{ "metadata": { "name": "", "signature": "sha256:6f27b63789233dbcd6b595c8e65a2bfbfddf8fdce1aec80ae9bb6f8c99f32cf1" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 6: Forced Convection Inside Tubes And Ducts" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.1: Page 365" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.1 \"\n", "\n", "#Inlet temperature in degree C\n", "Tin = 10;\n", "#Outlet temperature in degree C\n", "Tout = 40;\n", "#Diameter in m\n", "D = 0.02;\n", "#Massflow rate in kg/s\n", "m = 0.01;\n", "#Heat flux in W/m2\n", "q = 15000;\n", "\n", "#From Table 13 in Appendix 2, the appropriate properties of water at an\n", "#average temperature between inlet and outlet of 25\u00b0C are\n", "\n", "#Density in kg/m3\n", "rho = 997;\n", "#Specific heat in J/kgK\n", "c = 4180;\n", "#Thermal conductivity in W/mK\n", "k = 0.608;\n", "#Dynamic vismath.cosity in Ns/m2\n", "mu = 0.00091;\n", "\n", "print \"Reynolds Number is\"\n", "#Reynolds number\n", "Re = (4*m)/((math.pi*D)*mu)\n", "print int(Re)\n", "print \"Flow is Laminar\"\n", "\n", "#Since the thermal-boundary condition is one of uniform heat flux, Nu\u0005= 4.36 from Eq. (6.31)\n", "#Nusselt number\n", "Nu = 4.36;\n", "print \"Heat transfer coefficient in W/m2K\"\n", "#Heat transfer coefficient in W/m2K\n", "hc = (Nu*k)/D\n", "print int(hc)\n", "\n", "#The length of pipe needed for a 30\u00b0C temperature rise is obtained from a heat balance\n", "print \"Length of pipe in m\"\n", "#Length of pipe in m\n", "L = ((m*c)*(Tout-Tin))/((math.pi*D)*q)\n", "print round(L,2)\n", "\n", "print \"Inner surface temperature at outlet in degree C\"\n", "#Inner surface temperature at outlet in degree C\n", "Ts = q/hc+Tout\n", "print round(Ts,2)\n", "\n", "#The friction factor is found from Eq. (6.18)\n", "print \"Friction factor is\"\n", "#Friction factor is\n", "f = 64/Re\n", "print round(f,4)\n", "#Average velocity in m/s\n", "U = (4*m)/(((rho*math.pi)*D)*D);\n", "print \"The pressure drop in the pipe in N/m2\"\n", "#The pressure drop in the pipe in N/m2\n", "deltaP = ((((f*L)*rho)*U)*U)/(D*2)\n", "print round(deltaP,1)\n", "\n", "#Efficiency\n", "n = 0.5;\n", "#The pumping power P is obtained from Eq. 6.19\n", "print \"Pumping power in W is\"\n", "#Pumping power in W\n", "P = (m*deltaP)/(rho*n)\n", "print round(P,6)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.1 \n", "Reynolds Number is\n", "699\n", "Flow is Laminar\n", "Heat transfer coefficient in W/m2K\n", "132\n", "Length of pipe in m\n", "1.33\n", "Inner surface temperature at outlet in degree C\n", "153.17\n", "Friction factor is\n", "0.0915\n", "The pressure drop in the pipe in N/m2\n", "3.1\n", "Pumping power in W is\n", "6.2e-05\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.2: Page 369" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.2 \"\n", "\n", "#Diameter in m\n", "D = 0.01;\n", "#Wall thickness in m\n", "t = 0.02/100;\n", "#Massflow rate in kg/s\n", "m = 0.05;\n", "#Inlet temperature in degree C\n", "Tin = 35;\n", "#Outlet temperature in degree C\n", "Tout = 45.0;\n", "#Assuming a constant tube temp. in degree C\n", "T = 100.0;\n", "\n", "#From Table 16 in Appendix 2, we get the following properties for oil at\n", "#40\u00b0C\n", "\n", "#Density in kg/m3\n", "rho = 876.0;\n", "#Specific heat in J/kgK\n", "c = 1964.0;\n", "#Thermal conductivity in W/mK\n", "k = 0.144;\n", "#Dynamic vismath.cosity in Ns/m2\n", "mu = 0.21;\n", "#Prandtl number\n", "Pr = 2870.0;\n", "\n", "#Reynolds Number is\n", "Re = (4*m)/((math.pi*D)*mu);\n", "\n", "#For laminar flow and constant temperature assumption\n", "#Nusselt number\n", "Nu = 3.66;\n", "#Heat transfer coefficient in W/m2K\n", "hc = (Nu*k)/D;\n", "#Heat transfer rate in W\n", "q = (m*c)*(Tout-Tin);\n", "#LMTD in degree K\n", "LMTD = (T-Tout-(T-Tin))/math.log((T-Tout)/(T-Tin));\n", "\n", "print \"Length of pipe in m is\"\n", "#Length of pipe in m\n", "L = q/(((math.pi*D)*hc)*LMTD)\n", "print round(L,2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.2 \n", "Length of pipe in m is\n", "9.91\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.3: Page 375" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.3 \"\n", "\n", "#Bulk temperature in degree K\n", "T = 293;\n", "#Side of square duct in m\n", "b = 0.1;\n", "#Length of square duct in m\n", "L = 5;\n", "#Wall temperature in degree K\n", "Tw = 300;\n", "#Velocity in m/s\n", "U = 0.03;\n", "\n", "#Hydraulic diameter in m\n", "D = 4*((b*b)/(4*b));\n", "\n", "#Physical properties at 293 K from Table 19 in Appendix 2 are\n", "\n", "#Density in kg/m3\n", "rho = 810;\n", "#Specific heat in J/kgK\n", "c = 2366;\n", "#Thermal conductivity in W/mK\n", "k = 0.167;\n", "#Dynamic vismath.cosity in Ns/m2\n", "mu = 0.00295;\n", "#Prandtl number\n", "Pr = 50.8;\n", "\n", "#Reynolds Number is\n", "Re = ((U*D)*rho)/mu;\n", "\n", "#Hence, the flow is laminar. Assuming fully developed flow, we get the\n", "#Nusselt number for a uniform wall temperature from Table 6.1\n", "\n", "Nu = 2.98;\n", "#Heat transfer coefficient in W/m2K\n", "hc = (Nu*k)/D;\n", "\n", "#Similarly, from Table 6.1, the product Re*f=56.91\n", "\n", "print \"Friction factor is\"\n", "#Friction factor\n", "f = 56.91/Re\n", "print round(f,4)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.3 \n", "Friction factor is\n", "0.0691\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.4: Page 378" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.4 \"\n", "\n", "#Temperature of device camath.sing in degree K\n", "Ts = 353;\n", "#Length of holes in m\n", "L = 0.3;\n", "#Diameter of holes in m\n", "D = 0.00254;\n", "#Inlet temperature in degree K\n", "Tin = 333;\n", "#Velocity in m/s\n", "U = 0.2;\n", "\n", "#The properties of water at 333 K, from Table 13 in Appendix 2, are\n", "\n", "#Density in kg/m3\n", "rho = 983;\n", "#Specific heat in J/kgK\n", "c = 4181;\n", "#Thermal conductivity in W/mK\n", "k = 0.658;\n", "#Dynamic vismath.cosity in Ns/m2\n", "mu = 0.000472;\n", "#Prandtl number\n", "Pr = 3;\n", "\n", "#Reynolds Number is\n", "Re = ((U*D)*rho)/mu;\n", "\n", "if (((Re*Pr)*D)/L)>10 :\n", " #Eq. (6.42) can be used to evaluate the heat transfer coefficient.\n", " #But math.since the mean bulk temperature is not known, we shall evaluate all the properties first at the inlet bulk temperature Tb1 ,\n", " #then determine an exit bulk temperature, and then make a second iteration to obtain a more precise value.