{
"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": {}
}
]
}