{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

# Chapter 17: HEAT TRANSFER BY CONVECTION

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.01, page: 408

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "from scipy import integrate\n", "\n", "# Initialization of Variable\n", "\n", "#calculations:\n", "x2 = lambda x: x**-0.1\n", "ratio = integrate.quad(x2,0,1)\n", "\n", "#Results\n", "print \"The ratio of the average heat transfer coefficient is\", round(ratio,2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The ratio of the average heat transfer coefficient is 1.11\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.02, page: 415

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "Tinf = 300 #degC\n", "uinf = 10 #m/s\n", "L = 0.5 #m\n", "Ts = 27 #degC\n", "\n", "#calculations:\n", "#from Table HT-3\n", "Tf = 437 #K\n", "P = 1 #atm\n", "v = 30.84E-6 #m2/s\n", "k = 36.4E-3 #W/m.K\n", "Pr = 0.687\n", "#Reynolds number\n", "ReL = uinf*L/v\n", "#Correlation\n", "NuL = 0.664*ReL**0.5*Pr**(1/3)\n", "#average convection coefficient\n", "hbar = NuL*k/L\n", "#cooling rate per unit width of plate\n", "q1 = hbar*L*(Tinf - Ts)\n", "\n", "#Result\n", "print \"cooling rate per unit width of plate is\", round(q1,0),\"W/m\"\n", "#answer wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "cooling rate per unit width of plate is 2344.0 W/m\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.03, page: 416

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "Tinf = 25 #degC\n", "uinf = 60 #m/s\n", "Ts = 230 #degC\n", "d = 50 #mm\n", "L4 = 200 #mm\n", "L5 = 250 #mm\n", "\n", "#calculations:\n", "#from Table HT-3\n", "Tf = 400 #K\n", "P = 1 #atm\n", "v = 26.41E-6 #m2/s\n", "k = 0.0338 #W/m\n", "Pr = 0.690\n", "#reynolds num\n", "Re4 = uinf*L4*1E-3/v\n", "Re5 = uinf*L5*1E-3/v\n", "#\n", "h14bar = 0.664*Re4**0.5*Pr**(1/3)*k/(L4*1E-3)\n", "h15bar = k*(0.037*Re5**0.8 - 871)*Pr**(1/3)/(L5*1E-3)\n", "#the electrical power required\n", "qconv5 = (h15bar*L5*1E-3 - h14bar*L4*1E-3)*1*(Ts - Tinf)\n", "\n", "#Results\n", "print \"Electrical power required for the fifth heater is\", round(qconv5,0),\"W\"\n", "#answer wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Electrical power required for the fifth heater is 1018.0 W\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.04, page: 419

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "#Initialization of Variable\n", "Tinf = 26.2 #degC\n", "uinf = 10 #m/s\n", "Ts = 128.4 #degC\n", "Pe = 46.0 #W\n", "qconv = 0.85*Pe\n", "D = 12.7 #mm\n", "L = 94 #mm\n", "\n", "#calculations:\n", "#From Table HT-3\n", "Tf = 350 #K\n", "v = 20.92E-6 #m2/s\n", "k = 30E-3 #W/m.K\n", "Pr = 0.7\n", "#Area\n", "A = math.pi*D*L*1E-6\n", "#convection heat transfer coefficient\n", "hbar1 = qconv/(A*(Ts - Tinf))\n", "#reynolds num\n", "ReD = uinf*D*1E-3/v\n", "#Churchill-Bernstein correlation\n", "NuDbar = 0.3 + 0.62*ReD**0.5*Pr**(1/3)/(1 + (0.4/Pr)**(2/3))**0.25*(1 + (ReD/282000)**(5/8))**0.8\n", "#the convection coefficient\n", "hbar2 = NuDbar*k/(D*1E-3)\n", "\n", "#Results\n", "print \"Convection coefficient associated with the operating condition is\",round(hbar1,0),\"W/m2.K\"\n", "print \"Convection coefficient from an appropriate correlation is\", round(hbar2,0),\"W/m2.K\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Convection coefficient associated with the operating condition is 102.0 W/m2.K\n", "Convection coefficient from an appropriate correlation is 96.0 W/m2.K\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.05, page: 421

