{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2: Heat conduction concepts, thermal resistance, and the overall heat transfer coefficient "
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.3, Page number: 64"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#Variables\n",
"l=1; # tube length, m\n",
"m=0.01; # mass fraction\n",
"D12=2.84*10**-5; # diffusivity, m**2/s\n",
"a=1.18; # density, kg/m**3\n",
"\n",
"#Calculations\n",
"J=a*D12*m/l;\t\t\t\t\t\t\t\t #steady state flux of water from one side to the other,kg/(m**2*s)\n",
"\n",
"#Results\n",
"print \"Steady flux of water is\",J,\"kg/(m^2*s)\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Steady flux of water is 3.3512e-07 kg/(m^2*s)\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.7, Page number: 72"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variables\n",
"h=20; #convective heat transfer coefficient, W/(m**2*K)\n",
"k=0.074; #thermal conductivity, J/(m*K)\n",
"\n",
"#Calculations\n",
"Ro=k/h; # formula for critical thickness of insulation, m.\n",
"\n",
"#Results\n",
"print \"Critical thickness of insulation is :\",Ro,\"m\\n\"\n",
"print \"Insulation will not even start to do any good until ratio of outer radius and inner radius is 2.32 or outer radius is 0.0058 m.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Critical thickness of insulation is : 0.0037 m\n",
"\n",
"Insulation will not even start to do any good until ratio of outer radius and inner radius is 2.32 or outer radius is 0.0058 m.\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.8, Page number: 76"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variables\n",
"P=0.1; #dissipating power,W\n",
"D=0.0036; #outer diameter of cylinder, m\n",
"l=0.01; #length of cylinder, m\n",
"T=308; #temperature of air in the cabinet,K\n",
"Test=323; #Estimated temp of resistor, K\n",
"h=13; #convection coefficient, W/(m**2*K)\n",
"e=0.9;\t\t\t\t\t\t #emmisivity\n",
"A=1.33*math.pow(10,-4); #area of ressistor's surface, m**2\n",
"sigma=5.67*math.pow(10,-8); #Stefan-Boltzmann constant, Wm**-2K**-4\n",
"\n",
"#Calculations\n",
"Tm=(T+Test)/2; #ressistor's temperature at 50 K\n",
"Hr=4*sigma*math.pow(Tm,3)*e; #radiative heat transfer coefficient,W/(m**2*K)\n",
"Rteq=1/(A*(Hr+h)); #Equivalent thermal resistance K/W\n",
"Tres=T+P*Rteq; #Resistor's temp. C\n",
"#we guessed a ressistor's temperature of 323K in finding Hr,recomputing with this higher temperature,\n",
"#we have Tm=327K and Hr=7.17W/(m**2*K). if we repeat the rest of calculations, we get a new value Tres=345.3K,\n",
"#since the use of hr is an approximation, we should check its applicability: 1/4*((345.3-308)/327)**2=0.00325<<1,\n",
"#in this case, the approximation is a very good one.\n",
"Tr=Tres-273.06; #Resistor's temp. , K\n",
"\n",
"#Results\n",
"print \"Temperature of ressistor is :\",round(Tr,3),\"K\\n\"\n",
"print \"Since 1/4*(temperature diffference/mean temperature)= 1/4*((72.3-35)/327)^2=0.00325<<1, in this case, the approximation is a very good one.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Temperature of ressistor is : 73.676 K\n",
"\n",
"Since 1/4*(temperature diffference/mean temperature)= 1/4*((72.3-35)/327)^2=0.00325<<1, in this case, the approximation is a very good one.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.9, Page number: 77"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variables\n",
"k=10; #thermal conductivity of ressistor, W/(m*K)\n",
"a=2000; #density of ressistor, kg/m**3\n",
"l=0.01; #length of cylinder, m\n",
"A=1.33*math.pow(10,-4); #area of ressistor's surface, m**2\n",
