{
"metadata": {
"name": "",
"signature": "sha256:bcdb44fcb5c412a8fb12ecf8bc3409e5bc0d03dc35a4f7331daf1db849b5f7af"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Internal Flow"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.2 Page 499"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"m = .1; #[kg/s] mass flow rate of water\n",
"Ti = 20+273.; #[K] Inlet temp\n",
"To = 60+273.; #[K] Outlet temperature\n",
"Di = .02; #[m] Inner Diameter\n",
"Do = .04; #[m] Outer Diameter\n",
"q = 1000000.;\t #[w/m^3] Heat generation Rate\n",
"Tsi = 70+273.; #[K] Inner Surface Temp\n",
"#Table A.4 Air Properties T = 313 K\n",
"cp = 4179; #[J/kg.K] specific heat\n",
"#calculations\n",
"L = 4*m*cp*(To-Ti)/(math.pi*(Do*Do-Di*Di)*q);\n",
"\n",
"#From Newtons Law of cooling, Equation 8.27, local heat convection coefficient is\n",
"h = q*(Do*Do-Di*Di)/(Di*4*(Tsi-To));\n",
"#results\n",
"print '%s %.1f %s' %(\"\\n Length of tube needed to achieve the desired outlet temperature = \",L,\"m \")\n",
"print '%s %.1f %s' %(\"\\n Local convection coefficient at the outlet =\",h,\" W/m^2.K\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Length of tube needed to achieve the desired outlet temperature = 17.7 m \n",
"\n",
" Local convection coefficient at the outlet = 1500.0 W/m^2.K\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.3 Page 503 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"m = .25; \t#[kg/s] mass flow rate of water\n",
"Ti = 15+273.; \t#[K] Inlet temp\n",
"To = 57+273.; \t#[K] Outlet temperature\n",
"D = .05; \t\t#[m] Diameter\n",
"L = 6; \t\t#[m] Length of tube\n",
"Ts = 100+273.; \t#[K] outer Surface Temp\n",
"\n",
"#Table A.4 Air Properties T = 309 K\n",
"cp = 4178; \t#[J/kg.K] specific heat\n",
"#calculations\n",
"Tlm = ((Ts-To)-(Ts-Ti))/(2.30*math.log10((Ts-To)/(Ts-Ti)));\n",
"\n",
"h = m*cp*(To-Ti)/(math.pi*D*L*Tlm);\n",
"#results\n",
"print '%s %d %s' %(\"\\n Average Heat transfer Convection Coefficient = \",h,\"W/m^2.K\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Average Heat transfer Convection Coefficient = 754 W/m^2.K\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4 Page 506 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"m = .01; #[kg/s] mass flow rate of water\n",
"Ti = 20+273; \t#[K] Inlet temp\n",
"To = 80+273; \t#[K] Outlet temperature\n",
"D = .06; \t#[m] Diameter\n",
"q = 2000; \t#[W/m^2] Heat flux to fluid\n",
"\n",
"#Table A.4 Air Properties T = 323 K\n",
"cp = 4178; #[J/kg.K] specific heat\n",
"#Table A.4 Air Properties T = 353 K\n",
"k = .670; #[W/m] Thermal Conductivity\n",
"u = 352*math.pow(10,-6);#[N.s/m^2] Viscosity\n",
"Pr = 2.2; #Prandtl Number\n",
"cp = 4178; #[J/kg.K] specific heat\n",
"#calculations\n",
"L = m*cp*(To-Ti)/(math.pi*D*q);\n",
"\n",
"#Using equation 8.6\n",
"Re = m*4/(math.pi*D*u);\n",
"print '%s %.2f %s' %(\"\\n (a) Length of tube for required heating =\",L,\"m\")\n",
"print '%s %.2f %s' %(\"\\n\\n (b)As Reynolds Number is\",Re,\".The flow is laminar.\");\n",
"\n",
"Nu = 4.364; #Nusselt Number\n",
"h = Nu*k/D; #[W/m^2.K] Heat convection Coefficient\n",
