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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Introduction to Convection"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2 Page 356 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Operating Conditions\n",
"\n",
"h = .05; \t\t\t#[W/m^2.K] Heat Convection coefficient\n",
"D = .02; \t\t\t#[m] Diameter of cylinder\n",
"Cas = 5*math.pow(10,-6); #[kmol/m^3] Surface molar Conc\n",
"Casurr = 0; \t\t\t#[kmol/m^3] Surrounding molar Conc\n",
"Ma = 128; \t\t\t#[Kg/kmol] Molecular weight\n",
"#calculations\n",
"#From Eqn 6.15\n",
"Na = h*(math.pi*D)*(Cas-Casurr);\n",
"na = Ma*Na;\n",
"#results\n",
"print '%s %.2e %s' %(\"\\n\\n Mass sublimation Rate is =\",na,\" kg/s.m \");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Mass sublimation Rate is = 2.01e-06 kg/s.m \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3 Page 357"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"\n",
"Dab = .288*math.pow(10,-4); \t#[m^2/s] Table A.8 water vapor-air (319K)\n",
"pas = .1; \t\t\t\t#[atm] Partial pressure at surface\n",
"pasurr = .02; \t\t\t#[atm] Partial pressure at infinity\n",
"y0 = .003; \t\t\t\t#[m] Tangent at y = 0 intercepts y axis at 3 mm\n",
"#calculations\n",
"#From Measured Vapor Pressure Distribution\n",
"delp = (0 - pas)/(y0 - 0); #[atm/m]\n",
"hmx = -Dab*delp/(pas - pasurr); #[m/s] \n",
"#results\n",
"print '%s %.4f %s' %(\"\\n\\n Convection Mass Transfer coefficient at prescribed location =\",hmx,\" m/s\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Convection Mass Transfer coefficient at prescribed location = 0.0120 m/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4 Page 362 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 1; \t\t\t\t#[m/s] Velocity of water\n",
"L = 0.6; \t\t\t\t#[m] Plate length\n",
"Tw1 = 300.; \t\t\t\t#[K]\n",
"Tw2 = 350.; \t\t\t\t#[K]\n",
"#Coefficients [W/m^1.5 . K]\n",
"Clam1 = 395;\n",
"Cturb1 = 2330;\n",
"Clam2 = 477;\n",
"Cturb2 = 3600;\n",
"\n",
"#Water Properties at T = 300K\n",
"p1 = 997; \t\t\t\t#[kg/m^3] Density\n",
"u1 = 855*math.pow(10,-6); #[N.s/m^2] Viscosity\n",
"#Water Properties at T = 350K\n",
"p2 = 974; \t\t\t\t#[kg/m^3] Density\n",
"u2 = 365*math.pow(10,-6); #[N.s/m^2] Viscosity\n",
"\n",
"\n",
"Rec = 5*math.pow(10,5); #Transititon Reynolds Number\n",
"xc1 = Rec*u1/(p1*v); \t\t#[m]Transition length at 300K\n",
"xc2 = Rec*u2/(p2*v); \t\t#[m]Transition length at 350K\n",
"#calculations\n",
"#Integrating eqn 6.14\n",
"#At 300 K\n",
"h1 = (Clam1*math.pow(xc1,.5) /.5 + Cturb1*(math.pow(L,.8)-math.pow(xc1,.8))/.8)/L;\n",
"\n",
"#At 350 K\n",
"h2 = (Clam2*math.pow(xc2,.5) /.5 + Cturb2*(math.pow(L,.8)-math.pow(xc2,.8))/.8)/L;\n",
"#results\n",
"print '%s %.2f %s %.2f %s' %(\"\\n\\n Average Convection Coefficient over the entire plate for the two temperatures at 300K =\",h1,\" W/m^2.K and at 350K =\",h2,\" W/m^2.K\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Average Convection Coefficient over the entire plate for the two temperatures at 300K = 1622.45 W/m^2.K and at 350K = 3707.93 W/m^2.K\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5 Page 372"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#Operating Conditions\n",
"v = 160; \t\t\t\t#[m/s] Velocity of air\n",
"L = 0.04; \t\t\t\t\t#[m] Blade length\n",
"Tsurr = 1150+273.; \t\t\t#[K]\n",
"Ts = 800+273.; \t\t\t\t#[K] Surface Temp\n",
