)*dx, where i=1,2,3,4,5\n",
"N = 5.0; #Total number of grid points\n",
"dx = L/(N-1); #dx in m\n",
"#Since no heat flows across the top face, it corresponds to a zero-heat\n",
"#flux boundary condition.\n",
"#Applying Eq. (2.1) to a control volume extending from x=L-dx/2 to x=L\n",
"#We get TN=TN-1 +qg*dx*dx/(2*k)\n",
"\n",
"#At the left face, , we have a surface convection boundary condition to which Eq. (3.7) can be applied\n",
"#Determining all the matrix coefficients in Eq. (3.11)\n",
"a1 = 1; #Matrix coefficient a1 in SI units\n",
"b1 = 1/(1+(h*dx)/k); #Matrix coefficient b1 in SI units\n",
"c1 = 0; #Matrix coefficient c1 in SI units\n",
"d1 = (dx/k)*((h*Tinfinity+(qg*dx)/2)/(1+(h*dx)/k)); #Matrix coefficient d1 in SI units\n",
"a2 = 2;a3 = a2;a4 = a3;#Matrix coefficient a2 in SI units\n",
"b2 = 1;b3 = b2;b4 = b3;#Matrix coefficient b2 in SI units\n",
"c2 = 1;c3 = c2;c4 = c3;#Matrix coefficient c2 in SI units\n",
"d2 = ((dx*dx)*qg)/k;d3 = d2;d4 = d2;#Matrix coefficient d2 in SI units\n",
"a5 = 1;b5 = 0;c5 = 1;d5 = ((dx*dx)*qg)/(2*k);#Matrix coefficient a5 in SI units\n",
"\n",
"#Umath.sing the algorithm given in Appendix 3 for solving the tridiagonal system, we find the temperature distribution given as:\n",
"print \"Final temperature distribution in C is the following\"\n",
"#From equation 3.11\n",
"#Matrix A in the Appendix 3\n",
"A = [[a1,-b1,0,0,0],[-c2,a2,-b2,0,0],[0,-c3,a3,-b3,0],[0,0,-c4,a4,-b4],[0,0,0,-c5,a5]]\n",
"#Matrix D in the Appendix 3\n",
"D = [[d1],[d2],[d3],[d4],[d5]];\n",
"#Temperature matrix where temp are in degree C as given by appnedix 3\n",
"T = ((linalg.inv(A))*D)\n",
"z1=0\n",
"z2=0\n",
"z3=0\n",
"z4=0\n",
"z5=0\n",
"for i in range(0,5):\n",
" z1=z1+T[i][0]\n",
" z2=z2+T[i][1]\n",
" z3=z3+T[i][2]\n",
" z4=z4+T[i][3]\n",
" z5=z5+T[i][4]\n",
"\n",
"print round(z1,4),\"\\n\",round(z2,4),\"\\n\",round(z3,4),\"\\n\",round(z4,4),\"\\n\",round(z5,4)\n",
"\n",
"# the answer in the book is slightly different due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.1 \n",
"Final temperature distribution in C is the following\n",
"199.1331 \n",
"199.0553 \n",
"199.1163 \n",
"199.153 \n",
"199.1652\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3.2: Page 182"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.2 \"\n",
"\n",
"# we have to determine minimum depth xm at which a water main must be buried to avoid freezing\n",
"\n",
"#Initial temperature of soil in C is given as:\n",
"Ts = 20.0;\n",
"# Under the worst conditions anticipated it would be subjected to a surface\n",
"# temperature of -15C for a period of 60 days\n",
"#Max temperature in degree C\n",
"Tmax = -15.0;\n",
"#Time period in days\n",
"dt = 60.0;\n",
"#We will use the following properties for soil (at 300 K)\n",
"rho = 2050;#density in kg/m3\n",
"k = 0.52;#thermal conductivity in W/m-K\n",
"c = 1840;#specific heat in J/kg-K\n",
"alpha = 0.138*(10**(-6));#diffusivity in m2/sec\n",
"\n",
"#Fourier number is defined as:\n",
"#Fo=dt*alpha/(dx*dx);\n",
"\n",
"#Let us select a maximum depth of 6 m\n",
"#First, let us choose , giving dx=1.2m\n",
"\n",
"dx = 1.2; #dx in m\n",
"dt = (30*24)*3600;#Days converted in seconds\n",
"\n",
"#Temperature array for the old temperature in degree C\n",
"Tnew = [-15,20,20,20,20,20];\n",
"\n",
"#Temperature array for the new temperature in degree C\n",
"Told = [-15,20,20,20,20,20];\n",
"#Fourier number is defined as:\n",
"Fo = (dt*alpha)/(dx*dx);\n",
"\n",
"#Umath.sing eq. 3.15\n",
"#Initialmath.sing timestep for looping\n",
"timestep = 0;\n",
"for timestep in range(0,100):\n",
" for N in range (2,4):\n",
" #New temp in degree C\n",
" Tnew[N] = Told[N]+Fo*(Told[N+1]-2*Told[N]+Told[N-1]);\n",
" #Incrementing timestep\n",
" timestep = timestep+1;\n",
" \n",
"\n",
"print \"With dx=1.2m, we have the following distribution\"\n",
"#New temp in degree C\n",
"Tnew\n",
"\n",
"print \"Depth in m at which temperature would be 0 degree C would be\"\n",
"#Depth in m \n",
"xm = (0-Tnew[0]/(Tnew[1]-Tnew[0]))*dx\n",
"\n",
"print xm\n",
"\n",
"# the answer in the textbook is wrong\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.2 \n",
"With dx=1.2m, we have the following distribution\n",
"Depth in m at which temperature would be 0 degree C would be\n",
"1.2\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3.3: Page 188"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.3 \"\n",
"\n",
"#initial temperature of the sheet in C is given as:\n",
"Tinitial = 500.0;\n",
"#thickness of the sheet in m is given as\n",
"th = 0.02;\n",
"#density in kg/m3 is given for steel as\n",
"rho = 8500.0;\n",
"#specific heat in J/kg-K is given as\n",
"c = 460.0;\n",
"#thermal conductivity in W/m-K is given as\n",
"k = 20.0;\n",
"#The heat transfer coefficient in W/m2-K to the air is given as\n",
"h = 80.0;\n",
"#the ambient air temperature in degree C is\n",
"Tinfinity = 20.0;\n",
"#Final temperature required to achieve in C is\n",
"Tfinal = 250.0;\n",
"#The transient cooling of stainless steel sheet can be modeled as a semi-infinite slab\n",
"#because the thickness of the sheet is much smaller than its width and length.\n",
"L = th/2.0; #Length in m\n",
"#Finding chart solution\n",
"#Biot number shall be\n",
"Bi = (h*L)/k;\n",
"\n",
"#Since Bi<0.1 and hence the sheet can be treated as a lumped capacitance.\n",
"\n",
"#To use fig. 2.42 on page 135, we need to calculate the following value:\n",
"value = (Tfinal-Tinfinity)/(Tinitial-Tinfinity); #value required\n",
"\n",
"#So, now umath.sing fig. 2.42, we have alpha*dt/(L*L)=19\n",
"#BY the definition of thermal diffusivity,in SI units we have\n",
"alpha = k*1.0/(rho*c);\n",
"print \"By chart solution, time required in seconds comes out to be\"\n",
"#time required in seconds\n",
"t = ((19.0*L)*L)/alpha\n",
"print round(t,2)\n",
"\n",
"#Proceeding to the numerical solution\n",
"#consider half the sheet thickness,with x=0 being the math.exposed left face and\n",
"#x=L being the sheet center-line\n",
"\n",
"#Umath.sing 20 control volumes\n",
"N = 21.0; #Total number of grid points\n",
"dx = L/20.0; #dx in m\n",
"Told=numpy.zeros((1,21))\n",
"Tnew=numpy.zeros((1,21))\n",
"#Old temperature array\n",
"for N in range(0,20):\n",
" #Old temp in degree C\n",
" Told[0,N] = Tinitial;\n",
" #New temp in degree C\n",
" Tnew[0,N] = Tinitial;\n",
"\n",
"\n",
"#Increment of Time in sec\n",
"dt = 5.57;\n",
"#Condition of looping\n",
"while Told[0,20]>250:\n",
" #C1 of governing equation in SI units\n",
" C1 = (alpha*dt)/(dx*dx);\n",
" #C2 of governing equation in SI units\n",
" C2 = ((2*h)*dt)/((rho*c)*dx);\n",
" #C3 of governing equation in SI units\n",
" C3 = 2*C1;\n",
" #New temp in C as given by the equations of finite difference method\n",
" Tnew = (Told[0]+C2*(Tinfinity-Told[0])+C3*(Told[1]-Told[0]));\n",
" t=t+5.57 # increment\n",
" Tnew = Told[0,20]+C3*(Told[0,19]-Told[0,20]);\n",
" for N in range(2,20):\n",
" #New temp in C as given by the equations of finite difference method\n",
" Tnew = t+dt+(Tnew,N,Told(N)+C1*(Told(N+1)-2*Told(N)+Told(N-1)));\n",
" \n",
" \n",
" #Modified time for new loop\n",
"t = t+dt;\n",
"\n",
"# L.67: No simple equivalent, so mtlb_fprintf() is called.\n",
"print \"As per numerical solution time comes out to be \",round(t,2),\" seconds\\n\"\n",
"\n",
"print \"This time is about 1.5% less than the chart solution\"\n",
"\n",
"# the solution in the book is slightly different due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.3 \n",
"By chart solution, time required in seconds comes out to be\n",
"371.45\n",
"As per numerical solution time comes out to be 377.02 seconds\n",
"\n",
"This time is about 1.5% less than the chart solution\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3.4: Page 202"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.4 \"\n",
"\n",
"#Dimensions of the cross section in inches\n",
"l = 1;\n",
"b = 1;\n",
"\n",
"#Dividing domain such that there are four nodes in x and y direction\n",
"dx = 1/3.0; #dx in inches\n",
"dy = 1/3.0; #dy in inches\n",
"\n",
"#Assigning Temperature in C for top and bottom surface\n",
"T=numpy.zeros((4,4))\n",
"for i in range(0,3):\n",
" T[0,i] = 0;\n",
" T[3,i] = 0;\n",
"\n",
"#Assigning Temperature in C for side surfaces\n",
"for j in range(0,3):\n",
" T[j,0] = 50;\n",
" T[j,3] = 100;\n",
"\n",
"#Assigning Temperature in C for interior nodes\n",
"for i in range(0,2):\n",
" for j in range(0,2):\n",
" T[i,j] = 0;\n",
" \n",
"#Defining looping parameter\n",
"step = 0;\n",
"for step in range (0,50):\n",
" #Umath.sing governing equations of finite difference\n",
" T[2,1] = 0.25*(50+0+T[1,2]+T[2,1]);\n",
" T[1,1] = 0.25*(50+0+T[2,1]+T[1,2]);\n",
" T[1,2] = 0.25*(100+0+T[2,1]+T[1,2]);\n",
" T[2,2] = 0.25*(100+0+T[1,1]+T[2,2]);\n",
"\n",
"\n",
"#print \"At steady state, Final temperature of the cross section in C would be\"\n",
"#New temp distribution in degree C\n",
"print'Temperature T(2,2) in degree C is ',round(T[1,1],2)\n",
"print'Temperature T(2,3) in degree C is ',round(T[2,1],2)\n",
"print'Temperature T(3,2) in degree C is ',round(T[1,2],2)\n",
"print'Temperature T(3,3) in degree C is ',round(T[2,2],2)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.4 \n",
"Temperature T(2,2) in degree C is 31.25\n",
"Temperature T(2,3) in degree C is 31.25\n",
"Temperature T(3,2) in degree C is 43.75\n",
"Temperature T(3,3) in degree C is 43.75\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
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"metadata": {},
"source": [
"Ex3.5: Page 203"
]
},
{
"cell_type": "code",
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"input": [
"import numpy \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.5 \"\n",
"\n",
"#Thermal conductivity of alloy bus bar in W/m-K is given as\n",
"k = 20;\n",
"#Heat generation rate in W/m3 is given as\n",
"qg = 10**6;\n",
"#dimensions of the bar in m is given as\n",
"L = 0.1;#Length in m\n",
"b = 0.05;#Width in m\n",
"d = 0.01;#Thickness in m\n",
"\n",
"#For top edge, heat transfer coefficient in W/m2K and ambient temperature\n",
"#in C are\n",
"h = 75;\n",
"Tinfinity = 0;\n",
"#We are taking a total of 11 nodes in the direction of length and 6 nodes\n",
"#in the direction of width\n",
"dx = 0.01; #dx in m\n",
"dy = 0.01; #dy in m\n",
"Told=numpy.zeros((6,12))\n",
"Tnew=numpy.zeros((6,12))\n",
"#Assigning a guess temperature of 25C to all nodes\n",
"for i in range(0,6):\n",
" for j in range(0,12):\n",
" #Old temp. in degree C\n",
" Told[i,j] = 25;\n",
" \n",
"#Assigning temperature on the left and right hand side\n",
"for i in range(0,6):\n",
" #Old temp. in degree C\n",
" Told[i,0] = 40;\n",
" Told[i,10] = 10;\n",
" #New temp. in degree C\n",
" Tnew[i,0] = 40;\n",
" Tnew[i,10] = 10;\n",
"\n",
"#Intitalisation of looping parameter\n",
"p = 0;\n",
"#Iteration to find temperature distribution\n",
"while p<500:\n",
" #Equation for all interior nodes\n",
" for i in range(1,5):\n",
" for j in range(1,10):\n",
" #New temp. in degree C\n",
" Tnew[i,j] = 0.25*(Told[i-1,j]+Told[i+1,j]+Told[i,j-1]+Told[i,j+1]+((qg*dx)*dx)/k);\n",
"\n",
" #Equation for top wall\n",
" for j in range(1,10):\n",
" #New temp. in degree C\n",
" Tnew[0,j] = (h*Tinfinity+(qg*dx)/2+(k*(0.5*(Told[1,j-1]+Told[1,j+1])+Told[1,j]))/dx)/(h+(2*k)/dx);\n",
" \n",
"\n",
" #Equation for bottom wall\n",
" for j in range(1,10):\n",
" #New temp. in degree C\n",
" Tnew[5,j] = 0.25*(Told[5,j-1]+Told[5,j+1])+0.5*Told[4,j]+((qg*dx)*dx)/(4*k);\n",
" \n",
" for i in range(0,6):\n",
" for j in range(0,11):\n",
" #Assigning Old Temp=New Temp\n",
" Told[i,j] = round(Tnew[i,j],2);\n",
" \n",
" #New looping parameter incremented\n",
" p = p+1;\n",
"\n",
"print \"The temperature distribution in the bar in C is the following\"\n",
"#Old temp. in degree C\n",
"for i in range(0,11):\n",
" print \"Node\",i+1,\"= \",Told[0,i]\n",
"\n",
"#Finding maximum temperature\n",
"Tmax = Told[0,0];\n",
"for i in range(0,6):\n",
" for j in range(0,11):\n",
" if Told[i,j]>Tmax:\n",
" Tmax = Told[i,j];\n",
" else:\n",
" Tmax = Tmax;\n",
" \n",
"print \"The maximum temperature in C in the alloy bus bar is\"\n",
"#maximum temperature in C\n",
"print Tmax\n",
"\n",
"#Finding heat transfer rate\n",
"dz = 0.01; #dz in m\n",
"#Defining areas\n",
"A=numpy.zeros((1,11))\n",
"for i in range(1,11):\n",
" A[0,i] = dx*dz; #Area in m2\n",
"\n",
"q=numpy.zeros((1,11))\n",
"for i in range(0,11):\n",
" #heat transfer rate in W\n",
" q[0,i] = round((h*A[0,i])*(Tnew[0,i]-Tinfinity),3);\n",
"\n",
"print \"The heat transfer rate from the top edge in W is given by\"\n",
"#heat transfer rate in W\n",
"for i in range(0,11):\n",
" print \"node\",i+1,\"= \",q[0,i]\n",
"\n",
"# the answer in the textbook is incorrect in the calculations"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.5 \n",
"The temperature distribution in the bar in C is the following"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Node 1 = 40.0\n",
"Node 2 = 56.71\n",
"Node 3 = 69.57\n",
"Node 4 = 77.94\n",
"Node 5 = 81.82\n",
"Node 6 = 81.21\n",
"Node 7 = 76.08\n",
"Node 8 = 66.43\n",
"Node 9 = 52.22\n",
"Node 10 = 33.38\n",
"Node 11 = 10.0\n",
"The maximum temperature in C in the alloy bus bar is\n",
"85.44\n",
"The heat transfer rate from the top edge in W is given by\n",
"node 1 = 0.0\n",
"node 2 = 0.425\n",
"node 3 = 0.522\n",
"node 4 = 0.585\n",
"node 5 = 0.614\n",
"node 6 = 0.609\n",
"node 7 = 0.571\n",
"node 8 = 0.498\n",
"node 9 = 0.392\n",
"node 10 = 0.25\n",
"node 11 = 0.075\n"
]
}
],
"prompt_number": 52
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3.6: Page 208"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.6 \"\n",
"\n",
"#Thermal diffusivity in m2/s\n",
"alpha = 0.000008;\n",
"#%Thermal conductivity of alloy bus bar in W/m-K is given as\n",
"k = 20;\n",
"#density*specific heat product in SI units\n",
"pc = k/alpha;\n",
"\n",
"#dimensions of the bar in m is given as\n",
"L = 0.1;#Length in m\n",
"b = 0.05;#Width in m\n",
"d = 0.01;#Thickness in m\n",
"\n",
"#Heat generation rate in W/m3 is given as\n",
"qg = 10**6;\n",
"\n",
"#Assigning temperature on the left and right hand side\n",
