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|
{
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"External Flow"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1 Page 415"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 10; \t\t\t\t\t\t\t#[m/s] Air velocity\n",
"p = 6000; \t\t\t\t\t\t\t#[N/m^2] Air pressure\n",
"Tsurr = 300+273.; \t\t\t\t\t\t#[K] Surrounding Air Temperature\n",
"L = .5; \t\t\t\t\t\t\t#[m] Length of plate\n",
"Ts = 27+273.; \t\t\t\t\t\t#[K] Surface Temp\n",
"\n",
"#Table A.4 Air Properties at T = 437K \n",
"uv = 30.84*math.pow(10,-6)*(101325./6000.); #[m^2/s] Kinematic Viscosity at P = 6000 N/m^2\n",
"k = 36.4*math.pow(10,-3); \t\t#[W/m.K] Thermal COnductivity\n",
"Pr = .687; \t\t\t\t\t#Prandtl number\n",
"#calculations\n",
"Re = v*L/uv; \t\t\t\t\t\t#Reynolds number\n",
"print '%s %d %s' %(\"\\n Since Reynolds Number is\",Re,\", The flow is laminar over the entire plate\");\n",
"\n",
"#Correlation 7.30 \n",
"NuL = .664*math.pow(Re,.5)*math.pow(Pr,0.3334); #Nusselt Number over entire plate length\n",
"hL = NuL*k/L; # Average Convection Coefficient\n",
"#Required cooling rate per unit width of plate\n",
"q = hL*L*(Tsurr-Ts);\n",
"#results\n",
"print '%s %d %s' %(\"\\n\\n Required cooling rate per unit width of plate =\",q,\" W/m\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Since Reynolds Number is 9600 , The flow is laminar over the entire plate\n",
"\n",
"\n",
" Required cooling rate per unit width of plate = 570 W/m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2 Page 417"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 60; \t\t\t#[m/s] Air velocity\n",
"Tsurr = 25+273.; \t\t#[K] Surrounding Air Temperature\n",
"w = 1; \t\t\t#[m] Width of plate\n",
"L = .05; \t\t\t#[m] Length of stripper\n",
"Ts = 230+273.; \t\t#[K] Surface Temp\n",
"\n",
"#Table A.4 Air Properties at T = 400K \n",
"uv = 26.41*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"k = .0338; \t#[W/m.K] Thermal COnductivity\n",
"Pr = .690; \t#Prandtl number\n",
"#calculations\n",
"Re = v*L/uv; \t\t#Reynolds number\n",
"\n",
"Rexc = 5*math.pow(10,5); #Transition Reynolds Number\n",
"xc = uv*Rexc/v; \t\t#Transition Length\n",
"#results\n",
"print '%s %d' %(\"\\n Reynolds Number based on length L = .05m is \",Re)\n",
"print '%s %.2f %s' %(\"\\n And the transition occur at xc =\",xc,\" m ie fifth plate\");\n",
"\n",
"#For first heater\n",
"#Correlation 7.30 \n",
"Nu1 = .664*math.pow(Re,0.5)*math.pow(Pr,0.3334); #Nusselt Number \n",
"h1 = Nu1*k/L; # Average Convection Coefficient\n",
"q1 = h1*(L*w)*(Ts-Tsurr); # Convective Heat exchange\n",
"\n",
"#For first four heaters\n",
"Re4 = 4*Re;\n",
"L4 = 4*L;\n",
"Nu4 = .664*math.pow(Re4,0.5)*math.pow(Pr,0.3334); #Nusselt Number \n",
"h4 = Nu4*k/L4; # Average Convection Coefficient\n",
"print(h4)\n",
"#For Fifth heater from Eqn 7.38\n",
"Re5 = 5*Re;\n",
"A = 871; \n",
"L5 = 5*L;\n",
"Nu5 = (.037*math.pow(Re5,.8)-A)*math.pow(Pr,.3334); #Nusselt Number \n",
"h5 = Nu5*k/L5; # Average Convection Coefficient\n",