\n", "\n", " #At the wall temperature of 353 K\n", " #Vismath.cosity in SI units\n", " mus = 0.000352; \n", " #From Eq. (6.42)\n", " #Nusselt number\n", " Nu = (1.86*((((Re*Pr)*D)/L)**0.33))*((mu/mus)**0.14);\n", " #Heat transfer coefficient in W/m2K\n", " hc = (Nu*k)/D;\n", " #mass flow rate in kg/s\n", " m = ((((rho*math.pi)*D)*D)*U)/4;\n", "\n", " #Inserting the calculated values for hc and m into Energy balance equation, along with Tb1 and Ts and\n", " #gives Tb2=345K\n", "\n", " #For the second iteration, we shall evaluate all properties at the new average bulk temperature\n", " #Bulk temp. in degree C\n", " Tb = (345.0+Tin)/2;\n", "\n", " #At this temperature, we get from Table 13 in Appendix 2:\n", " #Density in kg/m3\n", " rho = 980.0;\n", " #Specific heat in J/kgK\n", " c = 4185;\n", " #Thermal conductivity in W/mK\n", " k = 0.662;\n", " #Dynamic vismath.cosity in Ns/m2\n", " mu = 0.000436;\n", " #Prandtl number\n", " Pr = 2.78;\n", "\n", " #New reynolds Number is\n", " Re = ((U*D)*rho)/mu;\n", "\n", " #With this value of Re, the heat transfer coefficient can now be calculated.\n", " #We obtain the following similarly\n", " #Nusselt number\n", " Nu = 5.67;\n", " #Heat transfer coefficient in W/m2K\n", " hc = (Nu*k)/D;\n", " #Similarly putting this value in energy balance yields\n", " #Bulk temperature in degree K\n", " Tb2 = 345; \n", "\n", " print \"Outlet temperature in degree K\"\n", " #Outlet temperature in degree K\n", " print round(Tb2,2)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.4 \n", "Outlet temperature in degree K\n", "345.0\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.5: Page 389" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.5 \"\n", "\n", "#Velocity in ft/s\n", "U = 10.0;\n", "#Outer diameter in inches\n", "D = 1.5;\n", "#Inner diameter in inches\n", "d = 1.0;\n", "#Temperature of water in degree F\n", "Tw = 180.0;\n", "#Temperature of wall in degree F\n", "Twall = 100.0;\n", "\n", "#The hydraulic diameter D for this geometry is 0.5 in.\n", "D = 0.5;\n", "\n", "#Umath.sing properties given in the table provided\n", "\n", "#Reynolds number\n", "Re = (((U*D)*3600)*60.8)/(12*0.75);\n", "#Prandtl number\n", "Pr = (1*0.75)/0.39;\n", "#The Nusselt number according to the Dittus-Boelter correlation [Eq. (6.60)] \n", "Nu = (0.023*(125000**0.8))*(Pr**0.3);\n", "print 'The Nusselt number according to the Dittus-Boelter correlation comes out to be \\n',int(Nu)\n", "\n", "#Umath.sing the Sieder-Tate correlation [Eq. (6.61)]\n", "#Nusselt number\n", "Nu = 358;\n", "print 'The Nusselt number according to the Sieder-Tate correlation comes out to be \\n',Nu\n", "\n", "#The Petukhov-Popov correlation [Eq. (6.63)] gives\n", "#Friction factor\n", "f = (1.82*log10(125000)-1.64)**(-2);\n", "#K1 of Eq. 6.63\n", "K1 = 1+3.4*f;\n", "#K2 of Eq. 6.63\n", "K2 = 11.7+1.8/(Pr**0.33);\n", "#Nusselt number\n", "Nu = 370;\n", "\n", "#The Sleicher-Rouse correlation [Eq. (6.64)] yields\n", "#a of Eq. 6.64\n", "a = 0.852;\n", "#b of Eq. 6.64\n", "b = 1/3.0+0.5/math.exp(0.6*4.64);\n", "#Reynolds number\n", "Re = 82237;\n", "#Nusselt number\n", "Nu = 5+(0.015*(Re**a))*(4.64**b);\n", "print 'Nusselt number according to The Sleicher-Rouse correlation comes out to be \\n',int(Nu)\n", "\n", "print \"Assuming that the correct answer is Nu=370\"\n", "print \"The first two correlations underpredict by about 10% and 3.5%, respectively\"\n", "print \"while the Sleicher-Rouse method overpredicts by about 10.5%.