"\n",
"Ts = q/h+To; #[K]\n",
"#results\n",
"print '%s %.2f %s' %(\"\\n Surface Temperature at tube outlet = \",Ts-273,\"degC\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" (a) Length of tube for required heating = 6.65 m\n",
"\n",
"\n",
" (b)As Reynolds Number is 602.86 .The flow is laminar.\n",
"\n",
" Surface Temperature at tube outlet = 121.04 degC\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.5 Page 509 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"um1 = .13; #[m/s] Blood stream\n",
"um2 = 3*math.pow(10,-3); #[m/s] Blood stream\n",
"um3 = .7*math.pow(10,-3); #[m/s] Blood stream\n",
"D1 = .003; #[m] Diameter\n",
"D2 = .02*math.pow(10,-3); #[m] Diameter\n",
"D3 = .008*math.pow(10,-3); #[m] Diameter\n",
"Tlm = .05;\n",
"kf = .5; #[W/m.K] Conductivity\n",
"#Table A. Water Properties T = 310 K\n",
"rho = 993.; #[kg/m^3] density\n",
"cp = 4178.; #[J/kg.K] specific heat\n",
"u = 695*math.pow(10,-6); #[N.s/m^2] Viscosity\n",
"kb = .628; #[W/m.K] Conductivity\n",
"Pr = 4.62; #Prandtl Number\n",
"i=1.;\n",
"#calculations\n",
"#Using equation 8.6\n",
"Re1 = rho*um1*D1/u;\n",
"Nu = 4;\n",
"hb = Nu*kb/D1;\n",
"hf = kf/D1;\n",
"U1 = 1/(1/hb + 1/hf);\n",
"L1 = -rho*um1*D1/U1*cp*2.303*math.log10(Tlm)/4.;\n",
"xfdh1 = .05*Re1*D1;\n",
"xfdr1 = xfdh1*Pr;\n",
"\n",
"Re2 = rho*um2*D2/u;\n",
"Nu = 4;\n",
"hb = Nu*kb/D2;\n",
"hf = kf/D2;\n",
"U2 = 1/(1/hb + 1/hf);\n",
"L2 = -rho*um2*D2/U2*cp*2.303*math.log10(Tlm)/4.;\n",
"xfdh2 = .05*Re2*D2;\n",
"xfdr2 = xfdh2*Pr;\n",
"\n",
"Re3 = rho*um3*D3/u;\n",
"Nu = 4;\n",
"hb = Nu*kb/D3;\n",
"hf = kf/D3;\n",
"U3 = 1/(1/hb + 1/hf);\n",
"L3 = -rho*um3*D3/U3*cp*2.303*math.log10(Tlm)/4.;\n",
"xfdh3 = .05*Re3*D3;\n",
"xfdr3 = xfdh3*Pr;\n",
"#results\n",
"print ' %s' %(\"\\n Vessel Re U(W/m^2.K) L(m) xfdh(m) xfdr(m)\")\n",
"print '%s %.3f %d %.1e %.1e %.1e' %(\"\\n Artery \",Re1, U1 ,L1, xfdh1 , xfdr1)\n",
"print '%s %.3f %d %.1e %.1e %.1e' %(\"\\n Anteriole \",Re2, U2 ,L2, xfdh2 , xfdr2)\n",
"print '%s %.3f %d %.1e %.1e %.1e' %(\"\\n Capillary \",Re3,U3,L3,xfdh3,xfdr3);\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" \n",
" Vessel Re U(W/m^2.K) L(m) xfdh(m) xfdr(m)\n",
"\n",
" Artery 557.223 138 8.7e+00 8.4e-02 3.9e-01\n",
"\n",
" Anteriole 0.086 20849 8.9e-06 8.6e-08 4.0e-07\n",
"\n",
" Capillary 0.008 52124 3.3e-07 3.2e-09 1.5e-08\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.6 Page 516 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"m = .05; \t#[kg/s] mass flow rate of water\n",
"Ti = 103+273.; \t#[K] Inlet temp\n",
"To = 77+273.; \t\t#[K] Outlet temperature\n",
"D = .15; \t\t#[m] Diameter\n",
"L = 5; \t\t#[m] length\n",
"ho = 6.; \t\t#[W/m^2.K] Heat transfer convective coefficient\n",
"Tsurr = 0+273.; \t\t#[K] Temperature of surrounding\n",
"\n",
"#Table A.4 Air Properties T = 363 K\n",
"cp = 1010; \t#[J/kg.K] specific heat\n",
"#Table A.4 Air Properties T = 350 K\n",
"k = .030; \t#[W/m] Thermal Conductivity\n",
"u = 20.82/1000000.; \t#[N.s/m^2] Viscosity\n",
"Pr = .7; \t\t#Prandtl Number\n",
"#calculations and results\n",
"q = m*cp*(To-Ti);\n",
"\n",
"Re = m*4/(math.pi*D*u);\n",