"q5 = (h5*L5-h4*L4)*w*(Ts-Tsurr);\n",
"\n",
"#For Sixth heater from Eqn 7.38\n",
"Re6 = 6*Re;\n",
"L6 = 6*L;\n",
"Nu6 = (.037*math.pow(Re6,.8)-A)*math.pow(Pr,.3334) ; #Nusselt Number \n",
"h6 = Nu6*k/L6 ; # Average Convection Coefficient\n",
"q6 = (h6*L6-h5*L5)*w*(Ts-Tsurr);\n",
"\n",
"print '%s %d %s %d %s %d %s' %(\"\\n\\n Power requirement are \\n qconv1 = \",q1,\"W qconv5 =\",q5,\" W qconv6 = \",q6,\"W\");\n",
"print '%s %d %s %d %s %d %s' %(\"\\n Hence\",q6,\">\",q1,\" >\",q5,\"and the sixth plate has largest power requirement\");\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Reynolds Number based on length L = .05m is 113593\n",
"\n",
" And the transition occur at xc = 0.22 m ie fifth plate\n",
"66.8395462952\n",
"\n",
"\n",
" Power requirement are \n",
" qconv1 = 1370 W qconv5 = 1017 W qconv6 = 1427 W\n",
"\n",
" Hence 1427 > 1370 > 1017 and the sixth plate has largest power requirement\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3 Page 420"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 2; \t\t\t#[m/s] Air velocity\n",
"Tsurr = 25+273.; \t\t#[K] Surrounding Air Temperature\n",
"H = .5; \t\t\t# Humidity\n",
"w = 6; \t\t\t#[m] Width of pool\n",
"L1 = 12; \t\t\t#[m] Length of pool\n",
"e = 1.5; \t\t\t#[m] Deck Wide\n",
"Ts = 25+273.; \t\t\t#[K] Surface Temp of water\n",
"#calculations\n",
"#Table A.4 Air Properties at T = 298K \n",
"uv = 15.7*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"#Table A.8 Water vapor-Air Properties at T = 298K \n",
"Dab = .26*math.pow(10,-4); \t#[m^2/s] Diffusion Coefficient\n",
"Sc = uv/Dab;\n",
"#Table A.6 Air Properties at T = 298K \n",
"rho = .0226; \t#[kg/m^3]\n",
"\n",
"L = L1+e;\n",
"Re = v*L/uv; \t\t#Reynolds number\n",
"\n",
"#Equation 7.41 yields\n",
"ShLe = .037*math.pow(Re,.8)*math.pow(Sc,.3334);\n",
"#Equation 7.44\n",
"p = 8.; #Turbulent Flow\n",
"ShL = (L/(L-e))*ShLe*math.pow((1-math.pow((e/L),((p+1)/(p+2)))),(p/(p+1)));\n",
"\n",
"hmL = ShL*(Dab/L);\n",
"n = hmL*(L1*w)*rho*(1-H);\n",
"#results\n",
"print '%s %.2e %s' %(\"\\n Reynolds Number is \",Re,\". Hence for turbulent Flow p = 8 in Equation 7.44.\")\n",
"print '%s %d %s' %(\"\\n Daily Water Loss due to evaporation is\",n*86400. ,\"kg/day\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Reynolds Number is 1.72e+06 . Hence for turbulent Flow p = 8 in Equation 7.44.\n",
"\n",
" Daily Water Loss due to evaporation is 406 kg/day\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4 Page 428"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 10; \t\t\t#[m/s] Air velocity\n",
"Tsurr = 26.2+273.; \t\t#[K] Surrounding Air Temperature\n",
"P = 46.; \t\t\t# [W] Power dissipation\n",
"L = .094; \t\t\t#[m] Length of cylinder\n",
"D = .0127; \t\t\t#[m] Diameter of cylinder\n",
"Ts = 128.4+273.; \t\t#[K] Surface Temp of water\n",
"q = 46.15*46; \t\t#[W] Actual power dissipation without the 15% loss\n",
"\n",
"#Table A.4 Air Properties at T = 300K \n",
"uv = 15.89*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"k = 26.3*math.pow(10,-3); #[W/m.K] Thermal conductivity\n",