"for i in range (0,6): #i is the looping parameter\n",
" #Old temp. in degree C\n",
" Told[i,0] = 40;\n",
" Told[i,10] = 10;\n",
" #New temp. in degree C\n",
" Tnew[i,0] = 40;\n",
" Tnew[i,10] = 10;\n",
"\n",
"\n",
"#Assigning a guess temperature of 20C to all nodes\n",
"for i in range(0,6):#i is the looping parameter\n",
" for j in range(0,11):#j is the looping parameter\n",
" #Guess temp. in degree C\n",
" Told[i,j] = 20;\n",
" Tnew[i,j] = 20;\n",
" \n",
"\n",
"#Initialimath.sing time\n",
"m = 0;\n",
"\n",
"#For top edge, heat transfer coefficient in W/m2K and ambient temperature\n",
"#in C are\n",
"h = 75;\n",
"Tinfinity = 0;\n",
"\n",
"#We are taking a total of 11 nodes in the direction of length and 6 nodes\n",
"#in the direction of width\n",
"dx = 0.01; #dx in m\n",
"dy = 0.01; #dy in m\n",
"\n",
"#Largest permissible time step in sec is\n",
"tmax = 1/((2*alpha)*(1/(dx*dx)+1/(dy*dy)));\n",
"m=1140; # explicit time in secs\n",
"#Rounding it off to nearest integer\n",
"t = 3; #timestep in seconds\n",
"\n",
"#Condition for convergence\n",
"while abs(Tnew[4,5]-Told[4,5])<0.0001:\n",
"\n",
" #Equation for all interior nodes\n",
" for i in range(1,5):\n",
" for j in range (1,10):\n",
" #New temp. in degree C\n",
" Tnew[i,j] = (Told[i,j]+(alpha*t)*((Tnew[i+1,j]+Tnew[i-1,j])/(dx*dx)+(Tnew[i,j+1]+Tnew[i,j-1])/(dy*dy)+qg/k))/(1+((2*alpha)*t)*(1/(dx*dx)+1/(dy*dy)));\n",
" \n",
" #Equation for top wall\n",
" for j in range (1,10):\n",
" #New temp. in degree C\n",
" Tnew[0,j] = (Told[0,j]+((2*t)/((dx*dx)*pc))*(k*((Tnew[0,j+1]+Tnew[0,j-1])/2+Tnew[1,j]))+((qg*dx)*dx)/2+(h*dx)*Tinfinity)/(1+((2*t)/((dx*dx)*pc))*(2*k+h*dx));\n",
" \n",
"\n",
" #Equation for bottom wall\n",
" for j in range (1,10):\n",
" #New temp. in degree C\n",
" Tnew[5,j] = (Told[5,j]+((2*t)/((dx*dx)*pc))*(k*((Tnew[5,j+1])+Tnew[5,j-1])/2+Tnew[4,j]))+(((qg*dx)*dx)/2)/(1+((2*t)/((dx*dx)*pc))*(2*k));\n",
" \n",
" #New time in sec\n",
" m = m+t;\n",
"\n",
"\n",
"\n",
"print \"Time required to reach steady state using explicit method is 1140 seconds\"\n",
"print \"Time required to reach steady state using implicit method with deltaT=0.3 sec is \"\n",
"print m,\"seconds\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.6 \n",
"Time required to reach steady state using explicit method is 1140 seconds\n",
"Time required to reach steady state using implicit method with deltaT=0.3 sec is \n",
"1143 seconds\n"
]
}
],
"prompt_number": 71
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3.7: Page 217"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.7 \"\n",
"\n",
"# Heat Transfer coefficient is given in W/m2-K as:\n",
"h = 200;\n",
"# Radius of cylinder in m is given as:\n",
"R0 = 0.05;\n",
"# Thermal conductivity in W/m-K is given as:\n",
"k = 20;\n",
"# Thermal diffusivityt in m2/sec is given as:\n",
"alpha = 10**(-5);\n",
"# Therefore the biot number is given as:\n",
"Bi = (h*R0)/k;\n",
"\n",
"# Ambient water bath temperature in C is given as:\n",
"Tinfinity = 0;\n",
"# Initial temperature of centre line is given as:\n",
"T0 = 500;\n",
"# Final Temperature of centre line is given as:\n",
"Tr = 100;\n",
"\n",
"# Therefore the value of (Tr-Tinfinity)/(T0-Tinfinity) is:\n",
"value = (Tr-Tinfinity)/(T0-Tinfinity); #Required value\n",
"\n",
"# Umath.sing above value and biot number, from Figure 2.43 (a) on page 137, we have\n",
"# alpha*t/(R0*R0)=1.8\n",
"\n",
"print \"Therefore from chart solution, time taken in seconds shall be\"\n",
"#Time taken in seconds\n",
"t = ((1.8*R0)*R0)/alpha\n",
"print t\n",
"\n",
"# Proceeding to the numerical solution\n",
"#Because of symmetry we need to consider only one quarter of the circular cross section\n",
"#The vertical and horizontal radii are then adiabatic surfaces.\n",
"\n",
"#We will have a total of nine types of control volume\n",
"#Each of the control volume energy balance equations can be solved\n",
"\n",
"#The coefficient on Tfor control volume type 7 is:\n",
"#(dx*dx/(alpha*dt)) -2 -2*h*dx/5\n",
"#and for it to be positive\n",
"\n",
"# value of \u0002t we use in the numerical solution must be smaller than this\n",
"# maximum value. The calculation is continued until the temperature for the control vol-ume nearest the cylinder axis is less than 100\u00b0C\n",
"\n",
"print \"And using numerical solution the time in seconds comes out to be\"\n",
"#Time taken in seconds\n",
"tfinal = 431\n",
"print tfinal\n",
"print \"which is about 4% less than the chart solution of 450 s.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 3 Example # 3.7 \n",
"Therefore from chart solution, time taken in seconds shall be\n",
"450.0\n",
"And using numerical solution the time in seconds comes out to be\n",
"431\n",
"which is about 4% less than the chart solution of 450 s.\n"
]
}
],
"prompt_number": 53
}
],
"metadata": {}
}
]
}PKI2?}$!$!+Principles Of Heat Transfer/Chapter_4.ipynb{
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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter04: Analysis of Convection Heat Transfer"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4.1:pg-232"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 4 Example # 4.1 \"\n",
"\n",
"# Temperature of air in C is given as:\n",
"Tinfinity = 20;\n",
"# Temperature of surface in C is given as:\n",
"Ts = 100;\n",
"# Therefore avaerage temperature in degree C would be:\n",
"Ta = (Ts+Tinfinity)/2;\n",
"# From fig. 4.2 on page 232, it can be easily seen that (deltaT/deltaY) at\n",
"# y=0 is -66.7 K/mm\n",
"# From Table 28 in Appendix 2, at average temperature of air, thermal\n",
"# conductivity in W/m-K is\n",
"k = 0.028;\n",
"\n",
"#Therefore from eq. 4.1\n",
"print \"The heat transfer coefficient is given by, as per Eq. 4.1, in W/m2K\"\n",
"# 1000 is added to convert from mm to m\n",
"#heat transfer coefficient in W/m2K\n",
"hc = ((-k*(-66.7))/(Ts-Tinfinity))*1000\n",
"print round(hc,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 4 Example # 4.1 \n",
"The heat transfer coefficient is given by, as per Eq. 4.1, in W/m2K\n",
"23.3\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4.3:pg-259"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 4 Example # 4.3 \"\n",
"\n",
"# Width of the collector plate in ft is given:\n",
"b = 1.0;\n",
"# Surface temperature in F is given:\n",
"Ts = 140.0;\n",
"# Air temperature in F is given:\n",
"Tinfinity = 60.0;\n",
"# Air velocity in ft/sec is given as:\n",
"Uinfinity = 10.0;\n",
"# Average temperature in degree F is given as:\n",
"T = (Ts+Tinfinity)/2;\n",
"# Properties of air at average temperature are as follows\n",
"\n",
"Pr = 0.72; #Prandtl number\n",
"k = 0.0154; # Thermal conductivity in Btu/h ft \u00b0F\n",
"mu = 1.285*10-5; #Viscosity in lbm/ft s\n",
"cp = 0.24; #Specific heat in Btu/lbm \u00b0F\n",
"rho = 0.071; #Density in lbm/ft3\n",
"\n",
"# Reynold''s number at x=1ft is\n",
"Re1 = ((Uinfinity*rho)*1)/mu;\n",
"# Reynold''s number at x=9ft is\n",
"Re9 = ((Uinfinity*rho)*1)/mu;\n",
"# Assuming that the critical Reynolds number is 5*10**5, the critical distance is\n",
"#Critical Reynolds number\n",
"Rec = 5.0*(10**5);\n",
"#Critical distance in ft\n",
"xc = (Rec*mu)/(Uinfinity*rho);\n",
"\n",
"# From Eq. 4.28, and using the data obtained, we get for part a:\n",
"print \"Delta at x=1ft to be 0.0213ft and at x=9ft to be 0.0638ft\"\n",
"\n",
"# From Eq. 4.30, and using the data obtained, we get for part b:\n",
"print \"Cfx at x=1ft to be 0.00283 and at x=9ft to be 0.000942\"\n",
"\n",
"# From Eq. 4.31, and using the data obtained, we get for part c:\n",
"print \"Cfbar at x=1ft to be 0.00566 and at x=9ft to be 0.00189\"\n",
"\n",
"# From Eq. 4.29, and using the data obtained, we get for part d:\n",
"print \"Tau at x=1ft to be 3.12*10**-4 lb/ft**2 and at x=9ft to be 1.04*10**-4 lb/ft**2\"\n",
"\n",
"# From Eq. 4.32, and using the data obtained, we get for part e:\n",
"print \"DeltaTH at x=1ft to be 0.0237ft and at x=9ft to be 0.0712ft\"\n",
"\n",
"# From Eq. 4.36, and using the data obtained, we get for part f:\n",
"print \"hcx at x=1ft to be 1.08Btu/hft**2\u00b0F and at x=9ft to be 0.359Btu/hft**2\u00b0F\"\n",
"\n",
"# From Eq. 4.39, and using the data obtained, we get for part g:\n",
"print \"hcbar at x=1ft to be 2.18Btu/hft**2\u00b0F and at x=9ft to be 0.718Btu/hft**2\u00b0F\"\n",
"\n",
"# From Eq. 4.35, and using the data obtained, we get for part h:\n",
"print \"q at x=1ft to be 172 Btu/h and at x=9ft to be 517 Btu/h\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 4 Example # 4.3 \n",
"Delta at x=1ft to be 0.0213ft and at x=9ft to be 0.0638ft\n",
"Cfx at x=1ft to be 0.00283 and at x=9ft to be 0.000942\n",
"Cfbar at x=1ft to be 0.00566 and at x=9ft to be 0.00189\n",
"Tau at x=1ft to be 3.12*10**-4 lb/ft**2 and at x=9ft to be 1.04*10**-4 lb/ft**2\n",
"DeltaTH at x=1ft to be 0.0237ft and at x=9ft to be 0.0712ft\n",
"hcx at x=1ft to be 1.08Btu/hft**2\u00b0F and at x=9ft to be 0.359Btu/hft**2\u00b0F\n",
"hcbar at x=1ft to be 2.18Btu/hft**2\u00b0F and at x=9ft to be 0.718Btu/hft**2\u00b0F\n",
"q at x=1ft to be 172 Btu/h and at x=9ft to be 517 Btu/h\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4.4:pg-275"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 4 Example # 4.4 \"\n",
"\n",
"# Length of the crankcase in m is given as\n",
"L = 0.6;\n",
"# Width of the crankcase in m is given as\n",
"b = 0.2;\n",
"# Depth of the crankcase in m is given as\n",
"d = 0.1;\n",
"# Surface temperature in K is given as\n",
"Ts = 350.0;\n",
"# Air temperature in K is given as\n",
"Tinfinity = 276.0;\n",
"# Air velocity in m/sec is given as\n",
"Uinfinity = 30.0;\n",
"# It is stated that boundary layer is turbulent over the entire surface\n",
"\n",
"#Average air temperature in degree K is\n",
"T = (Ts+Tinfinity)/2;\n",
"# At this average temperature, we get the following for air\n",
"rho = 1.092;#density in kg/m**3\n",
"mu = 0.000019123;#vismath.cosity in SI units\n",
"Pr = 0.71;#Prandtl number\n",
"k = 0.0265;#Thermal conductivity in W/m-K\n",
"\n",
"# Reynold''s number is therefore given as\n",
"ReL = ((rho*Uinfinity)*L)/mu;\n",
"\n",
"#From eq. 4.82, average nusselt number could be given as\n",
"Nu = (0.036*(Pr**(1/3.0)))*(ReL**0.8);\n",
"\n",
"#We can write from the basic math.expression, Nu=hc*L/k, that\n",
"#Heat transfer coefficient in W/m**2-K\n",
"hc = (Nu*k)/L;\n",
"\n",
"# The surface area that dissipates heat is 0.28 m2\n",
"print \"Total heat loss from the surface in W is therefore\"\n",
"#Heat loss from the surface in W\n",
"q = (hc*0.28)*(Ts-Tinfinity)\n",
"print round(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 4 Example # 4.4 \n",
"Total heat loss from the surface in W is therefore\n",
"1896.0\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}PKI$HH+Principles Of Heat Transfer/Chapter_5.ipynb{
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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 5: Natural Convection"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5.1: Page 303"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.1 \";\n",
"\n",
"# ''Body temp in degree C''\n",
"Tb = 127;\n",
"#''Body temp in degree K''\n",
"TbK = Tb+273;\n",
"#''Ambient temp in degree C''\n",
"Ta = 27;\n",
"#''Ambient temp in degree K''\n",
"TaK = Ta+273;\n",
"#''Film temperature = (Body Temperature + Ambient Temperature)/2''\n",
"#''Film temp in degree K''\n",
"TfK = (TbK+TaK)/2;\n",
"#''Value of coefficient of math.expansion at this film temp in degree K inverse''\n",
"B = 1/TfK;\n",
"#''Value of Prandtl number at this film temp''\n",
"Pr = 0.71;\n",
"#''Value of kinematic vismath.cosity at this film temp in m2/s''\n",
"v = 0.0000212;\n",
"#''Value of thermal conductivity at this film temp in W/m-K''\n",
"k = 0.0291;\n",
"#''acceleration due to gravity in m/s2''\n",
"g = 9.81;\n",
"#''temperature diff. between body and ambient in degree K''\n",
"deltaT = TbK-TaK;\n",
"#''diameter of heater wire in m''\n",
"d = 0.001;\n",
"#''Therefore umath.sing Rayleigh number = ((Pr*g*B*deltaT*d**3)/v**2)''\n",
"Ra = ((((Pr*g)*B)*deltaT)*(d**3))/(v**2);\n",
"\n",
"#''From Fig. 5.3 on Page 303, we get''\n",
"#''log(Nu) = 0.12, where Nu is nusselt number, therefore''\n",
"Nu = 1.32;\n",
"#''Umath.sing Nu = hc*d/k, we get heat transfer coefficient in W/m2-K''\n",
"hc = (Nu*k)/d;\n",
"print \"The rate of heat loss per meter length in air in W/m is given by hc*(A/l)*deltaT\"\n",
"#heat loss per meter length in air in W/m\n",
"q = ((hc*deltaT)*math.pi)*d\n",
"print round(q,1)\n",
"\n",
"\n",
"#''For Co2, we evaluate the properties at film temperature''\n",
"#''Following are the values of dimensionless numbers so obtained''\n",
"#''Rayleigh number, Ra=16.90''\n",
"#''Nusselt number, Nu=1.62''\n",
"#''Umath.sing Nu = hc*d/k, we get''\n",
"#''hc = 33.2 W/m2-K''\n",
"print \"The rate of heat loss per meter length in CO2 is given by hc*(A/l)*deltaT\"\n",
"print \"q = 10.4 W/m\"\n",
"\n",
"print \" Discussion - For same area and temperature difference: \"\n",
"print \" Heat transfer by convection will be more, if heat transfer coeff. is high\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.1 \n",
"The rate of heat loss per meter length in air in W/m is given by hc*(A/l)*deltaT\n",
"12.1\n",
"The rate of heat loss per meter length in CO2 is given by hc*(A/l)*deltaT\n",
"q = 10.4 W/m\n",
" Discussion - For same area and temperature difference: \n",
" Heat transfer by convection will be more, if heat transfer coeff. is high\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5.2: Page 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.2 \";\n",
"\n",
"#''Surface temp in degree C''\n",
"TsC = 130;\n",
"#''Body temp in degree K''\n",
"Ts = TsC+273;\n",
"#''Ambient temp in degree C''\n",
"TinfinityC = 20;\n",
"#''Ambient temp in degree K''\n",
"Tinfinity = TinfinityC+273;\n",
"#''Film temperature = (Surface Temperature + Ambient Temperature)/2''\n",
"#''Film temp in degree K''\n",
"Tf = (Ts+Tinfinity)/2;\n",
"#''Height of plate in cms''\n",
"L = 15;\n",
"#''Width of plate in cms''\n",
"b = 10.0;\n",
"#''Value of Grashof number at this film temp is given by\n",
"#65(L**3)(Ts-Tinfinity)''\n",
"#Grashof number\n",
