{
"metadata": {
"name": "",
"signature": "sha256:dd9802b686cdfc5d04064f27577856b20913db7526956cd0d6229f433fb9f632"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 20 - Advanced topics in heat transfer"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1 - Pg 437"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Surface temperature of transmission line, rate of heat generation and max temperature in the line\n",
"#Initialization of variables\n",
"import math\n",
"heat=54.5 #Btu/hr ft\n",
"d=0.811 #in\n",
"h=2.5 #Btu/hr ft**2 F\n",
"ts=100 #F\n",
"km=220 #Btu/hr ft F\n",
"#calculations\n",
"t2=heat*12/(h*math.pi*d) +ts\n",
"w=heat*4*144/(math.pi*d**2)\n",
"t1=w*(d/2)**2 /(4*144*km) + t2\n",
"#results\n",
"print '%s %.1f %s' %(\"Surface temperature of transmission line =\",t2,\" F\")\n",
"print '%s %d %s' %(\"\\n Rate of heat generation per unit volume of wire =\",w,\"Btu/hr ft^2\")\n",
"print '%s %.2f %s' %(\"\\n Max. temperature in the line =\",t1,\" F\")\n",
"print '%s' %(\"The answers in the textbook are a bit different due to rounding off errors\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Surface temperature of transmission line = 202.7 F\n",
"\n",
" Rate of heat generation per unit volume of wire = 15192 Btu/hr ft^2\n",
"\n",
" Max. temperature in the line = 202.70 F\n",
"The answers in the textbook are a bit different due to rounding off errors\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2 - Pg 442"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the heat rate, total hourly loss and approx. temp of the tip of the fin and total heat loss\n",
"#Initialization of variables\n",
"import math\n",
"d1=1. #in\n",
"l=1. #ft\n",
"r=0.5 #ft\n",
"L=0.5 #in\n",
"Ts=430. #F\n",
"Ta=170. #F\n",
"dela=0.0125 #ft\n",
"h=10. #Btu/hr ft^2 F\n",
"eta=0.77\n",
"eta2=0.94\n",
"n=60. #fins\n",
"thick=0.025 #in\n",
"k2=132. #Btu/hr ft F\n",
"#calculations\n",
"Q=h*math.pi*d1**2 *(Ts-Ta)/12\n",
"rate=(r+L)/r\n",
"k=26 #Btu/hr ft F\n",
"Lt=L/12 *(h*12/(k*dela))**(1/2)\n",
"dtm=eta*(Ts-Ta)\n",
"As=2*math.pi*((2*d1)**2 -d1**2)/4\n",
"Q1=h*n*As*dtm/144\n",
"Q2=h*math.pi*d1*(12-60*thick)*(Ts-Ta)/144\n",
"Qt=Q1+Q2\n",
"al=0.8\n",
"tl=Ta+(Ts-Ta)/math.cosh(al)\n",
"al2=r/12 *(h*12*2/(k2*thick))\n",
"dtm2=eta2*(Ts-Ta)\n",
"Q12=h*n*As*dtm2/144\n",
"Qt2=Q12+Q2\n",
"#results\n",
"print '%s %.1f %s' %(\"Heat rate per foot of bare tube =\",Q,\"Btu/hr\")\n",
"print '%s %.1f %s' %(\"\\n Total hourly heat loss per foot of finned tube =\",Qt,\"Btu/hr\")\n",
"print '%s %d %s' %(\"\\n Approx. temp for tip of the fin =\",tl,\"F\")\n",
"print '%s %.1f %s' %(\"\\n In case of Al, Total beat loss =\",Qt2,\" Btu/hr\")\n",
"print '%s' %(\"The answers in the textbook are a bit different due to rounding off errors\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat rate per foot of bare tube = 680.7 Btu/hr\n",
"\n",
" Total hourly heat loss per foot of finned tube = 4526.5 Btu/hr\n",
"\n",
" Approx. temp for tip of the fin = 364 F\n",
"\n",
" In case of Al, Total beat loss = 5394.4 Btu/hr\n",
"The answers in the textbook are a bit different due to rounding off errors\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3 - Pg 444"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Length required\n",
"#Initialization of variables\n",
"import math\n",
"tl=125. #F\n",
"t0=80. #F\n",
"t1=1000. #F\n",
"d=1. #in\n",
"k=25. #Btu/hr ft F\n",
"k2=0.0208\n",
"Nu=18.\n",
"#calculations\n",
"byal=(tl-t0)/(t1-t0)\n",
"al=math.acosh(1/byal)\n",
"b=math.pi*d/12.\n",
"A=math.pi*d**2 /(4*144)\n",
"tm=(tl+t1)/2. +460\n",
"hr=0.79*0.1714*((tm/100)**4 - ((t0+460)/100)**4)/(tm-460-t0)\n",