\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.5 \n", "The Nusselt number according to the Dittus-Boelter correlation comes out to be \n", "334\n", "The Nusselt number according to the Sieder-Tate correlation comes out to be \n", "358\n", "Nusselt number according to The Sleicher-Rouse correlation comes out to be \n", "409\n", "Assuming that the correct answer is Nu=370\n", "The first two correlations underpredict by about 10% and 3.5%, respectively\n", "while the Sleicher-Rouse method overpredicts by about 10.5%.\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.6: Page 394" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.6 \"\n", "\n", "#Mass flow rate in kg/s\n", "m = 3;\n", "#Diameter of tube in m\n", "D = 5/100.0;\n", "#Temperature of fluid in degree K\n", "Tb = 473.0;\n", "#Temperature of wall in degree K\n", "Ts = 503.0;\n", "\n", "#Density in kg/m3\n", "rho = 7700.0;\n", "#Specific heat in J/kgK\n", "c = 130.0;\n", "#Thermal conductivity in W/mK\n", "k = 12.0;\n", "#Kinematic vismath.cosity in m2/s\n", "nu = 0.00000008;\n", "#Prandtl number\n", "Pr = 0.011;\n", "\n", "#The rate of heat transfer per unit temperature rise in W is\n", "q = (m*c)*1;\n", "\n", "#Reynolds Number is\n", "Re = (D*m)/(((((rho*math.pi)*D)*D)*nu)/4);\n", "\n", "#The heat transfer coefficient in W/m2K is obtained from Eq. (6.67)\n", "hc = ((k*0.625)*((Re*Pr)**0.4))/D;\n", "\n", "#Surface area in m2\n", "A = q/(hc*(Ts-Tb));\n", "\n", "print \"Required length of tube in m is\"\n", "#Required length of tube in m\n", "L = A/(math.pi*D)\n", "print round(L,4)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.6 \n", "Required length of tube in m is\n", "0.0307\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex6.7: Page 405" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "print \"Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.7 \"\n", "\n", "#Temperature of airstream in degree C\n", "Tair = 20;\n", "#Velocity of air in m/s\n", "U = 1.8;\n", "#Side of circuit in m\n", "L = 27/1000.0;\n", "#Spacing in the circuit in m\n", "H = 17/1000.0;\n", "\n", "#At 20\u00b0C, the properties of air from Table 28, Appendix 2, are \n", "\n", "#Density in kg/m3\n", "rho = 7700.0;\n", "#Specific heat in J/kgK\n", "c = 130.0;\n", "#Thermal conductivity in W/mK\n", "k = 0.0251;\n", "#Kinematic vismath.cosity in m2/s\n", "nu = 0.0000157;\n", "#Prandtl number\n", "Pr = 0.011;\n", "\n", "#Reynolds number\n", "Re = (U*H)/nu;\n", "\n", "#From Fig. (6.27), we see that the second integrated circuit is in the inlet region and estimate Nu2 =\u000529.\n", "#Nusselt number in second circuit\n", "Nu2 = 29;\n", "print \"Heat transfer coefficient along 2nd circuit in W/m2K\"\n", "#Heat transfer coefficient in W/m2K\n", "hc2 = (Nu2*k)/L\n", "print round(hc2)\n", "\n", "#The sixth integrated circuit is in the developed region and from Eq. (6.79)\n", "#Nusselt number in sixth circuit\n", "Nu6 = 21.7;\n", "print \"Heat transfer coefficient along 6th circuit in W/m2K\"\n", "##Heat transfer coefficient in W/m2K\n", "hc6 = (Nu6*k)/L\n", "print round(hc6,1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 6 Example # 6.7 \n", "Heat transfer coefficient along 2nd circuit in W/m2K\n", "27.0\n", "Heat transfer coefficient along 6th circuit in W/m2K\n", "20.2\n" ] } ], "prompt_number": 27 } ], "metadata": {} } ] }