"print '%s %d %s' %(\"\\n As Reynolds Number is\",Re,\". The flow is Turbulent.\");\n",
"\n",
"#Equation 8.6\n",
"n = 0.3;\n",
"Nu = .023*math.pow(Re,.8)*math.pow(Pr,.3);\n",
"h = Nu*k/D;\n",
"q2 = (To-Tsurr)/(1/h + 1/ho);\n",
"Ts = -q2/h+To;\n",
"\n",
"print '%s %d %s' %(\"\\n\\n Heat Loss from the Duct over the Length L, q =\",q,\" W \")\n",
"print '%s %.1f %s %.1f %s' %(\"\\n Heat flux and suface temperature at x=L is\",q2,\"W/m^2 &\",Ts-273,\"degC respectively\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" As Reynolds Number is 20384 . The flow is Turbulent.\n",
"\n",
"\n",
" Heat Loss from the Duct over the Length L, q = -1313 W \n",
"\n",
" Heat flux and suface temperature at x=L is 304.3 W/m^2 & 50.7 degC respectively\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.7 Page 525"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"T1 = 125+273.; \t\t\t#[K] Chip Temperature 1\n",
"T2 = 25+273.; \t\t\t#[K] Chip Temperature 2\n",
"Ti = 5+273.; \t\t\t#[K] Inlet Temperature \n",
"D = .01; \t\t\t#[m] Diameter\n",
"L = .02; \t\t#[m] length\n",
"delP = 500*1000.; \t\t#[N/m^2] Pressure drop\n",
"#Dimensions\n",
"a = 40*math.pow(10,-6); \n",
"b = 160*math.pow(10,-6);\n",
"s = 40*math.pow(10,-6);\n",
"\n",
"#Table A.5 Ethylene Glycol Properties T = 288 K\n",
"rho = 1120.2; \t#[kg/m^3] Density\n",
"cp = 2359.; \t#[J/kg.K] Specific Heat\n",
"u = 2.82*math.pow(10,-2);\t#[N.s/m^2] Viscosity\n",
"k = 247*math.pow(10,-3); \t#[W/m.K] Thermal Conductivity\n",
"Pr = 269; \t\t#Prandtl number \n",
"#Table A.5 Ethylene Glycol Properties T = 338 K\n",
"rho2 = 1085.; \t#[kg/m^3] Density\n",
"cp2 = 2583.; \t#[J/kg.K] Specific Heat\n",
"u2 = .427*math.pow(10,-2);\t#[N.s/m^2] Viscosity\n",
"k2 = 261*math.pow(10,-3); \t#[W/m.K] Thermal Conductivity\n",
"Pr2 = 45.2; \t#Prandtl number\n",
"#calculations\n",
"P = 2*a+2*b; \t#Perimeter of microchannel\n",
"Dh = 4*a*b/P; \t#Hydraulic Diameter\n",
"\n",
"um2 = 2/73.*Dh*Dh/u2*delP/L;#[[m/s] Equation 8.22a\n",
"Re2 = um2*Dh*rho2/u2; #Reynolds Number\n",
"xfdh2 = .05*Dh*Re2; \t#[m] From Equation 8.3\n",
"xfdr2 = xfdh2*Pr2; \t#[m] From Equation 8.23\n",
"m2 = rho2*a*b*um2; \t#[kg/s]\n",
"Nu2 = 4.44; \t\t#Nusselt Number from Table 8.1\n",
"h2 = Nu2*k2/Dh; \t\t#[W/m^2.K] Convection Coeff\n",
"Tc2 = 124+273.; \t\t#[K]\n",
"xc2 = m2/P*cp2/h2*2.303*math.log10((T1-Ti)/(T1-Tc2));\n",
"tc2 = xc2/um2;\n",
"\n",
"um = 2/73.*Dh*Dh/u*delP/L; #[[m/s] Equation 8.22a\n",
"Re = um*Dh*rho/u; \t#Reynolds Number\n",
"xfdh = .05*Dh*Re; \t#[m] From Equation 8.3\n",
"xfdr = xfdh*Pr; \t\t#[m] From Equation 8.23\n",
"m = rho2*a*b*um; \t#[kg/s]\n",
"Nu = 4.44; \t\t#Nusselt Number from Table 8.1\n",
"h = Nu*k/Dh; \t\t#[W/m^2.K] Convection Coeff\n",
"Tc = 24+273.; \t\t#[K]\n",
"xc = m/P*cp/h*2.303*math.log10((T2-Ti)/(T2-Tc));\n",
"tc = xc/um;\n",
"\n",
"#results\n",
"print '%s %.1f %s' %(\"\\nTemp in case 2= \",T2-273,\" [degC]\")\n",
"print '%s %.1f %s' %(\"\\nTemp in case 1= \",T1-273,\" [degC]\")\n",
"print '%s %.3f %s' %(\"\\nFlow rate in case 2 = \",um2,\"[m/s]\")\n",
"print '%s %.3f %s' %(\"\\nFlow rate in case 1 = \",um,\"[m/s]\")\n",