"Pr = .707; \t#Prandtl Number\n",
"#Table A.4 Air Properties at T = 401K \n",
"Prs = .690; \t#Prandtl Number\n",
"#calculations\n",
"A = math.pi*D*L;\n",
"h = q/(A*(Ts-Tsurr));\n",
"\n",
"Re = v*D/uv; \t\t#Reynolds number\n",
"#Using Zukauskas Relation, Equation 7.53\n",
"C = .26;\n",
"m = .6;\n",
"n = .37;\n",
"Nu = C*math.pow(Re,m)*math.pow(Pr,n)*math.pow((Pr/Prs),.25);\n",
"havg = Nu*k/D;\n",
"#results\n",
"print '%s %d %s' %(\"\\n Convection Coefficient associated with operating conditions\",h,\"W/m^2.K.\") \n",
"print '%s %d %s' %(\"\\n Reynolds Number is \",Re,\". Hence taking suitable corresponding data from Table 7.4.\")\n",
"print '%s %d %s' %(\"\\n Convection Coefficient from an appropriate Zukauskas correlation\",havg,\" W/m^2.K\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Convection Coefficient associated with operating conditions 5538 W/m^2.K.\n",
"\n",
" Reynolds Number is 7992 . Hence taking suitable corresponding data from Table 7.4.\n",
"\n",
" Convection Coefficient from an appropriate Zukauskas correlation 104 W/m^2.K\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5 page 431"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 23; \t\t\t\t#[m/s] Air velocity\n",
"Tsurr = 296.; \t\t\t\t#[K] Surrounding Air Temperature\n",
"L = .8; \t\t\t\t#[m] Length of cylinder\n",
"Di = .1; \t\t\t\t#[m] Diameter of cylinder\n",
"t = .005; \t\t\t\t\t#[m] Thickness of cylinder\n",
"\n",
"#Table A.4 Air Properties at T = 285K \n",
"uv = 14.56*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"k = 25.2*math.pow(10,-3); #[W/m.K] Thermal conductivity\n",
"Pr = .712; \t\t#Prandtl Number\n",
"#Table A.1 AISI 316 Stainless steel Properties at T = 300K \n",
"kss = 13.4; \t\t#[W/m.K]Conductivity\n",
"\n",
"pH2 = 1.01; \t\t\t\t#[N]\n",
"Ti = -3550/(2.30*math.log10(pH2) - 12.9);\n",
"Eg = -(1.35*math.pow(10,-4))*(29.5*math.pow(10,6));\n",
"#calculations\n",
"Re = v*(Di+2*t)/uv; \t\t#Reynolds number\n",
"# Equation 7.54\n",
"Nu = .3+.62*math.pow(Re,.5)*math.pow(Pr,.3334) /math.pow((1+math.pow((.4/Pr),.6668)),.25) *math.pow(1+math.pow((Re/282000.),(5./8.)),.8);\n",
"h = Nu*k/(Di+2*t);\n",
"\n",
"qconv = (Tsurr-Ti)/((1/(math.pi*L*(Di+2*t)*h))+(2.30*math.log10((Di+2*t)/Di)/(2*math.pi*kss*L)));\n",
"\n",
"#results\n",
"print '%s %d %s' %(\"\\n Additional Thermal Energy must be supplied to canister to mainatin steady-state operating temperatue\",-qconv-Eg,\"W\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Additional Thermal Energy must be supplied to canister to mainatin steady-state operating temperatue 3581 W\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6 page 434"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 10; \t\t\t#[m/s] Air velocity\n",
"Tsurr = 23+273.; \t\t#[K] Surrounding Air Temperature\n",
"D = .01; \t\t\t#[m] Diameter of sphere\n",
"Ti = 75+273.; \t\t#[K] Initial temp\n",
"Tt = 35+273.; \t\t#[K] Temperature after time t\n",
"p = 1; \t\t#[atm]\n",
"\n",
"#Table A.1 Copper at T = 328K \n",
"rho = 8933; \t\t\t#[kg/m^3] Density\n",