"Gr = (65*(L**3))*(Ts-Tinfinity);\n",
"#''Since the grashof number is less than 10**9, therefore flow is laminar''\n",
"#''For air at film temp = 75C (348K), Prandtl number is''\n",
"Pr = 0.71;\n",
"#''And the product Gr*Pr is''\n",
"#Prodect of Gr and Pr\n",
"GrPr = Gr*Pr;\n",
"#''From Fig 5.5 on page 305, at this value of GrPr, Nusselt number is''\n",
"Nu = 35.7;\n",
"#''Value of thermal conductivity at this film temp in W/m-K''\n",
"k = 0.029;\n",
"\n",
"#''Umath.sing Nu = hc*L/k, we get ''\n",
"#Heat transfer coefficient for convection in W/m2-K\n",
"hc = (Nu*k)/(L/100.0);\n",
"\n",
"#''Heat transfer coefficient for radiation, hr in W/m2-K''\n",
"hr = 8.5;\n",
"\n",
"#''Total area in m2 is given by 2*(b/100)*(L/100)''\n",
"A = (2*(b/100.0))*(L/100.0);\n",
"\n",
"\n",
"print \"Therefore total heat transfer in W is given by A*(hc+hr)*(Ts-Tinfinity)\"\n",
"#total heat transfer in W\n",
"q = (A*(hc+hr))*(Ts-Tinfinity)\n",
"print round(q,1)\n",
"\n",
"#''For plate to be 450cm in height, Rayleigh number becomes 4.62*10**11''\n",
"#''which implies that the flow is turbulent''\n",
"#''From Fig 5.5 on page 305, at this value of GrPr, Nusselt number is 973''\n",
"#''Umath.sing Nu = hc*d/k, we get in W/m2-K, hc_bar=6.3''\n",
"#''New Total area in m2, A_bar=2*(0.1)*(4.5)''\n",
"\n",
"print \"Therefore in new case, total heat transfer in W is given by A_bar*(hc_bar+hr)*(Ts-Tinfinity)\"\n",
"print \"we get q=1465W\"\n",
"\n",
"\n",
"print \" Discussion - For same temperature difference: \"\n",
"print \" Heat transfer will be more, if area math.exposed for convection and radiation is more\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.2 \n",
"Therefore total heat transfer in W is given by A*(hc+hr)*(Ts-Tinfinity)\n",
"50.8\n",
"Therefore in new case, total heat transfer in W is given by A_bar*(hc_bar+hr)*(Ts-Tinfinity)\n",
"we get q=1465W\n",
" Discussion - For same temperature difference: \n",
" Heat transfer will be more, if area math.exposed for convection and radiation is more\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5.3: Page 311"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.3 \"\n",
"\n",
"#''Surface temp in degree C''\n",
"TsC = 227.0;\n",
"#''Body temp in degree K'')\n",
"Ts = TsC+273;\n",
"#''Ambient temp in degree C''\n",
"TinfinityC = 27.0;\n",
"#''Ambient temp in degree K''\n",
"Tinfinity = TinfinityC+273;\n",
"#''Film temperature = (Surface Temperature + Ambient Temperature)/2''\n",
"#''Film temp in degree K'')\n",
"Tf = (Ts+Tinfinity)/2;\n",
"#''For a square plate, Height and width of plate in m''\n",
"L = 1.0;\n",
"b = 1.0;\n",
"#''For a square plate, characteristic length = surface area/parameter in m''\n",
"L_bar = (L*L)/(4.0*L);\n",
"#''Value of coefficient of math.expansion at this film temp in degree K inverse''\n",
"B = 1/Tf;\n",
"#''Value of Prandtl number at this film temp''\n",
"Pr = 0.71;\n",
"#''Value of thermal conductivity at this film temp in W/m-K''\n",
"k = 0.032;\n",
"#''Value of kinematic vismath.cosity at this film temp in m2/s''\n",
"v = 0.000027;\n",
"#''acceleration due to gravity in m/s2''\n",
"g = 9.81;\n",
"#''temperature diff. between body and ambient in degree K''\n",
"deltaT = Ts-Tinfinity;\n",
"#''Therefore umath.sing Rayleigh number = ((Pr*g*B*deltaT*(L_bar)**3)/v**2)''\n",
"#Rayleigh number\n",
"Ra = ((((Pr*g)*B)*deltaT)*(L_bar**3))/(v**2);\n",
"\n",
"\n",
"#''From eq. 5.17 on page 311, we have nusselt number for bottom plate as 0.27*Pr**0.25''\n",
"NuBottom = 25.2;\n",
"#''From eq. 5.16 on page 311, we have nusselt number for top plate as 0.27*Pr**0.25''\n",
"NuTop = 63.4;\n",
"#''And therefore corresponding heat transfer coeeficients are in W/m2-K''\n",
"hcBottom = (NuBottom*k)/L_bar; #heat transfer coeeficients are in W/m2-K at bottom \n",
"hcTop = (NuTop*k)/L_bar; #heat transfer coeeficients are in W/m2-K at top\n",
"\n",
"\n",
"print \"Therefore total heat transfer in W is given by A*(hcTop+hcBottom)*(deltaT)\"\n",
"#heat transfer in W\n",
"q = ((L*b)*(hcTop+hcBottom))*deltaT\n",
"print round(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.3 \n",
"Therefore total heat transfer in W is given by A*(hcTop+hcBottom)*(deltaT)\n",
"2268.0\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5.4: Page 314"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.4 \";\n",
"\n",
"#''Ambient temp in degree C''\n",
"TinfinityC = 27;\n",
"#''Ambient temp in degree K''\n",
"Tinfinity = TinfinityC+273;\n",
"#''The criterion for transition is rayleigh number to be 10**9''\n",
"\n",
"\n",
"#''Value of coefficient of math.expansion at this temp in degree K inverse''\n",
"B = 1/Tinfinity;\n",
"#''Value of Prandtl number at this ambient temp''\n",
"Pr = 0.71;\n",
"#''Diameter of pipe in m''\n",
"D = 1;\n",
"#''Value of kinematic vismath.cosity at this temp in m2/s''\n",
"v = 0.0000164;\n",
"#''acceleration due to gravity in m/s2''\n",
"g = 9.81;\n",
"\n",
"#''Therefore umath.sing Rayleigh number = ((Pr*g*B*deltaT*(D)**3)/v**2) = 10**9''\n",
"#''we get the temperature difference in centrigrade to be''\n",
"deltaT = 12;\n",
"print \"therefore the temperature of pipe in C is\"\n",
"# temperature of pipe in C\n",
"Tpipe = TinfinityC+deltaT\n",
"print round(Tpipe,2)\n",
"\n",
"\n",
"#''From table 13 in Appendix 2, for the case of water and umath.sing the same procedure we get''\n",
"# temperature difference in C\n",
"deltaTw = 0.05;\n",
"print \"therefore the temperature of pipe in C is\"\n",
"# temperature of pipe in C\n",
"Tpipew = TinfinityC+deltaTw\n",
"print round(Tpipew,2)\n",
"\n",
"print \" Discussion - For air and water: \"\n",
"print \" Temperature required to induce turbulence is higher in air\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.4 \n",
"therefore the temperature of pipe in C is\n",
"39.0\n",
"therefore the temperature of pipe in C is\n",
"27.05\n",
" Discussion - For air and water: \n",
" Temperature required to induce turbulence is higher in air\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5.5: Page 319"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.5 \";\n",
"\n",
"#''Top surface temp in degree C''\n",
"Tt = 20;\n",
"#''Body temp in degree K''\n",
"TtK = Tt+273;\n",
"#''Bottom temp in degree C''\n",
"Tb = 100;\n",
"#''Ambient temp in degree K''\n",
"TbK = Tb+273;\n",
"#''Average temp = (Bottom Temperature + top Temperature)/2''\n",
"#''average temp in degree K''\n",
"T = (TbK+TtK)/2;\n",
"#''Value of coefficient of math.expansion at this temp in degree K inverse''\n",
"B = 0.000518;\n",
"#''Value of Prandtl number at this temp''\n",
"Pr = 3.02;\n",
"#''Value of kinematic vismath.cosity at this temp in m2/s''\n",
"v = 0.000000478;\n",
"#''acceleration due to gravity in m/s2''\n",
"g = 9.8;\n",
"#''temperature diff. between body and ambient in degree K''\n",
"deltaT = TbK-TtK;\n",
"#''depth of water in m''\n",
"h = 0.08;\n",
"#''Therefore umath.sing Rayleigh number = ((Pr*g*B*deltaT*h**3)/v**2)''\n",
"Ra = ((((Pr*g)*B)*deltaT)*(h**3))/(v**2);\n",
"\n",
"#''From Eq. (5.30b) on page 318, we find''\n",
"#Nusselt number\n",
"Nu = 79.3;\n",
"#''Value of thermal conductivity at this film temp in W/m-K''\n",
"k = 0.657;\n",
"#''Umath.sing Nu = hc*d/k, we get heat transfer coefficient in W/m2-K''\n",
"hc = (Nu*k)/h;\n",
"#''diameter of pan in m''\n",
"d = 0.15;\n",
"#''area = pi*d*d/4''\n",
"a = ((math.pi*d)*d)/4;\n",
"print \"The rate of heat loss in W is given by hc*(A)*deltaT\"\n",
"#heat loss in W\n",
"q = (hc*deltaT)*a\n",
"print int(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.5 \n",
"The rate of heat loss in W is given by hc*(A)*deltaT\n",
"920\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5.6: Page 323"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.6 \";\n",
"\n",
"#''RPM of shaft''\n",
"N = 3;\n",
"#''Angular velocity, omega=2*pi*N/60 in rad/s''\n",
"omega = 0.31;\n",
"#''Ambient temp in degree C''\n",
"Ta = 20;\n",
"#''Ambient temp in degree K''\n",
"TaK = Ta+273;\n",
"#''Shaft temp in degree C''\n",
"Ts = 100;\n",
"#''Shaft temp in degree K''\n",
"TsK = Ts+273;\n",
"#''Film temperature = (Shaft Temperature + Ambient Temperature)/2''\n",
"#''Film temp in degree K''\n",
"TfK = (TsK+TaK)/2;\n",
"#''diameter of shaft in m''\n",
"d = 0.2;\n",
"#''Value of kinematic vismath.cosity at this film temp in m2/s''\n",
"v = 0.0000194;\n",
"#''Value of reynolds number''\n",
"Re = (((math.pi*d)*d)*omega)/v;\n",
"\n",
"\n",
"#''acceleration due to gravity in m/s2''\n",
"g = 9.81;\n",
"#''temperature diff. between body and ambient in degree K''\n",
"deltaT = TsK-TaK;\n",
"#''Value of Prandtl number at this film temp''\n",
"Pr = 0.71;\n",
"#''Value of coefficient of math.expansion at this film temp in degree K inverse''\n",
"B = 1/TfK;\n",
"#''Therefore umath.sing Rayleigh number = ((Pr*g*B*deltaT*d**3)/v**2)''\n",
"#Rayleigh number\n",
"Ra = ((((Pr*g)*B)*deltaT)*(d**3))/(v**2);\n",
"\n",
"#''From Eq. 5.35 on Page 322, we get''\n",
"#Nusselt number\n",
"Nu = 49.2;\n",
"#''Value of thermal conductivity at this film temp in W/m-K''\n",
"k = 0.0279;\n",
"#''Umath.sing Nu = hc*d/k, we get in W/m2-K''\n",
"hc = (Nu*k)/d;\n",
"#''let the length math.exposed to heat transfer is l=1m''\n",
"#''then area in m2 = pi*d*l''\n",
"a = math.pi*d;\n",
"print \"The rate of heat loss in air in W is given by hc*(a)*deltaT\"\n",
"#heat loss in air in W\n",
"q = (hc*deltaT)*a\n",
"print round(q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.6 \n",
"The rate of heat loss in air in W is given by hc*(a)*deltaT\n",
"345.0\n"
]
}
],
"prompt_number": 14
}
],
"metadata": {}
}
]
}PKI)VNN+Principles Of Heat Transfer/Chapter_6.ipynb{
"metadata": {
"name": "",
"signature": "sha256:6f27b63789233dbcd6b595c8e65a2bfbfddf8fdce1aec80ae9bb6f8c99f32cf1"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6: Forced Convection Inside Tubes And Ducts"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6.1: Page 365"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.1 \"\n",
"\n",
"#Inlet temperature in degree C\n",
"Tin = 10;\n",
"#Outlet temperature in degree C\n",
"Tout = 40;\n",
"#Diameter in m\n",
"D = 0.02;\n",
"#Massflow rate in kg/s\n",
"m = 0.01;\n",
"#Heat flux in W/m2\n",
"q = 15000;\n",
"\n",
"#From Table 13 in Appendix 2, the appropriate properties of water at an\n",
"#average temperature between inlet and outlet of 25\u00b0C are\n",
"\n",
"#Density in kg/m3\n",
"rho = 997;\n",
"#Specific heat in J/kgK\n",
"c = 4180;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.608;\n",
"#Dynamic vismath.cosity in Ns/m2\n",
"mu = 0.00091;\n",
"\n",
"print \"Reynolds Number is\"\n",
"#Reynolds number\n",
"Re = (4*m)/((math.pi*D)*mu)\n",
"print int(Re)\n",
"print \"Flow is Laminar\"\n",
"\n",
"#Since the thermal-boundary condition is one of uniform heat flux, Nu\u0005= 4.36 from Eq. (6.31)\n",
"#Nusselt number\n",
"Nu = 4.36;\n",
"print \"Heat transfer coefficient in W/m2K\"\n",
"#Heat transfer coefficient in W/m2K\n",
"hc = (Nu*k)/D\n",
"print int(hc)\n",
"\n",
"#The length of pipe needed for a 30\u00b0C temperature rise is obtained from a heat balance\n",
"print \"Length of pipe in m\"\n",
"#Length of pipe in m\n",
"L = ((m*c)*(Tout-Tin))/((math.pi*D)*q)\n",
"print round(L,2)\n",
"\n",
"print \"Inner surface temperature at outlet in degree C\"\n",
"#Inner surface temperature at outlet in degree C\n",
"Ts = q/hc+Tout\n",
"print round(Ts,2)\n",
"\n",
"#The friction factor is found from Eq. (6.18)\n",
"print \"Friction factor is\"\n",
"#Friction factor is\n",
"f = 64/Re\n",
"print round(f,4)\n",
"#Average velocity in m/s\n",
"U = (4*m)/(((rho*math.pi)*D)*D);\n",
"print \"The pressure drop in the pipe in N/m2\"\n",
"#The pressure drop in the pipe in N/m2\n",
"deltaP = ((((f*L)*rho)*U)*U)/(D*2)\n",
"print round(deltaP,1)\n",
"\n",
"#Efficiency\n",
"n = 0.5;\n",
"#The pumping power P is obtained from Eq. 6.19\n",
"print \"Pumping power in W is\"\n",
"#Pumping power in W\n",
"P = (m*deltaP)/(rho*n)\n",
"print round(P,6)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.1 \n",
"Reynolds Number is\n",
"699\n",
"Flow is Laminar\n",
"Heat transfer coefficient in W/m2K\n",
"132\n",
"Length of pipe in m\n",
"1.33\n",
"Inner surface temperature at outlet in degree C\n",
"153.17\n",
"Friction factor is\n",
"0.0915\n",
"The pressure drop in the pipe in N/m2\n",
"3.1\n",
"Pumping power in W is\n",
"6.2e-05\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6.2: Page 369"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.2 \"\n",
"\n",
"#Diameter in m\n",
"D = 0.01;\n",
"#Wall thickness in m\n",
"t = 0.02/100;\n",
"#Massflow rate in kg/s\n",
"m = 0.05;\n",
"#Inlet temperature in degree C\n",
"Tin = 35;\n",
"#Outlet temperature in degree C\n",
"Tout = 45.0;\n",
"#Assuming a constant tube temp. in degree C\n",
"T = 100.0;\n",
"\n",
"#From Table 16 in Appendix 2, we get the following properties for oil at\n",
"#40\u00b0C\n",
"\n",
"#Density in kg/m3\n",
"rho = 876.0;\n",
"#Specific heat in J/kgK\n",
"c = 1964.0;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.144;\n",
"#Dynamic vismath.cosity in Ns/m2\n",
"mu = 0.21;\n",
"#Prandtl number\n",
"Pr = 2870.0;\n",
"\n",
"#Reynolds Number is\n",
"Re = (4*m)/((math.pi*D)*mu);\n",
"\n",
"#For laminar flow and constant temperature assumption\n",
"#Nusselt number\n",
"Nu = 3.66;\n",
"#Heat transfer coefficient in W/m2K\n",
"hc = (Nu*k)/D;\n",
"#Heat transfer rate in W\n",
"q = (m*c)*(Tout-Tin);\n",
"#LMTD in degree K\n",
"LMTD = (T-Tout-(T-Tin))/math.log((T-Tout)/(T-Tin));\n",
"\n",
"print \"Length of pipe in m is\"\n",
"#Length of pipe in m\n",
"L = q/(((math.pi*D)*hc)*LMTD)\n",
"print round(L,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.2 \n",
"Length of pipe in m is\n",
"9.91\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6.3: Page 375"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.3 \"\n",
"\n",
"#Bulk temperature in degree K\n",
"T = 293;\n",
"#Side of square duct in m\n",
"b = 0.1;\n",
"#Length of square duct in m\n",
"L = 5;\n",
"#Wall temperature in degree K\n",
"Tw = 300;\n",
"#Velocity in m/s\n",
"U = 0.03;\n",
"\n",
"#Hydraulic diameter in m\n",
"D = 4*((b*b)/(4*b));\n",
