{ "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": {} } ] }