"q = 95000; \t\t\t\t#[W/m^2] Original heat flux\n",
"#calculations\n",
"#Case 1\n",
"Ts1 = 700+273.; \t \t\t\t#[K] Surface Temp\n",
"q1 = q*(Tsurr-Ts1)/(Tsurr-Ts);\n",
"\n",
"#Case 2\n",
"L2 = .08; \t\t\t#[m] Length\n",
"q2 = q*L/L2; \t\t\t#[W/m^2] Heat flux\n",
"#results\n",
"\n",
"print '%s %d %s' %(\"\\n\\n (a) Heat Flux to blade when surface temp is reduced =\",q1/1000. ,\" KW/m^2\") \n",
"print '%s %.2f %s' %(\"\\n (b) Heat flux to a larger turbine blade = \",q2/1000. ,\"KW/m^2\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" (a) Heat Flux to blade when surface temp is reduced = 122 KW/m^2\n",
"\n",
" (b) Heat flux to a larger turbine blade = 47.50 KW/m^2\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6 Page 379"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 100; \t\t\t#[m/s] Velocity of air\n",
"Tsurr = 20+273.; \t\t#[K] Surrounding Air Temperature\n",
"L1 = 1; \t\t\t\t#[m] solid length\n",
"Ts = 80+273.; \t\t\t#[K] Surface Temp\n",
"qx = 10000; \t\t\t#[W/m^2] heat flux at a point x\n",
"Txy = 60+273.; \t\t#[K] Temp in boundary layer above the point\n",
"\n",
"#Table A.4 Air Properties at T = 323K\n",
"v = 18.2*math.pow(10,-6); #[m^2/s] Viscosity\n",
"k = 28*math.pow(10,-3); \t#[W/m.K] Conductivity\n",
"Pr = 0.7; \t\t\t#Prandttl Number\n",
"#Table A.6 Saturated Water Vapor at T = 323K\n",
"pasat = 0.082; \t\t\t#[kg/m^3]\n",
"Ma = 18; \t\t\t#[kg/kmol] Molecular mass of water vapor\n",
"#Table A.8 Water Vapor-air at T = 323K\n",
"Dab = .26*math.pow(10,-4);\t#[m^2/s]\n",
"#calculations\n",
"#Case 1\n",
"Casurr = 0;\n",
"Cas = pasat/Ma; \t\t#[kmol/m^3] Molar conc of saturated water vapor at surface\n",
"Caxy = Cas + (Casurr - Cas)*(Txy - Ts)/(Tsurr - Ts);\n",
"\n",
"#Case 2\n",
"L2 = 2.;\n",
"hm = L1/L2 * Dab/k * qx/(Ts-Tsurr);\n",
"Na = hm*(Cas - Casurr);\n",
"#results\n",
"\n",
"print '%s %.4f %s' %(\"\\n (a) Water vapor Concentration above the point =\",Caxy,\"Kmol/m^3 \\n\") \n",
"print '%s %.2e %s' %(\"(b) Molar flux to a larger surface = \",Na,\"Kmol/s.m^2\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" (a) Water vapor Concentration above the point = 0.0030 Kmol/m^3 \n",
"\n",
"(b) Molar flux to a larger surface = 3.53e-04 Kmol/s.m^2\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7 Page 383 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"Tsurr = 40+273.; \t\t#[K] Surrounding Air Temperature\n",
"#Volatile Wetting Agent A\n",
"hfg = 100; \t\t\t#[kJ/kg]\n",
"Ma = 200; \t\t\t#[kg/kmol] Molecular mass\n",
"pasat = 5000; \t\t\t#[N/m^2] Saturate pressure\n",
"Dab = .2*math.pow(10,-4); #[m^2/s] Diffusion coefficient\n",
"\n",
"#Table A.4 Air Properties at T = 300K\n",
"p = 1.16; \t#[kg/m^3] Density\n",
"cp = 1.007; \t#[kJ/kg.K] Specific Heat\n",
"alpha = 22.5*math.pow(10,-6)#[m^2/s] \n",
"R = 8.314; \t#[kJ/kmol] Universal Gas Constt\n",
"#calculations\n",
"#Applying Eqn 6.65 and setting pasurr = 0\n",
"# Ts^2 - Tsurr*Ts + B = 0 , where the coefficient B is\n",
"B = Ma*hfg*pasat*math.pow(10,-3) /(R*p*cp*math.pow((alpha/Dab),(2./3.)));\n",
"Ts = (Tsurr + math.sqrt(Tsurr*Tsurr - 4*B))/2. ;\n",
"#results\n",
"print '%s %.1f %s' %(\"\\n Steady State Surface Temperature of Beverage =\",Ts-273.,\"degC\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Steady State Surface Temperature of Beverage = 5.9 degC\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}