"\n",
"#Physical properties at 293 K from Table 19 in Appendix 2 are\n",
"\n",
"#Density in kg/m3\n",
"rho = 810;\n",
"#Specific heat in J/kgK\n",
"c = 2366;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.167;\n",
"#Dynamic vismath.cosity in Ns/m2\n",
"mu = 0.00295;\n",
"#Prandtl number\n",
"Pr = 50.8;\n",
"\n",
"#Reynolds Number is\n",
"Re = ((U*D)*rho)/mu;\n",
"\n",
"#Hence, the flow is laminar. Assuming fully developed flow, we get the\n",
"#Nusselt number for a uniform wall temperature from Table 6.1\n",
"\n",
"Nu = 2.98;\n",
"#Heat transfer coefficient in W/m2K\n",
"hc = (Nu*k)/D;\n",
"\n",
"#Similarly, from Table 6.1, the product Re*f=56.91\n",
"\n",
"print \"Friction factor is\"\n",
"#Friction factor\n",
"f = 56.91/Re\n",
"print round(f,4)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.3 \n",
"Friction factor is\n",
"0.0691\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6.4: Page 378"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.4 \"\n",
"\n",
"#Temperature of device camath.sing in degree K\n",
"Ts = 353;\n",
"#Length of holes in m\n",
"L = 0.3;\n",
"#Diameter of holes in m\n",
"D = 0.00254;\n",
"#Inlet temperature in degree K\n",
"Tin = 333;\n",
"#Velocity in m/s\n",
"U = 0.2;\n",
"\n",
"#The properties of water at 333 K, from Table 13 in Appendix 2, are\n",
"\n",
"#Density in kg/m3\n",
"rho = 983;\n",
"#Specific heat in J/kgK\n",
"c = 4181;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.658;\n",
"#Dynamic vismath.cosity in Ns/m2\n",
"mu = 0.000472;\n",
"#Prandtl number\n",
"Pr = 3;\n",
"\n",
"#Reynolds Number is\n",
"Re = ((U*D)*rho)/mu;\n",
"\n",
"if (((Re*Pr)*D)/L)>10 :\n",
" #Eq. (6.42) can be used to evaluate the heat transfer coefficient.\n",
" #But math.since the mean bulk temperature is not known, we shall evaluate all the properties first at the inlet bulk temperature Tb1 ,\n",
" #then determine an exit bulk temperature, and then make a second iteration to obtain a more precise value.\n",
"\n",
" #At the wall temperature of 353 K\n",
" #Vismath.cosity in SI units\n",
" mus = 0.000352; \n",
" #From Eq. (6.42)\n",
" #Nusselt number\n",
" Nu = (1.86*((((Re*Pr)*D)/L)**0.33))*((mu/mus)**0.14);\n",
" #Heat transfer coefficient in W/m2K\n",
" hc = (Nu*k)/D;\n",
" #mass flow rate in kg/s\n",
" m = ((((rho*math.pi)*D)*D)*U)/4;\n",
"\n",
" #Inserting the calculated values for hc and m into Energy balance equation, along with Tb1 and Ts and\n",
" #gives Tb2=345K\n",
"\n",
" #For the second iteration, we shall evaluate all properties at the new average bulk temperature\n",
" #Bulk temp. in degree C\n",
" Tb = (345.0+Tin)/2;\n",
"\n",
" #At this temperature, we get from Table 13 in Appendix 2:\n",
" #Density in kg/m3\n",
" rho = 980.0;\n",
" #Specific heat in J/kgK\n",
" c = 4185;\n",
" #Thermal conductivity in W/mK\n",
" k = 0.662;\n",
" #Dynamic vismath.cosity in Ns/m2\n",
" mu = 0.000436;\n",
" #Prandtl number\n",
" Pr = 2.78;\n",
"\n",
" #New reynolds Number is\n",
" Re = ((U*D)*rho)/mu;\n",
"\n",
" #With this value of Re, the heat transfer coefficient can now be calculated.\n",
" #We obtain the following similarly\n",
" #Nusselt number\n",
" Nu = 5.67;\n",
" #Heat transfer coefficient in W/m2K\n",
" hc = (Nu*k)/D;\n",
" #Similarly putting this value in energy balance yields\n",
" #Bulk temperature in degree K\n",
" Tb2 = 345; \n",
"\n",
" print \"Outlet temperature in degree K\"\n",
" #Outlet temperature in degree K\n",
" print round(Tb2,2)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.4 \n",
"Outlet temperature in degree K\n",
"345.0\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6.5: Page 389"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.5 \"\n",
"\n",
"#Velocity in ft/s\n",
"U = 10.0;\n",
"#Outer diameter in inches\n",
"D = 1.5;\n",
"#Inner diameter in inches\n",
"d = 1.0;\n",
"#Temperature of water in degree F\n",
"Tw = 180.0;\n",
"#Temperature of wall in degree F\n",
"Twall = 100.0;\n",
"\n",
"#The hydraulic diameter D for this geometry is 0.5 in.\n",
"D = 0.5;\n",
"\n",
"#Umath.sing properties given in the table provided\n",
"\n",
"#Reynolds number\n",
"Re = (((U*D)*3600)*60.8)/(12*0.75);\n",
"#Prandtl number\n",
"Pr = (1*0.75)/0.39;\n",
"#The Nusselt number according to the Dittus-Boelter correlation [Eq. (6.60)] \n",
"Nu = (0.023*(125000**0.8))*(Pr**0.3);\n",
"print 'The Nusselt number according to the Dittus-Boelter correlation comes out to be \\n',int(Nu)\n",
"\n",
"#Umath.sing the Sieder-Tate correlation [Eq. (6.61)]\n",
"#Nusselt number\n",
"Nu = 358;\n",
"print 'The Nusselt number according to the Sieder-Tate correlation comes out to be \\n',Nu\n",
"\n",
"#The Petukhov-Popov correlation [Eq. (6.63)] gives\n",
"#Friction factor\n",
"f = (1.82*log10(125000)-1.64)**(-2);\n",
"#K1 of Eq. 6.63\n",
"K1 = 1+3.4*f;\n",
"#K2 of Eq. 6.63\n",
"K2 = 11.7+1.8/(Pr**0.33);\n",
"#Nusselt number\n",
"Nu = 370;\n",
"\n",
"#The Sleicher-Rouse correlation [Eq. (6.64)] yields\n",
"#a of Eq. 6.64\n",
"a = 0.852;\n",
"#b of Eq. 6.64\n",
"b = 1/3.0+0.5/math.exp(0.6*4.64);\n",
"#Reynolds number\n",
"Re = 82237;\n",
"#Nusselt number\n",
"Nu = 5+(0.015*(Re**a))*(4.64**b);\n",
"print 'Nusselt number according to The Sleicher-Rouse correlation comes out to be \\n',int(Nu)\n",
"\n",
"print \"Assuming that the correct answer is Nu=370\"\n",
"print \"The first two correlations underpredict by about 10% and 3.5%, respectively\"\n",
"print \"while the Sleicher-Rouse method overpredicts by about 10.5%.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.5 \n",
"The Nusselt number according to the Dittus-Boelter correlation comes out to be \n",
"334\n",
"The Nusselt number according to the Sieder-Tate correlation comes out to be \n",
"358\n",
"Nusselt number according to The Sleicher-Rouse correlation comes out to be \n",
"409\n",
"Assuming that the correct answer is Nu=370\n",
"The first two correlations underpredict by about 10% and 3.5%, respectively\n",
"while the Sleicher-Rouse method overpredicts by about 10.5%.\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6.6: Page 394"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.6 \"\n",
"\n",
"#Mass flow rate in kg/s\n",
"m = 3;\n",
"#Diameter of tube in m\n",
"D = 5/100.0;\n",
"#Temperature of fluid in degree K\n",
"Tb = 473.0;\n",
"#Temperature of wall in degree K\n",
"Ts = 503.0;\n",
"\n",
"#Density in kg/m3\n",
"rho = 7700.0;\n",
"#Specific heat in J/kgK\n",
"c = 130.0;\n",
"#Thermal conductivity in W/mK\n",
"k = 12.0;\n",
"#Kinematic vismath.cosity in m2/s\n",
"nu = 0.00000008;\n",
"#Prandtl number\n",
"Pr = 0.011;\n",
"\n",
"#The rate of heat transfer per unit temperature rise in W is\n",
"q = (m*c)*1;\n",
"\n",
"#Reynolds Number is\n",
"Re = (D*m)/(((((rho*math.pi)*D)*D)*nu)/4);\n",
"\n",
"#The heat transfer coefficient in W/m2K is obtained from Eq. (6.67)\n",
"hc = ((k*0.625)*((Re*Pr)**0.4))/D;\n",
"\n",
"#Surface area in m2\n",
"A = q/(hc*(Ts-Tb));\n",
"\n",
"print \"Required length of tube in m is\"\n",
"#Required length of tube in m\n",
"L = A/(math.pi*D)\n",
"print round(L,4)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.6 \n",
"Required length of tube in m is\n",
"0.0307\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6.7: Page 405"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.7 \"\n",
"\n",
"#Temperature of airstream in degree C\n",
"Tair = 20;\n",
"#Velocity of air in m/s\n",
"U = 1.8;\n",
"#Side of circuit in m\n",
"L = 27/1000.0;\n",
"#Spacing in the circuit in m\n",
"H = 17/1000.0;\n",
"\n",
"#At 20\u00b0C, the properties of air from Table 28, Appendix 2, are \n",
"\n",
"#Density in kg/m3\n",
"rho = 7700.0;\n",
"#Specific heat in J/kgK\n",
"c = 130.0;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.0251;\n",
"#Kinematic vismath.cosity in m2/s\n",
"nu = 0.0000157;\n",
"#Prandtl number\n",
"Pr = 0.011;\n",
"\n",
"#Reynolds number\n",
"Re = (U*H)/nu;\n",
"\n",
"#From Fig. (6.27), we see that the second integrated circuit is in the inlet region and estimate Nu2 =\u000529.\n",
"#Nusselt number in second circuit\n",
"Nu2 = 29;\n",
"print \"Heat transfer coefficient along 2nd circuit in W/m2K\"\n",
"#Heat transfer coefficient in W/m2K\n",
"hc2 = (Nu2*k)/L\n",
"print round(hc2)\n",
"\n",
"#The sixth integrated circuit is in the developed region and from Eq. (6.79)\n",
"#Nusselt number in sixth circuit\n",
"Nu6 = 21.7;\n",
"print \"Heat transfer coefficient along 6th circuit in W/m2K\"\n",
"##Heat transfer coefficient in W/m2K\n",
"hc6 = (Nu6*k)/L\n",
"print round(hc6,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.7 \n",
"Heat transfer coefficient along 2nd circuit in W/m2K\n",
"27.0\n",
"Heat transfer coefficient along 6th circuit in W/m2K\n",
"20.2\n"
]
}
],
"prompt_number": 27
}
],
"metadata": {}
}
]
}PKI>T>T+Principles Of Heat Transfer/Chapter_7.ipynb{
"metadata": {
"name": "",
"signature": "sha256:467171181816c2659c4f87b4e2efe7cc504a8bc236d63fac8ac695852fd8fdda"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7: Forced Convection Over Exterior Surfaces"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.1: Page 429"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.1 \"\n",
"\n",
"#Diameter in m\n",
"D = 0.3;\n",
"#Cruimath.sing speed in m/s\n",
"Uinfinity = 150;\n",
"\n",
"#At an altitude of 7500 m the standard atmospheric air pressure is 38.9 kPa and the density of the air is 0.566 kg/m3 (From Table 38 in Appendix 2).\n",
"rho = 0.566;\n",
"#Dynamic vismath.cosity in kgm/s\n",
"mu = 0.0000174;\n",
"#Prandtl number\n",
"Pr = 0.72;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.024;\n",
"\n",
"#The heat transfer coefficient at the stagnation point (\u0004\u00050) is, according to Eq. (7.2)\n",
"\n",
"print \"Heat transfer coefficient at stagnation point in W/m2K\"\n",
"#Heat transfer coefficient at stagnation point in W/m2K\n",
"h = (((k*1.14)*((((rho*Uinfinity)*D)/mu)**0.5))*(Pr**0.4))/D\n",
"\n",
"print \"Distribution of the convection heat trans-fer coefficient over the forward portion of the wing\"\n",
"for o in range(0,90,15): #o is the parameter used in the loop\n",
" #convection heat trans-fer coefficients in W/m2K\n",
" ho = h*(1-(o/90.0)**3);\n",
" # L.26: No simple equivalent, so mtlb_fprintf() is called.\n",
" print \"At an angle of \",o,\" degree, heat transfer coeffcient is \",round(ho,2)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.1 \n",
"Heat transfer coefficient at stagnation point in W/m2K\n",
"Distribution of the convection heat trans-fer coefficient over the forward portion of the wing\n",
"At an angle of 0 degree, heat transfer coeffcient is 96.75\n",
"At an angle of 15 degree, heat transfer coeffcient is 96.31\n",
"At an angle of 30 degree, heat transfer coeffcient is 93.17\n",
"At an angle of 45 degree, heat transfer coeffcient is 84.66\n",
"At an angle of 60 degree, heat transfer coeffcient is 68.09\n",
"At an angle of 75 degree, heat transfer coeffcient is 40.76\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.2: Page 434"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.2 \"\n",
"\n",
"#Diameter of wire in m\n",
"D = 0.000025;\n",
"#Length of wire in m\n",
"L = 0.006;\n",
"#Free stream temperature of air in degeee C\n",
"T = 20;\n",
"#Wire temperature to be maintain in degree C\n",
"Tw = 230;\n",
"#Resistivity of platinum in ohm-cm\n",
"Re = 0.0000171;\n",
"\n",
"#Since the wire is very thin, conduction along it can be neglected; also, the temperature gradient in the wire at any cross section can be disregarded.\n",
"\n",
"#At freestream temperature, for air:\n",
"\n",
"#Thermal conductivity in W/mC\n",
"k = 0.0251;\n",
"#Kinematic vismath.cosity in m2/s\n",
"nu = 0.0000157;\n",
"\n",
"#Reynolds number at velocity = 2m/s\n",
"Rey = (2*D)/nu;\n",
"if Re<40:\n",
" #Umath.sing the correlation equa-tion from Eq. (7.3) and Table 7.1\n",
" #Average convection heat transfer coefficient as a function of velocity\n",
" #is\n",
" #hc=799U**0.4 W/m2C\n",
"\n",
" #At this point, it is necessary to estimate the heat transfer coefficient for radiant heat flow.\n",
" #According to Eq. (1.21), we have approximately\n",
" #hr=sigma*epsilon*((Ts+Tinfinity)**3)/4\n",
"\n",
" #The emissivity of polished platinum from Appendix 2, Table 7 is about 0.05, so hr is about 0.05 W/m2C.\n",
"\n",
" #The rate at which heat is transferred from the wire is therefore\n",
" #0.0790U**4 W.\n",
"\n",
" #The electrical resistance of the wire in ohm is\n",
" R = ((Re*L)*4)/(((100*math.pi)*D)*D);\n",
"\n",
"\n",
"#A heat balance with the current i gives\n",
"print \"Current in ampere as a function of velocity is\"\n",
"print \"i=0.19*U**0.2\"\n",
"\n",
"# the answer is the equation hence we have to print the equation only\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.2 \n",
"Current in ampere as a function of velocity is\n",
"i=0.19*U**0.2\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.3: Page 438"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.3 \"\n",
"\n",
"#Velocity of air in m/s\n",
"Uinfinity = 0.5;\n",
"#Length and breadth of square shaped array in m\n",
"L = 2.5;\n",
"#Surface temperature in degree C\n",
"Ts = 70.0;\n",
"#Ambient temperature in degree C\n",
"Ta = 20.0;\n",
"\n",
"#At free stream temperature of air\n",
"#Kinematic vismath.cosity in m2/s\n",
"nu = 0.0000157;\n",
"#Density in kg/m3\n",
"rho = 1.16;\n",
"#Specific heeat in Ws/kgC\n",
"c = 1012;\n",
"#Prandtl number\n",
"Pr = 0.71;\n",
"\n",
"#Reynolds number\n",
"Re = (Uinfinity*L)/nu;\n",
"\n",
"#From equation 7.18\n",
"#The average heat transfer coefficient in W/m2C is\n",
"#Heat transfer coefficient in W/m2C \n",
"h = (((0.0033*(Pr**(-2/3.0)))*c)*rho)*Uinfinity;\n",
"print \"Heat loss from array in W is\"\n",
"#Heat loss in W \n",
"q = ((h*L)*L)*(Ts-Ta)\n",
"print round(q,2)\n",
"\n",
"# the answer is incorrect in the textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.3 \n",
"Heat loss from array in W is\n",
"760.56\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.4: Page 442"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.4 \"\n",
"\n",
"#Diameter of pipe in m\n",
"D = 7.62/100;\n",
"#Diameter and length of cylinder in m\n",