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "Pinf = 1 #atm\n", "uinf = 10 #m/s\n", "Tinf = 23 #degC\n", "D = 10 #mm\n", "Ti = 75 #degC\n", "Tt = 35 #degC\n", "\n", "#calculations:\n", "#from Table HT-1\n", "pcu = 8933 #kg/m3\n", "ccu = 387 #J/kg.K\n", "kcu = 399 #W/m.K\n", "#from Table HT-3\n", "muTinf = 181.6E-7 #Ns/m2\n", "v = 15.36E-6 #m2/s\n", "k = 0.0258 #W/m.K\n", "Pr = 0.709\n", "muTs = 197.8E-7 #N.s/m2\n", "#reynolds Num\n", "ReD = uinf*D*1E-3/v\n", "#the average convection coefficient\n", "NuDbar = 2 + (0.4*ReD**0.5 + 0.06*ReD**(2/3))*Pr**0.4*(muTinf/muTs)**0.25\n", "hbar = NuDbar*k/D/1E-3\n", "#time\n", "t = pcu*ccu*D*1E-3/6/hbar*math.log((Ti - Tinf)/(Tt - Tinf))\n", "\n", "#Results\n", "print \"cooling time required is\", round(t,1),\"s\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "cooling time required is 69.1 s\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.06, page: 429

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "mdot = 0.1 #kg/s\n", "D0 = 0.040 #m\n", "Di = 0.020 #m\n", "Tmi = 20 #degC\n", "qdot = 1E6 #W/m3\n", "Ts0 = 70 #degC\n", "Tm0 = 60 #degC\n", "\n", "#calculations:\n", "#from Table HT-5\n", "Cp = 4179 #J/kg.K\n", "mu = 6.57E-4 #N.s/m2\n", "#required tube length\n", "L = 4*mdot*Cp*(Tm0 - Tmi)/(math.pi*(D0**2 - Di**2)*qdot)\n", "#Reynolds num\n", "ReD = 4*mdot/math.pi/Di/mu\n", "#local coefficient at the outlet\n", "qs2 = qdot*(D0**2 - Di**2)/4/Di\n", "h0 = qs2/(Ts0 - Tm0)\n", "\n", "#Results\n", "print \"tube length is\", round(L,1),\"m\"\n", "print \"reynolds number is\", round(ReD,0),\",the flow is fully turbulant\"\n", "print \"local convection coefficient at outlet is\", round(h0,0),\"W/m2.K\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "tube length is 17.7 m\n", "reynolds number is 9690.0 ,the flow is fully turbulant\n", "local convection coefficient at outlet is 1500.0 W/m2.K\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.07, page: 432

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "mdot = 0.25 #kg/s\n", "Tmi = 15 #degC\n", "D = 0.05 #m\n", "Ts = 100 #degC\n", "Tm0 = 57 #degC\n", "L = 6 #m\n", "\n", "#calculations:\n", "#from Table HT-5\n", "Cp = 4178 #J/kg.K\n", "#log mean temp diff\n", "dTlm = ((Ts - Tm0) - (Ts - Tmi))/math.log((Ts-Tm0)/(Ts-Tmi))\n", "#avg Convection Coeff\n", "hbar = mdot*Cp*(Tm0 - Tmi)/math.pi/D/L/dTlm\n", "\n", "#Results\n", "print \"Average convection heat transfer coefficient is\",round(hbar,0),\"W/m2.K\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Average convection heat transfer coefficient is 755.0 W/m2.K\n" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.08, page: 433