"hc=Nu*k2*12/d\n",
"a=((hc+hr)*b/(k*A))**(0.5)\n",
"L=al/a\n",
"#results\n",
"print '%s %.2f %s' %(\"Length required =\",L,\" ft\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Length required = 0.99 ft\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5 - Pg 452"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the time required\n",
"#Initialization of variables\n",
"import math\n",
"c=0.0947 #Btu/lbm F\n",
"rho=0.0551 #lbm/ft**3\n",
"mu=0.0553 #lbm/hr ft\n",
"t1=440. #F\n",
"ts=400. #F\n",
"t2=80. #F\n",
"d=0.1 #in\n",
"k=0.0194 #Btu/hr ft**2 F\n",
"rho2=558. #lbm/ft**3\n",
"v=10. #ft/s\n",
"#calculations\n",
"Re=d*3600*v*rho/(12*mu)\n",
"Nu=0.37*Re**0.6\n",
"hc=k*Nu*12/d\n",
"ex=math.log((t1-ts)/(t1-t2))\n",
"tau=-ex*d*rho2*c/(12*6*hc)\n",
"time=tau*3600\n",
"#results\n",
"print '%s %d %s' %(\"Time required =\",time,\"sec\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Time required = 22 sec\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6 - Pg 456"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Cooling time and Center temperature\n",
"#Initialization of variables\n",
"h=2 #Btu/hr ft**2 F\n",
"delta=1/6.\n",
"t=125. #F\n",
"t0=100. #F\n",
"ti=350. #F\n",
"k=0.167 #Btu/hr ft F\n",
"rho=80. #lbm/ft**3\n",
"c=0.4 #Btu/lbm F\n",
"#calculations\n",
"Bi=h*delta/k\n",
"tr=(t-t0)/(ti-t0)\n",
"tau=1.5*delta**2 *rho*c/k\n",
"tr2=0.21\n",
"tc=tr2*(ti-t0) + t0\n",
"#results\n",
"print '%s %.2f %s' %(\"Cooling time =\",tau,\" hr\")\n",
"print '%s %d %s' %(\"\\n Center temperature =\",tc,\" F\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Cooling time = 7.98 hr\n",
"\n",
" Center temperature = 152 F\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7 - Pg 458"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate if the thin layero f insulation would increase the heat dissipation from wire\n",
"#Initialization of variables\n",
"h=2.5 #Btu/hr ft^2 F\n",
"kc=0.1 #Btu/hr ft F\n",
"r1=0.811/2\n",
"#calculations\n",
"r2c=kc/h *12\n",
"#results\n",
"if r2c>=r1:\n",
" print '%s %.2f %s' %(\"Thin layer of insulation would increase the heat dissipation from wire, r2c =\",r2c,\"in\")\n",
"else:\n",
" print '%s %.2f %s' %(\"Thin layer of insulation would decrease the heat dissipation from wire. r2c=\",r2c,\"in\")\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Thin layer of insulation would increase the heat dissipation from wire, r2c = 0.48 in\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8 - Pg 465"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the heat transfer from surfaces 1,2,3 and Temperature of surface R\n",
"#Initialization of variables\n",
"F12=0.19\n",
"F13=F12\n",
"FR3=F13\n",
"F2R=0.38\n",
"J1=1714.\n",
"Wb2=0.1714\n",
"#calculations\n",
"print '%s' %(\"Upon solving the simultaneous equations\")\n",
"Q1=1774 #Btu/hr ft\n",
"Q2=-547 #Btu/r ft\n",
"Q3=-1227 #Btu/hr ft\n",
"J2=548 #Btu/hr ft^2\n",
"Tr=909 #R\n",
"#results\n",
"print '%s %d %s' %(\"Heat transfer rate from surface 1 =\",Q1,\" Btu/hr ft\")\n",
"print '%s %d %s' %(\"\\n Heat transfer rate from surface 2 =\",Q2,\" Btu/hr ft\")\n",
"print '%s %d %s' %(\"\\n Heat transfer rate from surface 3 =\",Q3,\" Btu/hr ft\")\n",
"print '%s %d %s' %(\"\\n Temperature of surface R =\",Tr,\"R\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Upon solving the simultaneous equations\n",
"Heat transfer rate from surface 1 = 1774 Btu/hr ft\n",
"\n",
" Heat transfer rate from surface 2 = -547 Btu/hr ft\n",
"\n",
" Heat transfer rate from surface 3 = -1227 Btu/hr ft\n",
"\n",
" Temperature of surface R = 909 R\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}