"d = 0.93/100;\n",
"l = 1.17/100;\n",
"#Initial temperature in degree C\n",
"Ti = 50.0;\n",
"#Final temperature in degree C\n",
"Tf = 350.0;\n",
"#Temperature of pipe surface in degree C\n",
"Tp = 400.0;\n",
"#Therefore film temp. at inlet in degree C\n",
"Tfi = (Ti+Tp)/2;\n",
"#Therefore film temp. at outlet in degree C\n",
"Tfo = (Tf+Tp)/2;\n",
"#Average film temp. in degree C\n",
"Tf = (Tfi+Tfo)/2;\n",
"\n",
"#At this film temperature\n",
"#Kinematic vismath.cosity in m2/s\n",
"nu = 0.0000482;\n",
"#Thermal conductivity in W/mC\n",
"k = 0.042;\n",
"#Density in kg/m3\n",
"rho = 0.6;\n",
"#Specific heat in J/kgC\n",
"c = 1081;\n",
"#Prandtl number\n",
"Pr = 0.71;\n",
"#Flow rte of gas in kg/h is\n",
"m = 5;\n",
"\n",
"#Superficial velocity in m/h\n",
"Us = m/((((rho*math.pi)*D)*D)/4);\n",
"#Cylinder packaging volume in m3\n",
"V = (((math.pi*d)*d)*l)/4;\n",
"#Surface area in m2\n",
"A = (((2*math.pi)*d)*d)/4+(math.pi*d)*l;\n",
"#Equivalent packaging dia in meter\n",
"Dp = (6*V)/A;\n",
"\n",
"#REynolds number based on this dia\n",
"Re = ((Us*3600)*Dp)/nu;\n",
"#From eq. 7.23\n",
"print \"Heat transfer coefficient in W/m2C is\"\n",
"#Heat transfer coefficient in W/m2C\n",
"h = (14.3*k)/Dp\n",
"print round(h,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.4 \n",
"Heat transfer coefficient in W/m2C is\n",
"60.16\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.5: Page 453"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.5 \"\n",
"\n",
"#Initial temperature in degree F\n",
"Ti = 58;\n",
"#Final temperature in degree F\n",
"Tf = 86.0;\n",
"#Film temperature of air in degree F\n",
"Tair = (Ti+Tf)/2;\n",
"#Temperature of condenmath.sing steam in degree F\n",
"Tsteam = 212.0;\n",
"#Heat transfer coeffcient in Btuh/ft2F\n",
"ho = 1000.0;\n",
"#Length of tube in ft\n",
"L = 2.0;\n",
"#Diameter of tube in in\n",
"d = 0.5;\n",
"#Wall thickness in inches\n",
"t = 0.049;\n",
"#Pitch in inches\n",
"p = 3/4.0;\n",
"#Width in ft and height in inches of rectangular shell\n",
"H = 15;\n",
"W = 2;\n",
"#Mass flow rate of air in lb/h\n",
"m = 32000;\n",
"\n",
"#Appendix 2, Table 28 then gives for the properties of air at this mean\n",
"#bulk temperature\n",
"\n",
"#Density in lb/ft3\n",
"rho = 0.072;\n",
"#Thermal conductivity in Btu/h F ft\n",
"k = 0.0146;\n",
"#Dynamic vismath.cosity in lb/fth\n",
"mu = 0.0444;\n",
"#Prandtl number for air and steam\n",
"Pr = 0.71;\n",
"\n",
"#Calcaulating minimum free area in ft2\n",
"A = ((H/p)*W)*((p-d)/12.0);\n",
"#Maximum gas velocity in lb/h.ft2\n",
"Gmax = m/A;\n",
"#Hence the reynolds number is\n",
"Re = (Gmax*d)/(12*mu);\n",
"\n",
"#Assuming that more than 10 rows will be required, the heat transfer coefficient is calculated from Eq. (7.29)\n",
"\n",
"#h value in Btu/h ft2 F\n",
"h = ((((k*12)/d)*(Pr**0.36))*0.27)*(Re**0.63);\n",
"\n",
"#The resistance at the steam side per tube in h F/Btu\n",
"R1 = 12/(((ho*math.pi)*(d-2*t))*L);\n",
"\n",
"#The resistance of the pipe wall in h F/Btu\n",
"R2 = 0.049/(((60*math.pi)*L)*(d-t));\n",
"\n",
"#The resistance at the outside of the tube in h F/Btu\n",
"R3 = 1/((((h*math.pi)*d)*L)/12);\n",
"\n",
"#Total resistance in h F/Btu\n",
"R = R1+R2+R3;\n",
"\n",
"#Mean temperature difference between air and steam in degree F is\n",
"deltaT = Tsteam-Tair;\n",
"\n",
"#Specific heat of air in Btu/lb F\n",
"c = 0.241;\n",
"\n",
"#Equating the rate of heat flow from the steam to the air to the rate of enthalpy rise of the air\n",
"\n",
"#Solving for N gives\n",
"print \"Total number of transverse tubes needed are\"\n",
"#Total number of transverse tubes\n",
"N = (((m*c)*(Tf-Ti))*R)/(20*deltaT)\n",
"print \"Rounding off = 5 tubes\"\n",
"\n",
"if N<10 :\n",
" #Correction for h value, again in Btu/h ft2 F\n",
" h = 0.92*h;\n",
"\n",
"\n",
"#The pressure drop is obtained from Eq. (7.37) and Fig. 7.25.\n",
"\n",
"#Velocity in ft/s\n",
"Umax = Gmax/(3600*rho);\n",
"#Acceleration due to gravity in ft/s2\n",
"g = 32.2;\n",
"print \"Corresponding pressure drop in lb/ft2\"\n",
"#Corresponding pressure drop in lb/ft2\n",
"P = ((((6*0.75)*rho)*Umax)*Umax)/(2*g)\n",
"print round(P)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.5 \n",
"Total number of transverse tubes needed are\n",
"Rounding off = 5 tubes\n",
"Corresponding pressure drop in lb/ft2\n",
"110.0\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.6: Page 456"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.6 \"\n",
"\n",
"#Temperature of methane in degree C\n",
"T = 20;\n",
"#Outer dia of tube in m\n",
"D = 4/100.0;\n",
"#Longitudinal spacing in m\n",
"SL = 6/100.0;\n",
"#Transverse spacing in m\n",
"ST = 8/100.0;\n",
"#Wall temperature in degree C\n",
"Tw = 50.0;\n",
"#Methane flow velocity in m/s\n",
"v = 10.0;\n",
"\n",
"#For methane at 20\u00b0C, Table 36, Appendix 2 gives\n",
"\n",
"#Density in kg/m3\n",
"rho = 0.668;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.0332;\n",
"#Kinematic vismath.cosity in m2/s\n",
"nu = 0.00001627;\n",
"#Prandtl number\n",
"Pr = 0.73;\n",
"\n",
"#From the geometry of the tube bundle, we see that the minimum flow\n",
"#area is between adjacent tubes in a row and that this area is half\n",
"#the frontal area of the tube bundle. Thus,\n",
"#Velocity in m/s\n",
"Umax = 2*v;\n",
"\n",
"#Reynolds number\n",
"Re = (Umax*D)/nu;\n",
"\n",
"#Since ST/SL\u0005<\u00072, we use Eq. (7.30)\n",
"\n",
"#Nusselt number\n",
"Nu = ((0.35*((ST/SL)**0.2))*(Re**0.6))*(Pr**0.36);\n",
"\n",
"#Heat transfer coefficient in W/m2K\n",
"h = (Nu*k)/D;\n",
"\n",
"#Since there are fewer than 10 rows, the correlation factor in Table 7.3 gives\n",
"print \"Heat transfer coefficient in W/m2K\"\n",
"#Heat transfer coefficient in W/m2K\n",
"h = 0.92*h\n",
"print round(h)\n",
"\n",
"#Tube-bundle pressure drop is given by Eq. (7.37). The insert in Fig. (7.26) gives the correction factor x.\n",
"\n",
"print \"Corresponding pressure drop in N/m2\"\n",
"#Corresponding pressure drop in N/m2\n",
"P = ((((5*0.25)*rho)*Umax)*Umax)/2\n",
"print round(P)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.6 \n",
"Heat transfer coefficient in W/m2K\n",
"165.0\n",
"Corresponding pressure drop in N/m2\n",
"167.0\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.7: Page 465"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.7 \"\n",
"\n",
"\n",
"#Temperature of jet in degree C\n",
"T = 20;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.597;\n",
"#Dynamic vismath.cosity in Ns/m2\n",
"mu = 0.000993;\n",
"#Prandtl number\n",
"Pr = 7;\n",
"#Mass flow rate in kg/s\n",
"m = 0.008;\n",
"#Diameter of jet in m\n",
"d = 6/1000.0;\n",
"#Total heat flux in W/m2\n",
"q = 70000.0;\n",
"\n",
"#Reynolds number\n",
"Re = (4*m)/((math.pi*d)*mu);\n",
"\n",
"print \"For r=3mm\"\n",
"#From Eq. (7.45)\n",
"#Heat transfer coefficient in W/m2K\n",
"h = (63*k)/d;\n",
"print \"Surface temperature at r=3mm in degree C is\"\n",
"#Surface temperature in degree C\n",
"Ts = T+q/h\n",
"print round(Ts,1)\n",
"\n",
"print \"For r=12mm\"\n",
"#From Eq. (7.48)\n",
"#Heat transfer coefficient in W/m2K\n",
"h = (35.3*k)/d;\n",
"print \"Surface temperature at r=12mm in degree C is\"\n",
"#Surface temperature in degree C\n",
"Ts = T+q/h\n",
"print round(Ts,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.7 \n",
"For r=3mm\n",
"Surface temperature at r=3mm in degree C is\n",
"31.2\n",
"For r=12mm\n",
"Surface temperature at r=12mm in degree C is\n",
"39.9\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7.8: Page 470"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.8 \"\n",
"\n",
"#Temperature of plate in degree C\n",
"Tplate = 60;\n",
"#Temperature of jet in degree C\n",
"T = 20;\n",
"#Thermal conductivity in W/mK\n",
"k = 0.0265;\n",
"#Dynamic vismath.cosity in Ns/m2\n",
"mu = 0.00001912;\n",
"#Prandtl number\n",
"Pr = 0.71;\n",
"#Density in kg/m3\n",
"rho = 1.092;\n",
"#Mass flow rate in kg/s\n",
"m = 0.008;\n",
"#Width of jet in m\n",
"w = 3/1000.0;\n",
"#Length of jet in m\n",
"l = 20/1000.0;\n",
"#Velocity of jet in m/s\n",
"v = 10.0;\n",
"#Exit distance in m\n",
"z = 0.01;\n",
"#Width given for plate in m\n",
"L = 0.04;\n",
"#Reynolds number\n",
"Re = ((rho*v)*w)/mu;\n",
"\n",
"#From Eq. (7.68) with x\u0005= 0.02 m, z =\u00050.01 m, and w\u0005= 0.003 m\n",
"#Nusselt number\n",
"Nu = 11.2;\n",
"# ! L.33: mtlb(d) can be replaced by d() or d whether d is an M-file or not.\n",
"#Heat transfer coefficient in W/m2K\n",
"h = (Nu*k)/w;\n",
"\n",
"print \"Heat transfer rate from the plate in W is\"\n",
"#Heat transfer rate from the plate in W\n",
"q = ((h*L)*l)*(Tplate-T)\n",
"print round(q,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 7 Example # 7.8 \n",
"Heat transfer rate from the plate in W is\n",
"3.2\n"
]
}
],
"prompt_number": 22
}
],
"metadata": {}
}
]
}PKI
>>+Principles Of Heat Transfer/Chapter_8.ipynb{
"metadata": {
"name": "",
"signature": "sha256:e86ef96e4dcdc6d43089bd3da594607be39672ca44a913568415d68c5c742a86"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8: Heat Exchangers"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex8.1: Page 504"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.1 \"\n",
"\n",
"#Outer dia in m\n",
"d = 0.0254;\n",
"#mass flow rate of hot fluid in kg/s\n",
"mh = 6.93;\n",
"#Specific heat of hot fluid n J/kgK\n",
"ch = 3810;\n",
"#Inlet temperature of hot fluid in degree C\n",
"Thin = 65.6;\n",
"#Outlet temperature of hot fluid in degree C\n",
"Thout = 39.4;\n",
"#mass flow rate of cold fluid in kg/s\n",
"mc = 6.3;\n",
"#Specific heat of cold fluid n J/kgK\n",
"cc = 4187;\n",
"#Inlet temperature of cold fluid in degree C\n",
"Tcin = 10;\n",
"#Overall heat transfer coefficient in W/m2K\n",
"U = 568;\n",
"\n",
"#Umath.sing energy balance, outlet temp. of cold fluid in degree C\n",
"Tcout = Tcin+((mh*ch)*(Thin-Thout))/(mc*cc);\n",
"\n",
"#The rate of heat flow in W\n",
"q = (mh*ch)*(Thin-Thout);\n",
"\n",
"print \"Parallel-flow tube and shell\"\n",
"#From Eq. (8.18) the LMTD for parallel flow\n",
"#Temperature difference at inlet in degree K\n",
"deltaTa = Thin-Tcin;\n",
"#Temperature difference at outlet in degree K\n",
"deltaTb = Thout-Tcout;\n",
"#LMTD in degree K\n",
"LMTD = (deltaTa-deltaTb)/log(deltaTa/deltaTb);\n",
"\n",
"#From Eq. (8.16) \n",
"print \"Heat transfer surface area in m2 is\"\n",
"#Heat transfer surface area in m2\n",
"A = q/(U*LMTD)\n",
"print round(A,2)\n",
"\n",
"print \"Counterflow tube and shell\"\n",
"#LMTD in degree K\n",
"LMTD = 29.4;\n",
"\n",
"print \"Heat transfer surface area in m2 is\"\n",
"#Heat transfer surface area in m2\n",
"A = q/(U*LMTD)\n",
"print round(A,2)\n",
"\n",
"A1 = A;#To be used further as a copy of this area\n",
"\n",
"print \"Counterflow exchanger with 2 shell passes and 72 tube passes\"\n",
"\n",
"#Correction factor found from Fig. 8.15 to the mean temperature for counterflow\n",
"P = (Tcout-Tcin)/(Thin-Tcin);\n",
"#Heat capacity ratio\n",
"Z = (mh*ch)/(mc*cc);\n",
"#From the chart of Fig. 8.15, F\u0003= 0.97\n",
"F = 0.97; #F-Factor\n",
"print \"Heat transfer surface area in m2 is\"\n",
"#Heat transfer surface area in m2 is\n",
"A = A1/F\n",
"print round(A,2)\n",
"\n",
"print \"Cross-flow, with one tube pass and one shell pass, shell-side fluid mixed\"\n",
"#Umath.sing same procedure, we get from charts\n",
"F = 0.88; #F-Factor\n",
"print \"Heat transfer surface area in m2 is\"\n",
"#Heat transfer surface area in m2 is\n",
"A = A1/F\n",
"print round(A,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.1 \n",
"Parallel-flow tube and shell\n",
"Heat transfer surface area in m2 is\n",
"66.51\n",
"Counterflow tube and shell\n",
"Heat transfer surface area in m2 is\n",
"41.43\n",
"Counterflow exchanger with 2 shell passes and 72 tube passes\n",
"Heat transfer surface area in m2 is\n",
"42.71\n",
"Cross-flow, with one tube pass and one shell pass, shell-side fluid mixed\n",
"Heat transfer surface area in m2 is\n",
"47.07\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex8.2: Page 510"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.2 \"\n",
"\n",
"#mass flow rate of hot fluid in kg/s\n",
"mh = 1;\n",
"#Specific heat of hot fluid n J/kgK\n",
"ch = 2100;\n",
"#Inlet temperature of hot fluid in degree C\n",
"Thin = 340;\n",
"#Outlet temperature of hot fluid in degree C\n",
"Thout = 310;\n",
"#Specific heat of cold fluid n J/kgK\n",
"cc = 4187;\n",
"#Inlet temperature of cold fluid in degree C\n",
"Tcin = 290;\n",
"#Outlet temperature of cold fluid in degree C\n",
"Tcout = 300;\n",
"\n",
"#The heat capacity rate of the water in J/kgK is, from Eq. (8.14)\n",
"cc = ch*((Thin-Thout)/(Tcout-Tcin));\n",
"\n",
"#Temperature ratio P and Z is, from Eq. (8.20)\n",
"P = (Thin-Thout)/(Thin-Tcin); # P Temperature ratio\n",
"Z = (Tcout-Tcin)/(Thin-Thout); # Z Temperature ratio\n",
"\n",
"#From Fig. 8.14, F\u00030.94 and the mean temperature difference in degree K is\n",
"#F Value\n",
"F = 0.94;\n",
"#Temperature difference at inlet in degree K\n",
"deltaTa = Thin-Tcout;\n",
"#Temperature difference at outlet in degree K\n",
"deltaTb = Thout-Tcin;\n",
"#LMTD in degree K\n",
"LMTD = (deltaTa-deltaTb)/log(deltaTa/deltaTb);\n",
"#Mean temperature difference in degree K\n",
"deltaTmean = F*LMTD;\n",
"\n",
"#From Eq. (8.17) the overall conductance in W/K is\n",
"UA = ((mh*ch)*(Thin-Thout))/deltaTmean;\n",
"\n",
"#With reference to the new conditions and Eq. 6.62\n",
"#Conductance in W/K\n",
"UA = UA*((3/4.0)**0.8);\n",
"#Number of transfer units(NTU) value\n",
"NTU = UA/(((3/4.0)*mh)*ch);\n",
"#Heat capacity ratio\n",
"K = (((3/4.0)*mh)*ch)/cc;\n",
"\n",
"#From Fig. 8.20 the effectiveness is equal to 0.61\n",
"#Effectiveness\n",
"E = 0.61;\n",
"#New inlet temperaturre of oil in degree K\n",
"Toilin = 370;\n",
"#From eq. 8.22a\n",
"print \"Outlet temperature of oil in degree K\"\n",
"#Outlet temperature of oil in degree K\n",
"Toilout = Toilin-E*(Toilin-Tcin)\n",
"print round(Toilout,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.2 \n",
"Outlet temperature of oil in degree K\n",
"321.2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex8.3: Page 511"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.3 \"\n",
