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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Free Convection"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.1 Page 569"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"Ts = 70+273.; \t\t\t\t\t#[K] Surface Temperature\n",
"Tsurr = 25+273.; \t\t\t\t#[K] Surrounding Temperature\n",
"v1 = 0; \t\t\t\t\t#[m/s] Velocity of free air\n",
"v2 = 5; \t\t\t\t\t#[m/s] Velocity of free air\n",
"L = .25; \t\t\t\t#[m] length\n",
"#calculations and results\n",
"#Table A.4 Air Properties T = 320 K\n",
"uv = 17.95*math.pow(10,-6);\t\t\t#[m^2/s] Kinematic Viscosity\n",
"be = 3.12*math.pow(10,-3); \t\t\t#[K^-1] Tf^-1\n",
"Pr = 269; \t\t\t# Prandtl number \n",
"g = 9.81; \t\t\t\t\t#[m^2/s]gravitational constt\n",
"\n",
"Gr = g*be*(Ts-Tsurr)*L*L*L/(uv*uv);\n",
"del1 = 6*L/math.pow((Gr/4),.25);\n",
"print '%s %.3f %s' %(\"\\n Boundary Layer thickness at trailing edge for no air stream\",del1,\"m\");\n",
"\n",
"Re = v2*L/uv;\n",
"print '%s %.2e %s' %(\"\\n\\n For air stream at 5 m/s As the Reynolds Number is \",Re,\"the free convection boundary layer is Laminar\");\n",
"del2 = 5*L/math.pow((Re),.5);\n",
"print '%s %.4f %s' %(\"\\n Boundary Layer thickness at trailing edge for air stream at 5 m/s is\",del2,\"m\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Boundary Layer thickness at trailing edge for no air stream 0.023 m\n",
"\n",
"\n",
" For air stream at 5 m/s As the Reynolds Number is 6.96e+04 the free convection boundary layer is Laminar\n",
"\n",
" Boundary Layer thickness at trailing edge for air stream at 5 m/s is 0.0047 m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.2 Page 572 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"Ts = 232+273.; \t\t\t#[K] Surface Temperature\n",
"Tsurr = 23+273.; \t\t#[K] Surrounding Temperature\n",
"L = .71; \t\t#[m] length\n",
"w = 1.02; \t\t#[m] Width\n",
"\n",
"#Table A.4 Air Properties T = 400 K\n",
"k = 33.8*math.pow(10,-3) \t;#[W/m.K]\n",
"uv = 26.4*math.pow(10,-6) \t;#[m^2/s] Kinematic Viscosity\n",
"al = 38.3*math.pow(10,-6)\t;#[m^2/s]\n",
"be = 2.5*math.pow(10,-3) \t;#[K^-1] Tf^-1\n",
"Pr = .69 \t\t;# Prandtl number \n",
"g = 9.81 \t;#[m^2/s] gravitational constt\n",
"#calculations and results\n",
"Ra = g*be*(Ts-Tsurr)/al*L*L*L/uv;\n",
"print '%s %.2e %s' %(\"\\n\\n As the Rayleigh Number is\",Ra,\"the free convection boundary layer is turbulent\");\n",
"#From equatiom 9.23\n",
"Nu = math.pow(.825 + .387*math.pow(Ra,.16667) /math.pow((1+math.pow((.492/Pr),(9./16.))),(8./27.)),2);\n",
"h = Nu*k/L;\n",
"q = h*L*w*(Ts-Tsurr);\n",
"\n",
"print '%s %d %s' %(\"\\n Heat transfer by convection between screen and room air is\",q,\"W\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" As the Rayleigh Number is 1.81e+09 the free convection boundary layer is turbulent\n",
"\n",
" Heat transfer by convection between screen and room air is 1060 W\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.3 Page 577"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"Ts = 45+273.; \t\t\t\t#[K] Surface Temperature\n",
"Tsurr = 15+273. \t\t\t\t;#[K] Surrounding Temperature\n",
"H = .3 \t\t\t\t;#[m] Height \n",
"w = .75 \t\t\t\t;#[m] Width\n",
"\n",
"#Table A.4 Air Properties T = 303 K\n",
"k = 26.5*math.pow(10,-3) \t\t;#[W/m.K]\n",
"uv = 16.2*math.pow(10,-6) ;#[m^2/s] Kinematic Viscosity\n",
"al = 22.9*math.pow(10,-6) ;#[m^2/s] alpha\n",
"be = 3.3*math.pow(10,-3) ;#[K^-1] Tf^-1\n",
"Pr = .71 \t\t\t;# Prandtl number \n",
"g = 9.81 \t\t;#[m^2/s] gravitational constt\n",