"print '%s %.1f' %(\"\\nReynolds number in case 2 = \",Re2)\n",
"print '%s %.1f' %(\"\\nReynolds number in case 1 = \",Re)\n",
"print '%s %.1f' %(\"\\nHydrodynamic entrance Length [m] =\",xfdh)\n",
"print '%s %.1f' %(\"\\nHydrodynamic entrance Length in case 2 [m] =\",xfdh2) \n",
"print '%s %.1e' %(\"\\nThermal entrance Length [m] = \",xfdr)\n",
"print '%s %.1e' %(\"\\nThermal entrance Length in case 2 [m] = \",xfdr2)\n",
"print '%s %.2e' %(\"\\nMass Flow rate [kg/s] = \",m)\n",
"print '%s %.2e' %(\"\\nMass Flow rate in case 2 [kg/s] = \",m2)\n",
"print '%s %.2e' %(\"\\nConvective Coeff [W/m^2.K] = \",h)\n",
"print '%s %.2e' %(\"\\nConvective Coeff in case 2 [W/m^2.K] = \",h2)\n",
"print '%s %.2e' %(\"\\nTransition Length [m] = \",xc)\n",
"print '%s %.2e' %(\"\\nTransition Length in case 2 [m] = \",xc2)\n",
"print '%s %.3f' %(\"\\nRequired Time [s] = \",tc)\n",
"print '%s %.3f' %(\"\\nRequired Time in case 2 [s] = \",tc2)\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Temp in case 2= 25.0 [degC]\n",
"\n",
"Temp in case 1= 125.0 [degC]\n",
"\n",
"Flow rate in case 2 = 0.657 [m/s]\n",
"\n",
"Flow rate in case 1 = 0.099 [m/s]\n",
"\n",
"Reynolds number in case 2 = 10.7\n",
"\n",
"Reynolds number in case 1 = 0.3\n",
"\n",
"Hydrodynamic entrance Length [m] = 0.0\n",
"\n",
"Hydrodynamic entrance Length in case 2 [m] = 0.0\n",
"\n",
"Thermal entrance Length [m] = 2.2e-04\n",
"\n",
"Thermal entrance Length in case 2 [m] = 1.5e-03\n",
"\n",
"Mass Flow rate [kg/s] = 6.91e-07\n",
"\n",
"Mass Flow rate in case 2 [kg/s] = 4.56e-06\n",
"\n",
"Convective Coeff [W/m^2.K] = 1.71e+04\n",
"\n",
"Convective Coeff in case 2 [W/m^2.K] = 1.81e+04\n",
"\n",
"Transition Length [m] = 7.12e-04\n",
"\n",
"Transition Length in case 2 [m] = 7.79e-03\n",
"\n",
"Required Time [s] = 0.007\n",
"\n",
"Required Time in case 2 [s] = 0.012\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8 Page 529"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#Operating Conditions\n",
"m = .0003; \t\t#[kg/s] mass flow rate of water\n",
"T = 25+273; \t\t\t\t#[K] Temperature of surrounding and tube\n",
"D = .01; \t\t\t#[m] Diameter\n",
"L = 1; \t\t\t#[m] length\n",
"#calculations and results\n",
"#Table A.4 Air Properties T = 298 K\n",
"uv = 15.7*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n",
"u = 18.36*math.pow(10,-6); #[N.s/m^2] Viscosity\n",
"#Table A.8 Ammonia-Air Properties T = 298 K\n",
"Dab = .28*math.pow(10,-4); #[m^2/s] Diffusion coeff\n",
"Sc = .56;\n",
"\n",
"Re = m*4/(math.pi*D*u);\n",
"print '%s %d %s' %(\"\\n As Reynolds Number is\",Re,\". The flow is Laminar.\");\n",
"\n",
"#Using Equation 8.57\n",
"Sh = 1.86*math.pow((Re*Sc*D/L),.3334);\n",
"h = Sh*Dab/D;\n",
"print '%s %.3f %s' %(\"\\n Average mass trasnfer convection coefficient for the tube\",h,\"m/s\");\n",
"\n",
"#END"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" As Reynolds Number is 2080 . The flow is Laminar.\n",
"\n",
" Average mass trasnfer convection coefficient for the tube 0.012 m/s\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}