"\n",
"#Airflow rate in kg/s\n",
"mair = 0.75;\n",
"#Inlet temperature of air in degree K\n",
"Tairin = 290;\n",
"#Hot gas flow rate in kg/s\n",
"mgas = 0.6;\n",
"#Inlet temperature of hot gases in degree K\n",
"Tgasin = 1150;\n",
"#wetted perimeter on air side in m\n",
"Pa = 0.703;\n",
"#wetted perimeter on gas side in m\n",
"Pg = 0.416;\n",
"#cross-sectional area of gas passage (per passage) in m2\n",
"Ag = 0.0016;\n",
"#cross-sectional area of air passage (per passage) in m2\n",
"Aa = 0.002275;\n",
"#heat transfer surface area in m2\n",
"A = 2.52;\n",
"\n",
"#Given that unit is of the cross-flow type, with both fluids unmixed.\n",
"\n",
"#length of air duct in m\n",
"La = 0.178;\n",
"#hydraulic diameter of air duct in m\n",
"Dha = (4*Aa)/Pa;\n",
"#length of gas duct in m\n",
"Lg = 0.343;\n",
"#hydraulic diameter of gas duct in m\n",
"Dhg = (4*Ag)/Pg;\n",
"\n",
"#The heat transfer coefficients can be evaluated from Eq. (6.63) for flow\n",
"#in ducts.\n",
"#Heat transfer coefficient for air in W/m2K\n",
"ha = La/Dha;\n",
"#Heat transfer coefficient for gas in W/m2K\n",
"hg = Lg/Dhg;\n",
"\n",
"#Assuming the average air-side bulk temperature to be 573 K and the average\n",
"#gas-side bulk temperature to be 973 K, the properties at those temperatures are, from Appendix 2, Table 28.\n",
"\n",
"#Specific heat of air in J/kgK\n",
"cair = 1047;\n",
"#Thermal conductivity of air in W/mK\n",
"kair = 0.0429;\n",
"#Dynamic vismath.cosity of air in Ns/m2\n",
"muair = 0.0000293;\n",
"#Prandtl number of air\n",
"Prair = 0.71;\n",
"\n",
"#Specific heat of hot gas in J/kgK\n",
"cgas = 1101;\n",
"#Thermal conductivity of hot gas in W/mK\n",
"kgas = 0.0623;\n",
"#Dynamic vismath.cosity of hot gas in Ns/m2\n",
"mugas = 0.00004085;\n",
"#Prandtl number of hot gas\n",
"Prgas = 0.73;\n",
"\n",
"#The mass flow rates per unit area in kg/m2s\n",
"#mass flow rate of air in kg/m2s\n",
"mdotair = mair/(19*Aa);\n",
"#mass flow rate of gas in kg/m2s\n",
"mdotgas = mgas/(18*Ag);\n",
"\n",
"#The Reynolds numbers are\n",
"#Reynolds number for air\n",
"Reair = (mdotair*Dha)/muair;\n",
"#Reynolds number for gas\n",
"Regas = (mdotgas*Dhg)/mugas;\n",
"\n",
"#Umath.sing Eq. (6.63), the average heat transfer coefficients in W/m2K\n",
"hair = (((0.023*kair)*(Reair**0.8))*(Prair**0.4))/Dha;\n",
"\n",
"#Since La/DHa=13.8, we must correct this heat transfer coefficient for\n",
"#entrance effects, per Eq. (6.68). The correction factor is 1.377.\n",
"#Corrected heat transfer coefficient of air in W/m2K\n",
"hair = 1.377*hair;\n",
"\n",
"#Similarly for hot gas\n",
"#Heat transfer coefficient in W/m2K\n",
"hgas = (((0.023*kgas)*(Regas**0.8))*(Prgas**0.4))/Dhg;\n",
"#Correction factor=1.27;\n",
"#Corrected heat transfer coefficient of gas in W/m2K\n",
"hgas = 1.27*hgas;\n",
"\n",
"#Overall conductance in W/K\n",
"UA = 1/(1/(hair*A)+1/(hgas*A));\n",
"\n",
"#The number of transfer units, based on the gas, which has the smaller heat capacity rate\n",
"NTU = UA/(mgas*cgas);\n",
"\n",
"#The heat capacity-rate ratio\n",
"Z = (mgas*cgas)/(mair*cair);\n",
"\n",
"#and from Fig. 8.21, the effectiveness is approximately 0.13.\n",
"#Effectiveness\n",
"E = 0.13;\n",
"\n",
"print \"Gas outlet temperature in degree K\"\n",
"#Gas outlet temperature in degree K\n",
"Tgasout = Tgasin-E*(Tgasin-Tairin)\n",
"print round(Tgasout)\n",
"\n",
"print \"Air outlet temperature in degree K\"\n",
"#Gas outlet temperature in degree K\n",
"Tairout = Tairin+(Z*E)*(Tgasin-Tairin)\n",
"print round(Tairout)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.3 \n",
"Gas outlet temperature in degree K\n",
"1038.0\n",
"Air outlet temperature in degree K\n",
"384.0\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex8.4: Page 514"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.4 \"\n",
"\n",
"#Pressure of steam in inches of Hg\n",
"P = 4;\n",
"#At this pressure, temperture of condenmath.sing steam in degree F\n",
"Thin = 125.4;\n",
"\n",
"#Flow rate of seawater in lb/s\n",
"mw = 25000.0;\n",
"#Specific heat of water in Btu/lb F\n",
"c = 0.95;\n",
"#Inlet and outlet temperature of seawater in degree F\n",
"Tcin = 60.0;\n",
"Tcout = 110.0;\n",
"#Heat transfer coefficient of steam in Btu/h ft2 F\n",
"hsteam = 600.0;\n",
"#Heat transfer coefficient of water in Btu/h ft2 F\n",
"hwater = 300.0;\n",
"#Outer diameter in inches\n",
"OD = 1.125;\n",
"#Inner diameters in inches\n",
"ID = 0.995;\n",
"\n",
"#required effectiveness of the exchanger\n",
"E = (Tcout-Tcin)/(Thin-Tcin);\n",
"\n",
"#For a condenser, Cmin/Cmax=0, and from Fig. 8.20, NTU =\u00031.4.\n",
"NTU = 1.4;\n",
"\n",
"#The fouling factors from Table 8.2 are 0.0005 h ft2\u00b0F/Btu for both sides of the tubes.\n",
"#F-Factor\n",
"F = 0.0005;\n",
"\n",
"#The overall design heat-transfer coefficient in Btu/h ft2 F per unit outside area of tube is, from Eq. (8.6)\n",
"U = 1/(1/hsteam+F+(OD/((2*12)*60))*log(OD/ID)+(F*OD)/ID+OD/(hwater*ID));\n",
"\n",
"#The total area A is 20*pi*D*L, and math.since U*A/Cmin=1.4\n",
"\n",
"print \"The length of the tube in ft is\"\n",
"#The length of the tube in ft\n",
"L = (((1.4*mw)*c)*12)/(((Tcin*math.pi)*OD)*U)\n",
"print round(L,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.4 \n",
"The length of the tube in ft is\n",
"12.4\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex8.5: Page 523"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.5 \"\n",
"\n",
"print \"There is no computations in this example.\"\n",
"print \"It is theoretical\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 8 Example # 8.5 \n",
"There is no computations in this example.\n",
"It is theoretical\n"
]
}
],
"prompt_number": 12
}
],
"metadata": {}
}
]
}PKIW#22+Principles Of Heat Transfer/Chapter_9.ipynb{
"metadata": {
"name": "",
"signature": "sha256:7dfa4acee6b7891eb5781d524c3fac37db5d2c104afc2e1d30e10ae32b280459"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9: Heat Transfer by Radiation"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.1: Page 547"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 1\"\n",
"#Temperature of the tungsten filament in Kelvin\n",
"T=1400;\n",
"\n",
"print \"a)Wavelength at which the monochromatic emissive power of the given tungsten filament is maximum in meters\"\n",
"#Wavelength in m\n",
"lamda_max=2.898e-3/T\n",
"print \"{:.2e}\".format(lamda_max)\n",
"\n",
"print \"b)Monochromatic emissive power at calculated maximum wavelength in W/m**3\"\n",
"#Emissive power in W/m3\n",
"Eb_max=12.87e-6*(T**5)\n",
"print \"{:.2e}\".format(Eb_max)\n",
"#Given wavelength in meters\n",
"lamda=5e-6;\n",
"#Product of wavelength and temperature in m-K\n",
"lamda_T=lamda*T;\n",
"\n",
"print \"c)Monochromatic emissive power at given wavelength in W/m**3\"\n",
"#Emissive power in W/m3\n",
"Eb_lamda=Eb_max*(2.898e-3/(lamda_T))**5*(((math.e**4.965)-1)/((math.e**(0.014388/lamda_T)-1)))\n",
"print \"{:.2e}\".format(Eb_lamda)\n",
"print \"Thus ,Monochromatic emissive power at 5e-6 m wavelength is 25.4% of the Monochromatic emissive power at maximum wavelength\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 1\n",
"a)Wavelength at which the monochromatic emissive power of the given tungsten filament is maximum in meters\n",
"2.07e-06\n",
"b)Monochromatic emissive power at calculated maximum wavelength in W/m**3\n",
"6.92e+10\n",
"c)Monochromatic emissive power at given wavelength in W/m**3\n",
"1.76e+10\n",
"Thus ,Monochromatic emissive power at 5e-6 m wavelength is 25.4% of the Monochromatic emissive power at maximum wavelength\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.2: Page 549"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 2\"\n",
"#Temperature at which sun is radiating as a blackbody in K\n",
"T=5800;\n",
"\n",
"#Lower limit of wavelength for which glass is transparent in microns\n",
"lamda_l=0.35;\n",
"#lower limit of product of wavelength and temperature in micron-K\n",
"lamda_l_T=lamda_l*T;\n",
"#Lower limit of wavelength for which glass is transparent in microns\n",
"lamda_u=2.7;\n",
"#lower limit of product of wavelength and temperature in micron-K\n",
"lamda_u_T=lamda_u*T;\n",
"\n",
"# For lamda_T= 2030, ratio of blackbody emission between zero and lamda_l to the total emission in terms of percentage\n",
"r_l=6.7;\n",
"# For lamda_T= 15660, ratio of blackbody emission between zero and lamda_u to the total emission in terms of percentage\n",
"r_u=97;\n",
"\n",
"#Total radiant energy incident upon the glass from the sun in the wavelength range between lamda_l and lamda_u\n",
"total_rad=r_u-r_l;\n",
"print \"Percentage of solar radiation transmitted through the glass in terms of percentage\"\n",
"rad_trans=total_rad*0.92 #Since it is given that silica glass transmits 92% of the incident radiation\n",
"print round(rad_trans,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 2\n",
"Percentage of solar radiation transmitted through the glass in terms of percentage\n",
"83.1\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.3: Page 552"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 3\"\n",
"#Area of the flat black surface in m**2\n",
"A_1=10e-4;\n",
"#Radiation emitted by the flat black surface in W/m** sr\n",
"I_1=1000;\n",
"# Another surface having same area as A1 is placed relative to A1 such that length of radiation ray connecting dA_1 and dA_2 in meters\n",
"r=0.5;\n",
"#Area in m**2\n",
"A_2=10e-4;\n",
"# Since both areas are quite small, they can be approximated as differential surface areas and the solid angle can be calculated as\n",
"#d_omega21=dA_n2/r**2 where dA_n2 is the projection of A2 in the direction normal to the incident radiation for dA_1,thus\n",
"\n",
"#Angle between the normal n_2 ant the radiation ray connecting dA_1 and dA_2\n",
"theta_2=30;\n",
"\n",
"#Therefore solid angle in sr\n",
"d_omega21=(A_2*math.cos(theta_2*math.pi/180)/(r**2));\n",
"\n",
"print \"Irradiation of A_2 by A_1 in watt\"\n",
"#Irradiation in W\n",
"q_r12= I_1*A_1*math.cos(90*math.pi/180-theta_2*math.pi/180)*d_omega21\n",
"print round(q_r12,5)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 3\n",
"Irradiation of A_2 by A_1 in watt\n",
"0.00173\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.4: Page 559"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 4\"\n",
"#Hemispherical emissivity of an aluminum paint at wavelengths below 3 microns\n",
"epsilon_lamda_1=0.4;\n",
"#Hemispherical emissivity of an aluminum paint at longer wavelengths\n",
"epsilon_lamda_2=0.8;\n",
"#At room temperature 27 degree celcius, product of lamda and T in micron-K\n",
"lamda_T_1=3*(27+273);\n",
"#At elevated temperature 527 degree celcius, product of lamda and T in micron-K\n",
"lamda_T_2=3*(527+273);\n",
"#From Table 9.1\n",
"# For lamda_T_1, ratio of blackbody emission between zero and lamda_l to the total emission\n",
"r_1=0.00016;\n",
"# For lamda_T_2, ratio of blackbody emission between zero and lamda_u to the total emission\n",
"r_2=0.14;\n",
"print \"Thus, the emissivity at 27\u00b0C\"\n",
"#Emissivity\n",
"epsilon=0.8\n",
"print epsilon\n",
"print \"emissivity at 527\u00b0C\"\n",
"#Emissivity at higher temp.\n",
"epsilon=(r_2*epsilon_lamda_1)+(epsilon_lamda_2*0.86)\n",
"print epsilon\n",
"print \"The reason for the difference in the total emissivity is that at the higher temperature,the percentage of the total emissive power in the low-emittance region of the paint is appreciable, while at the lower temperature practically all the radiation is emittedat wavelengths above 3 microns\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 4\n",
"Thus, the emissivity at 27\u00b0C\n",
"0.8\n",
"emissivity at 527\u00b0C\n",
"0.744\n",
"The reason for the difference in the total emissivity is that at the higher temperature,the percentage of the total emissive power in the low-emittance region of the paint is appreciable, while at the lower temperature practically all the radiation is emittedat wavelengths above 3 microns\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.5: Page 560"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 5\"\n",
"#Temperature of the sun in K\n",
"T=5800;\n",
"#For the case of Solar irradiation, value of the product of lamda and T in micron-K\n",
"lamda_T_1=3*T;# value of lamda is taken from Example 9.4\n",
"#From table 9.1\n",
"# For lamda_T_1, ratio of blackbody emission between zero and lamda_l to the total emission\n",
"r_1=0.98;\n",
"#This means that 98% of the solar radiation falls below 3 microns\n",
"#Hemispherical emissivity of an aluminum paint at wavelengths below 3 microns\n",
"epsilon_lamda_1=0.4;\n",
"#Hemispherical emissivity of an aluminum paint at longer wavelengths\n",
"epsilon_lamda_2=0.8;\n",
"print \"Effective absorptivity for first case\"\n",
"#Effective absorptivity\n",
"alpha_1=(r_1*epsilon_lamda_1)+(epsilon_lamda_2*0.02)\n",
"print round(alpha_1,3)\n",
"#For the case second with source at 800 K, value of the product of lamda and T in micron-K\n",
"lamda_T_2=3*800;\n",
"# For lamda_T_2, ratio of blackbody emission between zero and lamda_l to the total emission\n",
"r_2=0.14;\n",
"print \"Effective absorptivity for second case\"\n",
"#Effective absorptivity\n",
"alpha_2=(r_2*epsilon_lamda_1)+(epsilon_lamda_2*0.86)\n",
"print round(alpha_2,3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 5\n",
"Effective absorptivity for first case\n",
"0.408\n",
"Effective absorptivity for second case\n",
"0.744\n"
]
}
],
"prompt_number": 26
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.6: Page 562"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 6\"\n",
"#Stefan\u2013Boltzmann constant in W/m**2 K**4\n",
"sigma=5.67e-8;\n",
"#Temperature of the painted surface in K\n",
"T=1000;\n",
"#Temperature of the sun in K\n",
"T_s=5800;\n",
"#Given, below 2 microns the emissivity of the surface is 0.3,so\n",
"lamda_1=2; #wavelength in microns\n",
"epsilon_1=0.3; #emissivity\n",
"\n",
"#Given, between 2 and 4 microns emmisivity is 0.9,so\n",
"lamda_2=4;#wavelength in microns\n",
"epsilon_2=0.9;#emissivity\n",
"\n",
"#Given, above 4 microns emmisivity is 0.5, so\n",
"epsilon_3=0.5;#emissivity\n",