"T1=308; #temperature of air in the cabinet,K\n",
"Cp=700; #heat capacity of ressistor, J/kg/K\n",
"Heff=18.44; #the effective heat transfer coefficient of parallel convection and radiation process, W/(m**2*K)\n",
"D=0.0036; #outer diameter of cylinder, m\n",
"\n",
"#Calculations\n",
"Bi=Heff*(D/2)/k; #Biot no.\n",
"T=a*Cp*math.pi*l*math.pow(D,2)/(4*Heff*A); #since from previous example,To=72.3C, we have Tres=T1+(To-T)*exp(-t/T),Tres=308+(37.3)*.exp(-t/T). 95% of the temperature drop has occured when t=T*3=174s.\n",
"t=3*T; #Time for 95 percent cooling of ressistor, seconds.\n",
"\n",
"#Results\n",
"print \"Time for 95 percent cooling of ressistor is :\",t,\"s\\n\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Time for 95 percent cooling of ressistor is : 174.313737829 s\n",
"\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.10, Page number: 79"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variables\n",
"h1=200; #convective heat transfer coefficient, W/(m**2*K)\n",
"a=1/160000; #1/a=l/Kal, l=0.001m, Kal=160 W/(m*K)\n",
"h2=5000; #convective heat transfer coefficient during boiling,W/(m**2*K)\n",
"\n",
"#Calculations\n",
"U=1/(1/h1+a+1/h2); \t\t\t\t #Overall heat transfer coefficient,W/(m^2*K) \n",
"\n",
"#Results\n",
"print \"Overall heat transfer coefficient is :\",round(U,3),\"W/(m^2*K)\\n\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Overall heat transfer coefficient is : 192.077 W/(m^2*K)\n",
"\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.12, Page number: 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variables\n",
"Rf=0.0005; #fouling ressistance,m**2*K/W\n",
"U=5; #heat transfer coefficient,W/(m**2*K)\n",
"\n",
"#Calculations\n",
"Ucor=(U*Rf+1)/(U);\t\t\t\t\t #Corrected heat transfer coefficient, W/m^2.K\n",
"\n",
"#Results\n",
"print \"Corrected heat transfer coefficient is :\", Ucor,\"W/(m^2*K)\\n Therefore the fouling is entirely irrelevant to domestic heat holds.\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Corrected heat transfer coefficient is : 0.2005 W/(m^2*K)\n",
" Therefore the fouling is entirely irrelevant to domestic heat holds.\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.13, Page number: 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#Variables\n",
"U1=4000; # overall heat transfer coefficient of water cooled steam condenser, W/(m**2*K)\n",
"Rf1=0.0006; # lower limit of fouling ressistance of water side, m**2*K/W\n",
"Rf2=0.0020; # upper limit of fouling ressistance of water side, m**2*K/W\n",
"\n",
"#Calculations\n",
"U2=U1/(U1*Rf1+1);\t\t\t\t\t\t\t #Upper limit of the corrected overall heat transfer coefficient\n",
"U3=U1/(U1*Rf2+1);\t\t\t\t\t\t\t #Lower limit of corrected overall heat transfer coefficient\n",
"\n",
"#Results\n",
"print \"Upper limit of the corrected overall heat transfer coefficient is :\",round(U2,3),\"W/(m^2*K)\\n\"\n",
"print \"Lower limit of corrected overall heat transfer coefficient is :\",round(U3,3),\"W/m^2/K, U is reduced from 4000 to between 444 and 1176 W/(m^2*K),fouling is crucial in this case and engineering was in serious error.\\n\"\n",
" #end\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Upper limit of the corrected overall heat transfer coefficient is : 1176.471 W/(m^2*K)\n",
"\n",
"Lower limit of corrected overall heat transfer coefficient is : 444.444 W/m^2/K, U is reduced from 4000 to between 444 and 1176 W/(m^2*K),fouling is crucial in this case and engineering was in serious error.\n",
"\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}