"#calculations\n",
"Ra = g*be*(Ts-Tsurr)/al*H*H*H/uv; #Length = Height\n",
"#From equatiom 9.27\n",
"Nu = (.68 + .67*math.pow(Ra,.25) /math.pow((1+math.pow((.492/Pr),(9./16.))),(4./9.)));\n",
"#for Sides\n",
"hs = Nu*k/H;\n",
"\n",
"Ra2 = g*be*(Ts-Tsurr)/al*(w/2.)*(w/2.)*(w/2.)/uv; #Length = w/2\n",
"#For top eq 9.31\n",
"ht = k/(w/2.)*.15*math.pow(Ra2,.3334);\n",
"#For bottom Eq 9.32\n",
"hb = k/(w/2.)*.27*math.pow(Ra2,.25);\n",
"\n",
"q = (2*hs*H+ht*w+hb*w)*(Ts-Tsurr);\n",
"#results\n",
"print '%s %d %s' %(\"\\n Rate of heat loss per unit length of duct is\",q,\" W/m\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Rate of heat loss per unit length of duct is 246 W/m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4 Page 580 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"Ts = 165+273.; \t\t\t\t#[K] Surface Temperature\n",
"Tsurr = 23+273.; \t\t\t#[K] Surrounding Temperature\n",
"D = .1 \t\t\t\t;#[m] Diameter\n",
"e = .85 \t\t\t\t;# emissivity\n",
"stfncnstt=5.67*math.pow(10,(-8))# [W/m^2.K^4] - Stefan Boltzmann Constant \n",
"\n",
"#Table A.4 Air Properties T = 303 K\n",
"k = 31.3*math.pow(10,-3) ;#[W/m.K] Conductivity\n",
"uv = 22.8*math.pow(10,-6) ;#[m^2/s] Kinematic Viscosity\n",
"al = 32.8*math.pow(10,-6) ;#[m^2/s] alpha\n",
"be = 2.725*math.pow(10,-3) \t;#[K^-1] Tf^-1\n",
"Pr = .697 \t\t;# Prandtl number \n",
"g = 9.81 \t\t;#[m^2/s] gravitational constt\n",
"#calculations\t\n",
"Ra = g*be*(Ts-Tsurr)/al*D*D*D/uv; \n",
"#From equatiom 9.34\n",
"Nu = math.pow((.60 + .387*math.pow(Ra,(1./6.))/math.pow(1+math.pow((.559/Pr),(9./16.)),(8./27.))),2);\n",
"h = Nu*k/D;\n",
"\n",
"qconv = h*math.pi*D*(Ts-Tsurr);\n",
"qrad = e*math.pi*D*stfncnstt*(Ts*Ts*Ts*Ts-Tsurr*Tsurr*Tsurr*Tsurr);\n",
"#results\n",
"print '%s %d %s' %(\"\\n Rate of heat loss per unit length of pipe is \",qrad+qconv,\"W/m\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Rate of heat loss per unit length of pipe is 763 W/m\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.5 Page 592"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"To = 35+273. \t\t\t;#[K] Shield Temperature\n",
"Ti = 120+273. \t\t\t;#[K] Tube Temperature\n",
"Di = .1 \t\t\t;#[m] Diameter inner\n",
"Do = .12 \t\t;#[m] Diameter outer\n",
"L = .01 \t\t\t;#[m] air gap insulation\n",
"\n",
"#Table A.4 Air Properties T = 350 K\n",
"k = 30*math.pow(10,-3) ;#[W/m.K] Conductivity\n",
"uv = 20.92*math.pow(10,-6) ;#[m^2/s] Kinematic Viscosity\n",
"al = 29.9*math.pow(10,-6) ;#[m^2/s] alpha\n",
"be = 2.85*math.pow(10,-3) ;#[K^-1] Tf^-1\n",
"Pr = .7 \t\t;# Prandtl number \n",
"g = 9.81 \t;#[m^2/s] gravitational constt\n",
"#Table A.3 Insulation glass fiber T=300K\n",
"kins = .038 \t;#[W/m.K] Conductivity\n",
"#calculations\n",
"Lc = 2*math.pow((2.303*math.log10(Do/Di)),(4./3.))/math.pow((math.pow((Di/2.),(-3./5.))+math.pow((Do/2.),(-3./5.))),(5./3.));\n",
"Ra = g*be*(Ti-To)/al*Lc*Lc*Lc/uv; \n",
"keff = .386*k*math.pow((Pr/(.861+Pr)),.25) *math.pow(Ra,.25);\n",
"q = 2*math.pi*keff*(Ti-To)/(2.303*math.log10(Do/Di));\n",
"\n",
"#From equatiom 9.58 and 3.27\n",
"qin = q*kins/keff;\n",
"#results\n",
"print '%s %d %s' %(\"\\n Heat Loss from pipe per unit of length is \",q,\"W/m\")\n",
"print '%s %d %s' %(\" \\n Heat Loss if air is filled with glass-fiber blanket insulation\",qin,\"W/m\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Heat Loss from pipe per unit of length is 100 W/m\n",
" \n",
" Heat Loss if air is filled with glass-fiber blanket insulation 111 W/m\n"
]
}
],
"prompt_number": 5
}
],
"metadata": {}
}
]
}