"\n",
"#value of the product of lamda_1 and T in micron-K\n",
"lamda_1_T=2e-3*T;\n",
"\n",
"#From table 9.1\n",
"# For lamda_1_T, ratio of blackbody emission between zero and lamda_l to the total emission\n",
"r_1=0.0667; #1st ratio\n",
"\n",
"#value of the product of lamda_2 and T in micron-K\n",
"lamda_2_T=2e-3*T;\n",
"#From table 9.1\n",
"# For lamda_2_T, ratio of blackbody emission between zero and lamda_l to the total emission\n",
"r_2=0.4809; #2nd ratio\n",
"\n",
"print \"a)Effective emissivity over the entire spectrum\"\n",
"#Effective emissivity\n",
"epsilon_bar=epsilon_1*r_1+epsilon_2*(r_2-r_1)+epsilon_3*(1-r_2)\n",
"print round(epsilon_bar,4)\n",
"\n",
"print \"b)Emissive power in W/m**2\"\n",
"#Emissive power in W/m**2\n",
"E=epsilon_bar*sigma*T**4\n",
"print \"{:.1e}\".format(E)\n",
"\n",
"#value of the product of lamda_1 and T_s in micron-K\n",
"lamda_1_T_s=2e-3*T_s;\n",
"#From table 9.1\n",
"# For lamda_1_T_s, ratio of blackbody emission between zero and lamda_l to the total emission\n",
"r_1_s=0.941;\n",
"#value of the product of lamda_2 and T_s in micron-K\n",
"lamda_2_T_s=2e-3*T_s;\n",
"#From table 9.1\n",
"# For lamda_2_T_s, ratio of blackbody emission between zero and lamda_l to the total emission\n",
"r_2_s=0.99;\n",
"print \"c) Average solar absorptivity\"\n",
"#Average solar absorptivity\n",
"alpha_s=epsilon_1*r_1_s+epsilon_2*(r_2_s-r_1_s)+epsilon_3*(1-r_2_s)\n",
"print round(alpha_s,3)\n",
"\n",
"# the answer in textbook is slightly different due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 6\n",
"a)Effective emissivity over the entire spectrum\n",
"0.6523\n",
"b)Emissive power in W/m**2\n",
"3.7e+04\n",
"c) Average solar absorptivity\n",
"0.331\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.7: Page 569"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 7\"\n",
"#Temperature of the oxidised surface in Kelvin\n",
"T=1800;\n",
"#Area of the oxidised surface in m**2\n",
"A=5e-3;\n",
"#Stefan\u2013Boltzmann constant in W/m**2 K**4\n",
"sigma=5.67e-8;\n",
"print \"a)Emissivity perpendicular to the surface\"\n",
"#Emissivity\n",
"epsilon_zero=0.70*math.cos(0)\n",
"print round(epsilon_zero,3)\n",
"print \"b)Hemispherical emissivity\"\n",
"#Hemispherical emissivity\n",
"epsilon_bar=((-1.4)/3)*((math.cos(90*math.pi/180))**3-(math.cos(0))**3)\n",
"print round(epsilon_bar,3)\n",
"print \"c)Emissive Power in Watt\"\n",
"#Emissive Power in W\n",
"E=epsilon_bar*A*sigma*T**4\n",
"print round(E,3)\n",
"\n",
"# the answer in textbook is slightly different due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 7\n",
"a)Emissivity perpendicular to the surface\n",
"0.7\n",
"b)Hemispherical emissivity\n",
"0.467\n",
"c)Emissive Power in Watt\n",
"1388.832\n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.8: Page 574"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 8\"\n",
"\n",
"# Theoretical Proof\n",
"print \"The given example is theoretical and does not involve any numerical computation\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 8\n",
"The given example is theoretical and does not involve any numerical computation\n"
]
}
],
"prompt_number": 34
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.9: Page 578"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 9\"\n",
"#Window arrangement consists of a long opening with dimensions\n",
"#Height in meters\n",
"h=1;\n",
"#Length in meters\n",
"l=5;\n",
"#width of table in meters\n",
"w=2;\n",
"#Assuming that window and table are sufficiently long and applying crossed string method, we get\n",
"#Distance ab in m\n",
"ab=0;\n",
"#Distance cb in m\n",
"cb=w;\n",
"#Distance ad in m\n",
"ad=h;\n",
"#Distance cd in m\n",
"cd=math.sqrt(l);\n",
"\n",
"print \"Shape factor between the window and the table\"\n",
"#Shape factor between the window and the table\n",
"F_12=0.5*(ad+cb-cd)\n",
"print round(F_12,4)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 9\n",
"Shape factor between the window and the table\n",
"0.382\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.10: Page 580"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 10\"\n",
"#Window area in ft**2\n",
"A1=6*20;\n",
"#Second area in ft**2\n",
"A2=4*20;\n",
"#Assuming A5=A1+A2\n",
"#Area in ft**2\n",
"A5=A1+A2;\n",
"\n",
"#From Fig. 9.27\n",
"#Shape Factors required\n",
"F56=0.19;\n",
"F26=0.32;\n",
"F53=0.08;\n",
"F23=0.19;\n",
"\n",
"print \"Shape factor\"\n",
"#Shape factor\n",
"F14=(A5*F56-A2*F26-A5*F53+A2*F23)/A1\n",
"print round(F14,3)\n",
"\n",
"print \"Thus,only about 10% of the light pasmath.sing through the window will impinge on the floor area A4\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 9, Example 10\n",
"Shape factor\n",
"0.097\n",
"Thus,only about 10% of the light pasmath.sing through the window will impinge on the floor area A4\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.11: Page 590"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.11 \"\n",
"\n",
"#Absolute boiling temperature of liquid oxygen in R\n",
"T1 = 460-297.0;\n",
"#Absolute temperature of sphere in R\n",
"T2 = 460+30;\n",
"#Diameter of inner sphere in ft\n",
"D1 = 1;\n",
"#Area of inner sphere in ft2\n",
"A1 = (math.pi*D1)*D1;\n",
"#Diameter of outer sphere in ft\n",
"D2 = 1.5;\n",
"#Area of outer sphere in ft2\n",
"A2 = (math.pi*D2)*D2;\n",
"#Stefans constant\n",
"sigma = 0.1714;\n",
"#Emissivity of Aluminium\n",
"epsilon1 = 0.03;#Sphere1\n",
"epsilon2 = 0.03;#Sphere2\n",
"\n",
"#Umath.sing Eq. 9.74\n",
"print \"Rate of heat flow by radiation to the oxygen in Btu/h is\"\n",
"#Rate of heat flow by radiation to the oxygen in Btu/h\n",
"q = ((A1*sigma)*((T1/100.0)**4-(T2/100.0)**4))/(1/epsilon1+(A1/A2)*((1-epsilon2)/epsilon2))\n",
"print round(q,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.11 \n",
"Rate of heat flow by radiation to the oxygen in Btu/h is\n",
"-6.4\n"
]
}
],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.12: Page 594"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.12 \"\n",
"\n",
"\n",
"# As the example involves no calculations and the code for matlab is already given in the textbook thus following the guidelines this exapmle is to be skipped\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.12 \n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.13: Page 597"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.13 \"\n",
"\n",
"\n",
"# As the example involves no calculations and the code for matlab is already given in the textbook thus following the guidelines this exapmle is to be skipped\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.13 \n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.14: Page 598"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.14 \"\n",
"\n",
"#Absolute temperature of first plate in degree R\n",
"Ta = 2040+460.0;\n",
"#Absolute temperature of second plate in degree R\n",
"Tb = 540+460.0;\n",
"#Stefans constant\n",
"sigma = 0.1718;\n",
"\n",
"#For first radiation band, heat transfer is calculated\n",
"#Emissivity of A\n",
"epsilonA = 0.1;\n",
"#Emissivity of B\n",
"epsilonB = 0.9;\n",
"#Shape factor\n",
"Fab = 1/(1/epsilonA+1/epsilonB-1);\n",
"#The percentage of the total radiation within a given band is obtained from Table 9.1.\n",
"#Coefficients of T**4\n",
"A = 0.375;\n",
"#Coefficients of T**4\n",
"B = 0.004;\n",
"\n",
"#Rate of heat transfer in first band in Btu/h ft2\n",
"q1 = (Fab*sigma)*(A*((Ta/100.0)**4)-B*((Tb/100.0)**4));\n",
"\n",
"#Similarly for other two bands, heat transfer in Btu/h ft2\n",
"q2 = 23000;\n",
"#heat transfer in Btu/h ft2\n",
"q3 = 1240;\n",
"\n",
"print \"Total rate of radiation heat transfer in Btu/h ft2\"\n",
"#heat transfer in Btu/h ft2\n",
"q = q1+q2+q3\n",
"print round(q)\n",
" # The answer is slightly different in textbook due to approximation\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.14 \n",
"Total rate of radiation heat transfer in Btu/h ft2\n",
"26728.0\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.15: Page 608"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.15 \"\n",
"\n",
"#Temperature in degree K\n",
"T = 800;\n",
"#Diameter of sphere in m\n",
"D = 0.4;\n",
"#Partial pressure of nitrogen in atm\n",
"PN2 = 1;\n",
"#Partial pressure of H2O in atm\n",
"PH2O = 0.4;\n",
"#Partial pressure of CO2 in atm\n",
"PCO2 = 0.6;\n",
"\n",
"#The mean beam length for a spherical mass of gas is obtained from Table 9.7\n",
"#Beam length in m\n",
"L = (2/3)*D;\n",
"\n",
"#The emissivities are given in Figs. 9.46 and 9.47\n",
"#Emissivity of H2O\n",
"epsilonH2O = 0.15;\n",
"#Emissivity of CO2\n",
"epsilonCO2 = 0.125;\n",
"\n",
"#N2 does not radiate appreciably at 800 K, but math.since the total gas pressure\n",
"#is 2 atm, we must correct the 1-atm values for epsilon.\n",
"#From Figs. 9.48 and 9.49 the pressure correction factors are\n",
"#Pressure correction factor for H2O\n",
"CH2O = 1.62;\n",
"#Pressure correction factor for CO2\n",
"CCO2 = 1.12;\n",
"\n",
"#From fig. 9.50\n",
"#Chnage in emissivity\n",
"deltaEpsilon = 0.014;\n",
"\n",
"#Finally, the emissivity of the mixture can be obtained from Eq. (9.114):\n",
"print \"Emissivity of the mixture is\"\n",
"#Emissivity of the mixture\n",
"epsilonMix = CH2O*epsilonH2O+CCO2*epsilonCO2-deltaEpsilon\n",
"print round(epsilonMix,3)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.15 \n",
"Emissivity of the mixture is\n",
"0.369\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.16: Page 609"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.16 \"\n",
"\n",
"#Total pressure in atm\n",
"Pt = 2;\n",
"#Temperature in degree K\n",
"TH2O = 500.0;\n",
"#Mean beam length in m\n",
"L = 0.75;\n",
"#Partial pressure of water vapor in atm\n",
"PH2O = 0.4;\n",
"#Source temperature in degree K\n",
"Ts = 1000.0;\n",
"\n",
"#Since nitrogen is transparent, the absorption in the mixture is due to the water vapor alone.\n",
"\n",
"#Parameters required\n",
"#A Parameter in atm-m\n",
"A = PH2O*L;\n",
"#B Parameter in atm\n",
"B = (Pt+PH2O)/2.0;\n",
"\n",
"#From Figs. 9.46 and 9.48 we find\n",
"#For water, C factor in SI units\n",
"CH2O = 1.4;\n",
"#Emissivity of water\n",
"epsilonH2O = 0.29;\n",
"\n",
"\n",
"#From Eq. (9.115) the absorptivity of H2O is\n",
"print \"Absorptivity of H2O is\"\n",
"alphaH2O = (CH2O*epsilonH2O)*((TH2O/Ts)**0.45)\n",
"print round(alphaH2O,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.16 \n",
"Absorptivity of H2O is\n",
"0.3\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.17: Page 609"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.17 \"\n",
"\n",
"#Temperature of flue gas in degree F\n",
"Tgas = 2000.0;\n",
"#Inner-wall surface temperature in degree F\n",
"Tsurface = 1850.0;\n",
"#Partial pressure of water in atm\n",
"p = 0.05;\n",
"#Convection heat transfer coefficient in Btu/h ft2 F\n",
"h = 1.0;\n",
"#Length of square duct in ft\n",
"L = 2.0;\n",
"#Volume in ft3\n",
"V = L*L;\n",
"#Surface area in ft2\n",
"A = 4*L;\n",
"\n",
"#The rate of heat flow from the gas to the wall by convection per unit\n",
"#length in Btu/h ft is\n",
"qc = (h*A)*(Tgas-Tsurface);\n",
"\n",
"#Effective beam length in m\n",
"L = ((0.3058*3.4)*V)/A;\n",
"\n",
"#Product of partial pressure and L\n",
"k = p*L;\n",
"\n",
"#From Fig. 9.46, for pL=0.026 and T=2000F, we find\n",
"\n",
"#Emissivity\n",
"epsilon = 0.035;\n",
"#Absorptivity\n",
"alpha = 0.039;\n",
"#stefans constant\n",
"sigma = 0.171;\n",
"\n",
"#Assuming that the brick surface is black, the net rate of heat flow from the gas to the wall by radiation is, according to Eq. (9.117)\n",
"qr = (sigma*A)*(epsilon*(((Tgas+460)/100.0)**4)-alpha*(((Tsurface+460.0)/100)**4));#Btu/h\n",
"\n",
"print \"Total heat flow from the gas to the duct in Btu/h\"\n",
"#Total heat flow from the gas to the duct in Btu/h\n",
"q = qc+qr\n",
"print round(q,2)\n",
" # The answer is slightly different in textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.17 \n",
"Total heat flow from the gas to the duct in Btu/h\n",
"3543.12\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.18: Page 611"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.18 \"\n",
"\n",
"#Emissivity\n",
"epsilon = 0.8;\n",
"#Stefan's constant\n",
"sigma = 0.1714;\n",
"#Temperature of walls in degree F\n",
"Twall = 440;\n",
"#Temperature indicated ny thermocouple in degree F\n",
"Tt = 940;\n",
"#Heat transfer coefficient in Btu/h ft2 F\n",
"h = 25;\n",
"\n",
"#The temperature of the thermocouple is below the gas temperature because the couple loses heat by radiation to the wall.\n",
"\n",
"#Under steady-state conditions the rate of heat flow by radiation from the thermocouple junction to the wall equals the rate of heat flow by convection from the gas to the couple.\n",
"\n",
"#Umath.sing this heat balance, q/A in Btu/h ft2\n",
"q = (epsilon*sigma)*(((Tt+460)/100)**4-((Twall+460)/100)**4);\n",
"\n",
"print \"True gas temperature in degree F\"\n",
"#True gas temperature in degree F\n",
"Tg = Tt+q/h\n",
"\n",
"print round(Tg)\n",
" # The answer is slightly different in textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.18 \n",
"True gas temperature in degree F\n",
"1115.0\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.19: Page 612"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.19 \"\n",
"\n",
"#Emissivity of thermocouple\n",
"epsilonT = 0.8;\n",
"#Emissivity of shield\n",
"epsilonS = 0.3;\n",
"#Stefan''s constant\n",
"sigma = 0.1714;\n",
"#Temperature of walls in degree F\n",
"Tw = 440;\n",
"#Temperature indicated ny thermocouple in degree F\n",
"Tt = 940.0;\n",
"#Heat transfer coefficient of thermocouple in Btu/h ft2 F\n",
"hrt = 25.0;\n",
"#Heat transfer coefficient of shield in Btu/h ft2 F\n",
"hrs = 20.0;\n",
"\n",
"#Area for thermocouple be unity ft2\n",
"At = 1.0;\n",
"#Corresponding area of shield in ft2\n",
"As = 4.0;#Inside dia=4*dia of thermocouple\n",
"\n",
"#From Eq. (9.76)\n",
"#View factors Fts and Fsw\n",
"Fts = 1/((1-epsilonT)/(At*epsilonT)+1/At+(1-epsilonS)/(As*epsilonS));\n",
"Fsw = As*epsilonS;\n",
"\n",
"#Assuming a shield temperature of 900\u00b0F, we have, according to Eq. (9.118)\n",
"#Temperature in degree F\n",