"k = 399; \t\t\t#[W/m.K] Conductivity\n",
"cp = 388; \t\t\t#[J/kg.K] specific \n",
"#Table A.4 Air Properties T = 296 K\n",
"u = 182.6*math.pow(10,-7); #[N.s/m^2] Viscosity\n",
"uv = 15.53*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"k = 25.1*math.pow(10,-3); #[W/m.K] Thermal conductivity\n",
"Pr = .708; \t#Prandtl Number\n",
"#Table A.4 Air Properties T = 328 K\n",
"u2 = 197.8*math.pow(10,-7); #[N.s/m^2] Viscosity\n",
"#calculations\n",
"Re = v*D/uv; \t\t#Reynolds number\n",
"#Using Equation 7.56\n",
"Nu = 2+(0.4*math.pow(Re,.5) + 0.06*math.pow(Re,.668))*math.pow(Pr,.4)*math.pow((u/u2),.25);\n",
"h = Nu*k/D;\n",
"#From equation 5.4 and 5.5\n",
"t = rho*cp*D*2.30*math.log10((Ti-Tsurr)/(Tt-Tsurr))/(6*h);\n",
"#results\n",
"print '%s %.1f %s' %(\"\\nTime required for cooling is\",t,\"sec\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Time required for cooling is 71.2 sec\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7 Page 443"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"v = 6; \t\t\t#[m/s] Air velocity\n",
"Tsurr = 15+273.; \t \t\t#[K] Surrounding Air Temperature\n",
"D = .0164; \t\t\t#[m] Diameter of tube\n",
"Ts = 70+273.; \t\t#[K] Temp of tube\n",
"#Staggered arrangement dimensions\n",
"St = .0313; \t\t\t#[m]\n",
"Sl = .0343; \t\t\t#[m]\n",
"\n",
"#Table A.4 Air Properties T = 288 K\n",
"rho = 1.217; \t\t#[kg/m^3] Density\n",
"cp = 1007; \t\t#[J/kg.K] specific heat\n",
"uv = 14.82*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"k = 25.3*math.pow(10,-3); #[W/m.K] Thermal conductivity\n",
"Pr = .71; \t#Prandtl Number\n",
"#Table A.4 Air Properties T = 343 K\n",
"Pr2 = .701; \t#Prandtl Number\n",
"#Table A.4 Air Properties T = 316 K\n",
"uv3 = 17.4*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"k3 = 27.4*math.pow(10,-3); #[W/m.K] Thermal conductivity\n",
"Pr3 = .705; \t#Prandtl Number\n",
"#calculations\n",
"Sd = math.pow((Sl*Sl + (St/2)*(St/2)),.5);\n",
"Vmax = St*v/(St-D);\n",
"\n",
"Re = Vmax*D/uv; \t\t#Reynolds number\n",
"\n",
"C = .35*math.pow((St/Sl),.2);\n",
"m = .6;\n",
"C2 = .95;\n",
"N = 56;\n",
"Nt = 8;\n",
"#Using Equation 7.64 & 7.65\n",
"Nu = C2*C*math.pow(Re,m)* math.pow(Pr,.36) *math.pow((Pr/Pr2),.25);\n",
"h = Nu*k/D;\n",
"\n",
"#From Eqnn 7.67\n",
"Tso = (Ts-Tsurr)*math.exp(-(math.pi*D*N*h)/(rho*v*Nt*St*cp));\n",
"Tlm = ((Ts-Tsurr) - Tso)/(2.30*math.log10((Ts-Tsurr)/Tso));\n",
"q = N*(h*math.pi*D*Tlm);\n",
"\n",
"Pt = St/D;\n",
"#From Fig 7.14\n",
"X = 1.04;\n",
"f = .35;\n",
"NL = 7;\n",
"press = NL*X*(rho*Vmax*Vmax/2.)*f;\n",
"#results\n",
"print '%s %.1f %s' %(\"\\n Air side Convection coefficient h = \",h,\"W/m^2.k\"); \n",
"print '%s %.1f %s' %(\"\\n and Heat rate q = \",q/1000. ,\" kW/m\"); \n",
"print '%s %.2e %s' %(\"\t\\n Pressure Drop =\",press/100000. ,\" bars\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Air side Convection coefficient h = 137.0 W/m^2.k\n",
"\n",
" and Heat rate q = 19.6 kW/m\n",
"\t\n",
" Pressure Drop = 2.46e-03 bars\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|