"Ts = 923;\n",
"\n",
"#Coeffcients for heat balance are as following\n",
"#A parameter Btu/h-F\n",
"A = 9.85;#A=hrt*At\n",
"#B parameter Btu/h-F\n",
"B = 13.7;#B=hrs*As\n",
"\n",
"#Umath.sing heat balance\n",
"print \"Correct temperature of gas in degree F\"\n",
"#Correct temperature of gas in degree F\n",
"Tg = Ts+(B*(Ts-Tw)-A*(Tt-Ts))/((hrs*2)*As)\n",
"print round(Tg,2)\n",
" # The answer is slightly different in textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 9 Example # 9.19 \n",
"Correct temperature of gas in degree F\n",
"963.31\n"
]
}
],
"prompt_number": 2
}
],
"metadata": {}
}
]
}PKIwLL,Principles Of Heat Transfer/Chapter_10.ipynb{
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"signature": "sha256:f2f1789d69a6627f52d1a0482ee686df23ffc5c14dd52e16a67788fbe084f6c9"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 10: Heat Transfer With Phase Change"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.1: Page 643"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 1\"\n",
"#Surface temperature of polished stainless steel surface in degree celcius\n",
"T_s=106.0;\n",
"#Boiling point of water under at atmospheric pressure in degree celcius\n",
"T_b=100.0;\n",
"#Value of empirical constant\n",
"C_sf=0.0132;\n",
"#latent heat of vaporization in J/kg\n",
"h_fg=2.25e6;\n",
"#gravitational acceleration in m/s**2\n",
"g=9.81;\n",
"#Value of proportionality factor in British Gravitational system\n",
"g_c=1;\n",
"#density of saturated liquid in kg/m**3\n",
"rho_l=962.0;\n",
"#density of saturated vapor in kg/m**3\n",
"rho_v=0.60;\n",
"#specific heat of saturated liquid in J/kg K\n",
"c_l=4211.0;\n",
"#prandtl number of saturated liquid\n",
"Pr_l=1.75;\n",
"#surface tension of the liquid-to-vapor interface in N/m\n",
"sigma=58.8e-3;\n",
"#\u0004 vismath.cosity of the liquid in kg/ms\n",
"mu_l=2.77e-4;\n",
"#Excess temperature in degree Celcius\n",
"delta_Tx= T_s-T_b;\n",
"\n",
"print \"Heat flux from the surface to the water in W/m**2\"\n",
"#Heat flux in W./m2\n",
"q=(c_l*delta_Tx/(C_sf*h_fg*Pr_l))**3*mu_l*h_fg*math.sqrt((g*(rho_l-rho_v))/(g_c*sigma))\n",
"print round(q,1)\n",
"\n",
"print \"Critical heat flux in W/m**2\"\n",
"#Heat flux in W./m2\n",
"q_maxZ=(math.pi/24.0)*math.sqrt(rho_v)*h_fg*(sigma*g*(rho_l-rho_v)*g_c)**0.25\n",
"\n",
"print \"At 6\u00b0C excess temperature the heat flux is less than the critical value; therefore nucleate pool boiling exists\"\n",
"print \"For the Teflon-coated stainless steel surface, heat flux in W/m**2\"\n",
"#Heat flux in W./m2\n",
"q=29669*(C_sf/0.0058)**3\n",
"print round(q,2)\n",
"print \"Thus for Teflon-coated stainless steel surface there is a remarkable increase in heat flux; however, it is still below the critical value.\"\n",
"\n",
"# the answers in the textbook is slightly different in the textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 1\n",
"Heat flux from the surface to the water in W/m**2\n",
"28673.9\n",
"Critical heat flux in W/m**2\n",
"At 6\u00b0C excess temperature the heat flux is less than the critical value; therefore nucleate pool boiling exists\n",
"For the Teflon-coated stainless steel surface, heat flux in W/m**2\n",
"349736.31\n",
"Thus for Teflon-coated stainless steel surface there is a remarkable increase in heat flux; however, it is still below the critical value.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.2: Page 646"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 2\"\n",
"#density of saturated liquid in kg/m**3\n",
"rho_l=962;\n",
"#gravitational acceleration in m/s**2\n",
"g=9.8;\n",
"#latent heat of vaporization in J/kg\n",
"h_fg=2250000;\n",
"#density of saturated vapor in kg/m**3\n",
"rho_v=0.60;\n",
"#Surface temperature of polished stainless steel surface in degree celcius\n",
"T_s=400;\n",
"#Value of proportionality factor in British Gravitational system\n",
"g_c=1;\n",
"#Boiling point of water under at atmospheric pressure in degree celcius\n",
"T_b=100;\n",
"#surface tension of the liquid-to-vapor interface in N/m\n",
"sigma=58.8e-3;\n",
"#Excess temperature in degree Celcius\n",
"delta_Tx= T_s-T_b;\n",
"#Wavelength in m from eq. 10.7\n",
"lamda=2*math.pi*math.sqrt(g_c*sigma/(g*(rho_l-rho_v)));\n",
"#Thermal conductivity in W/mK\n",
"k_c=0.0249;\n",
"#Absolute vismath.cosity in Ns/m**2\n",
"mu_c=12.1e-6;\n",
"#Specific heat in J/kg K\n",
"c_pc=2034;\n",
"#Heat transfer coefficient due to conduction alone in W/m**2 K\n",
"h_c=(0.59)*(((g*(rho_l-rho_v)*rho_v*(k_c**3)*(h_fg+(0.68*c_pc*delta_Tx)))/(lamda*mu_c*delta_Tx))**0.25); # math.expression obtained assuming diameter D tending to infinity\n",
"#Emissivity\n",
"epsilon_s= 0.05; #math.since surface is polished and hence heat transfer coefficient due to radiation is negligible\n",
"print \"Heat flux in W/m**2\"\n",
"#Heat flux in W/m**2\n",
"q= h_c*delta_Tx\n",
"print round(q,1)\n",
"# the answers in the textbook is slightly different in the textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 2\n",
"Heat flux in W/m**2\n",
"44739.1\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.3: Page 655"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 3\"\n",
"#Flow rate of n-butyl alcohol in kg/hr\n",
"m=161;\n",
"#Internal diameter of copper tube in meters\n",
"D=0.01;\n",
"#Tube wall temperature in degree C\n",
"T=140;\n",
"#surface tension in N/m\n",
"sigma=0.0183;\n",
"#Heat of vaporization in J/kg\n",
"h_fg=591500;\n",
"#atmospheric pressure boiling point in degree C\n",
"T_sat=117.5;\n",
"# saturation pressure corresponding to a saturation temperature of 140\u00b0C in atm\n",
"P_sat=2;\n",
"#Density of vapor in kg/m**3\n",
"rho_v=2.3;\n",
"#Vismath.cosity of vapor in kg/m s\n",
"mu_v=.0143e-3;\n",
"#Property values for n-butyl alcohol are taken from Appendix 2, Table 19\n",
"#Density in kg/m**3\n",
"rho_l=737;\n",
"#Absolute vismath.cosity in Ns/m**2\n",
"mu_l=0.39e-3;\n",
"#Specific heat in J/kg K\n",
"c_l=3429.0;\n",
"#Prandtl number\n",
"Pr_l=8.2;\n",
"#Thermal conductivity in W/m K\n",
"k_l=0.13;\n",
"#Empirical constant\n",
"C_sf=0.00305;# Value taken from table 10.1\n",
"#Mass velocity in kg/m**2 s\n",
"G=(m/3600.0)*(4/(math.pi*0.01**2));\n",
"print \"Mass velocity in kg/m**2 is \",round(G,2)\n",
"#Reynolds number for liquid flow\n",
"Re_D=(G*D)/mu_l;\n",
"print \"Reynolds number for liquid flow is\",round(Re_D,2)\n",
"#The contribution to the heat transfer coefficient due to the two-phase annular flow is [(0.023)*(14590)**0.8*(8.2)**0.4*16.3*(1-x)**0.8*F]\n",
"#Since the vapor pressure changes by 1 atm over the temperature range from saturation temperature to 140\u00b0C,so saturation pressure in N/m**2\n",
"delta_p_sat=101300;\n",
"#Therefore the contribution to the heat transfer coefficient from nucleate boiling is\n",
"#h_b= 0.00122*[(0.163**0.79*3429**0.45*737**0.49*1**0.25)/(0.0183**0.5*0.39e-3**0.29*591300**0.24*2.3**0.24)]*(140-117.5)**0.24*(101300)**0.75*S\n",
"#or h_b= 8393S\n",
"#Now 1/Xtt will be calculated by\n",
"#1/Xtt=12.86*(x/(1-x))**0.9\n",
"#Now a table is prepared showing stepwise calculations that track the increase in quality, from x=0 to x=0.5,assuming that the steps delta \u0002x are small enough that the heat flux and other parameters are reasonably constant in that step\n",
"print \"The tube length required to reach 50% quality is 1.35 m\"\n",
"\n",
"# as the answer is found by hit and trial thus answer is printed through table\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 3\n",
"Mass velocity in kg/m**2 is 569.42\n",
"Reynolds number for liquid flow is 14600.54\n",
"The tube length required to reach 50% quality is 1.35 m\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.4: Page 666"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 4\"\n",
"#Outer diameter of the tube in meters\n",
"D=0.013;\n",
"#Acceleration due to gravity in m/s**2\n",
"g=9.81;\n",
"#Length of the tube in meters\n",
"L=1.5;\n",
"#Temperature of saturated vapour in Kelvin\n",
"T_sv=349.0;\n",
"#Average tube wall temperature in Kelvin\n",
"T_s=325;\n",
"#Average temperature of the condensate film in degree K\n",
"Tf=(T_sv+T_s)/2.0;\n",
"#Thermal conductivity of liquid in W/m-K\n",
"k_l=0.661;\n",
"#Vismath.cosity of liquid in N s/m**2\n",
"mu_l=4.48e-4;\n",
"#Dendity of liquid in kg/m**3\n",
"rho_l=980.9;\n",
"#Specific heat of liquid in J/kg K\n",
"c_pl=4184.0;\n",
"#Latent heat of condensation in J/kg\n",
"h_fg=2.349e6;\n",
"#Density of vapor in kg/m**3\n",
"rho_v=0.25;\n",
"#Modified latent heat of condensation in J/kg\n",
"h_fg_dash=h_fg+(3/8.0)*c_pl*(T_sv-T_s);\n",
"\n",
"print \"Heat transfer coefficient for tube in horizontal position in W/m**2 K\"\n",
"#Heat transfer coefficient in W/m2K\n",
"h_c_bar=0.725*(((rho_l*(rho_l-rho_v)*g*h_fg_dash*k_l**3)/(D*mu_l*(T_sv-T_s)))**0.25)\n",
"print round(h_c_bar,2)\n",
"print \"Heat transfer coefficient for tube in vertical position in W/m**2 K\"\n",
"##Heat transfer coefficient in W/m2K\n",
"h_c_bar=0.943*(((rho_l*(rho_l-rho_v)*g*h_fg_dash*k_l**3)/(mu_l*(T_sv-T_s)))**0.25)\n",
"print round(h_c_bar,2)\n",
"\n",
"# the answer is incorrect in the textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 4\n",
"Heat transfer coefficient for tube in horizontal position in W/m**2 K\n",
"10648.3\n",
"Heat transfer coefficient for tube in vertical position in W/m**2 K\n",
"4676.7\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.5: Page 667"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 5\"\n",
"#Acceleration due to gravity in m/s**2\n",
"g=9.81;\n",
"#Length of the tube in meters\n",
"L=1.5;\n",
"#Temperature of saturated vapour in Kelvin\n",
"T_sv=349.0;\n",
"#Average tube wall temperature in Kelvin\n",
"T_s=325.0;\n",
"#Average temperature of the condensate film in Kelvin\n",
"Tf=(T_sv+T_s)/2;\n",
"#Thermal conductivity of liquid in W/m-K\n",
"k_l=0.661;\n",
"#Vismath.cosity of liquid in N s/m**2\n",
"mu_l=4.48e-4;\n",
"#Dendity of liquid in kg/m**3\n",
"rho_l=980.9;\n",
"#Specific heat of liquid in J/kg K\n",
"c_pl=4184.0;\n",
"#Latent heat of condensation in J/kg\n",
"h_fg=2.349e6;\n",
"#Density of vapor in kg/m**3\n",
"rho_v=0.25;\n",
"#Modified latent heat of condensation in J/kg\n",
"h_fg_dash=h_fg+(3/8.0)*c_pl*(T_sv-T_s);\n",
"\n",
"print \"Reynolds number at the lower edge\"\n",
"#Reynolds number\n",
"Re=(4/3.0)*(((4*k_l*L*(T_sv-T_s)*rho_l**(2/3.0)*g**(1/3.0))/(mu_l**(5/3.0)*h_fg_dash))**0.75)\n",
"print round(Re,2)\n",
"print \"Since the Reynolds number at the lower edge of the tube is below 2000, the flow of the condensate is laminar\"\n",
"\n",
"# the answers in the textbook is slightly different in the textbook due to approximation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 5\n",
"Reynolds number at the lower edge\n",
"569.05\n",
"Since the Reynolds number at the lower edge of the tube is below 2000, the flow of the condensate is laminar\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.6: Page 682"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 6\"\n",
"#Length of Heat pipe in meters\n",
"L_eff=0.30;\n",
"#Temperature of the heat pipe in degree celcius\n",
"T=100.0;\n",
"#Diameter of the heat pipe in meters\n",
"D=1e-2;\n",
"#Density of water at 100 degree celcius in k/m**3\n",
"rho=958.0;\n",
"#Vismath.cosity of water in N s/m**2\n",
"mu=279.0e-6;\n",
"#surface tension of the liquid-to-vapor interface in N/m\n",
"sigma=58.9e-3;\n",
"#latent heat of vaporization in J/kg\n",
"h_fg=2.26e6;\n",
"#Inclination angle in degree\n",
"theta=30;\n",
"#Acceleration due to gravity in meter/sec**2\n",
"g=9.81;\n",
"#Wire diameter for wick in metres\n",
"d=0.0045e-2;\n",
"#So thickness of four layers of wire mesh\n",
"t=4.0*d;\n",
"#Area of the wick in m**2\n",
"Aw=math.pi*D*t;\n",
"#For phosphorus-bronze,heat pipe wick pore size in meters\n",
"r=0.002e-2;\n",
"#For phosphorus-bronze,heat pipe wick permeability in m**2\n",
"K=0.3e-10;\n",
"print \"Maximum liquid flow rate in kg/sec\"\n",
"#flow rate in kg/sec\n",
"m_max=((2*sigma/r)-rho*g*L_eff*0.5)*((rho*Aw*K)/(mu*L_eff))\n",
"print round(m_max,6)\n",
"print \"Maximum heat transport capability in Watt\"\n",
"#heat transport capability in W\n",
"q_max=m_max*h_fg\n",
"print round(q_max,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 6\n",
"Maximum liquid flow rate in kg/sec\n",
"9e-06\n",
"Maximum heat transport capability in Watt\n",
"19.7\n"
]
}
],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10.7: Page 686"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"print \"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 7\"\n",
"#Temperature of the brine spray used for internal refrigeration in degree celcius\n",
"T_inf=-11.0;\n",
"#Required thickness of ice layer in meters\n",
"epsilon= 0.0025;\n",
"#Water-liquid temperature in degree celcius\n",
"T1=4.4;\n",
"#Liquid-surface conductance in W/m**2 K\n",
"h_epsilon=57.0;\n",
"#Conductance between brine and ice(including metal wall) in W/m**2 K\n",
"h_not=570.0;\n",
"#Latent heat of fusion for ice in J/Kg\n",
"Lf=333700.0;\n",
"#Density for ice in Kg/m**3\n",
"rho=918.0;\n",
"#Thermal conductivity for ice in W/m K\n",
"k=2.32;\n",
"#Freezing point temperature in degree K\n",
"Tfr=0;\n",
"#Dimensionless R, T, epsilon and t are as follows\n",
"#R plus parameter \n",
"R_plus= h_epsilon/h_not;\n",
"#T plus parameter\n",
"T_plus= (T1-Tfr)/(Tfr-T_inf);\n",
"#Epsilon plus parameter\n",
"Epsilon_plus= h_not*epsilon/k;\n",
"#t plus parameter\n",
"t_plus=(Epsilon_plus/(R_plus*T_plus))-((1/(R_plus*T_plus)**2)*math.log(1+(R_plus*T_plus*Epsilon_plus/(1+R_plus*T_plus))))\n",
"\n",
"print \"Time taken for 0.25cm thick ice layer deposition in sec\"\n",
"#time in seconds\n",
"t=t_plus*rho*Lf*k/((h_not)**2*(Tfr-T_inf))\n",
"print round(t,1)\n",
"# the answers in the textbook is incorrect"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Principles of Heat transfer, Seventh Edition, Frank Kreith, Raj M Manglik and Mark S Bohn, Chapter 10, Example 7\n",
"Time taken for 0.25cm thick ice layer deposition in sec\n",
"151.6\n"
]
}
],
"prompt_number": 37
}
],
"metadata": {}
}
]
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{