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "Tinf = 37 #degC\n", "h0bar = 2 #W/m2.K\n", "Tmi = 7 #degC\n", "D = 0.3 #m\n", "L = 15 #m\n", "mdot = 0.05 #kg/s\n", "hibar = 3 #W/m2.K\n", "\n", "#calculations:\n", "Cp = 1007 #J/kg.K\n", "#overall heat transfer\n", "Ubar = (1/hibar + 1/h0bar)**-1\n", "#Area\n", "As = math.pi*D*L\n", "#Temp\n", "Tm0 = Tinf - (Tinf - Tmi)*math.e**(-1*Ubar*As/(mdot*Cp))\n", "#heat transfer rate\n", "q = mdot*Cp*(Tm0 - Tmi)\n", "\n", "#Results\n", "print \"Chilled air exit temperature and the heat transfer rate are\", round(Tm0,1),\"degC and\",round(q,0),\"W respectively\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Chilled air exit temperature and the heat transfer rate are 15.6 degC and 432.0 W respectively\n" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.09, page: 434

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "D = 0.06 #m\n", "mdot = 0.01 #kg/s\n", "Tmi = 20 #degC\n", "Tmo = 80 #degC\n", "qs2 = 2000 #W/m2\n", "\n", "#calculations:\n", "Cp = 4181 #J/kg.K\n", "k = 0.670 #W/m.K\n", "mu = 352E-6 #Ns/m2\n", "Pr = 2.2\n", "#Length\n", "L = mdot*Cp*(Tmo - Tmi)/qs2/math.pi/D\n", "#Reynolds num\n", "ReD = 4*mdot/math.pi/D/mu\n", "#local coeff\n", "h = 4.36*k/D\n", "#surface temp at outlet\n", "Tso = qs2/h + Tmo\n", "\n", "#Results\n", "print \"a)tube length\", round(L,2),\"m\"\n", "print \"b)surface temperature at outlet section is\", round(Tso,0),\"degC\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a)tube length 6.65 m\n", "b)surface temperature at outlet section is 121.0 degC\n" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.10, page: 436

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "mdot = 2 #kg/s\n", "Tmi = 25 #degC\n", "Ts = 95 #degC\n", "L = 4 #m\n", "D = 0.04 #m\n", "\n", "#calculations:\n", "Cp = 4178 #J/kg.K\n", "mu = 695E-6 #Ns/m2\n", "k = 0.628 #W/m.K\n", "Pr = 4.62\n", "mus = 296E-6 #Ns/m2\n", "#Reynolds NUm\n", "ReD = 4*mdot/math.pi/D/mu\n", "#avg coeff\n", "hbar = (0.023*ReD**0.8*Pr*0.4)*k/D\n", "#Temp\n", "Tmo = Ts - (Ts - Tmi)*math.e**(-1*math.pi*D*L*hbar/mdot/Cp)\n", "#heat rate\n", "q = mdot*Cp*(Tmo - Tmi)\n", "\n", "#Results\n", "print \"outlet water temperature is\", round(Tmo,1),\"degC\"\n", "print \"rate of heat transfer to the water is\", round(q/1000,0),\"kW\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "outlet water temperature is 46.9 degC\n", "rate of heat transfer to the water is 183.0 kW\n" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.11, page: 441

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "L = 0.71 #m\n", "w = 1.02 #m\n", "Ts = 232 #degC\n", "Tinf = 23 #degC\n", "g = 9.8 #m/s2\n", "\n", "#calculations:\n", "k = 33.8E-3 #W/m.K\n", "v = 26.4E-6 #m2/s\n", "a = 38.3E-6 #m2/s\n", "Pr = 0.69\n", "b = 0.0025 #1/K\n", "#Rayleigh num\n", "RaL = g*b*(Ts - Tinf)*L**3/a/v\n", "#Churchill-Chu correlation\n", "NuLbar = (0.825 + 0.387*RaL**(1/6)/(1 + (0.492/Pr)**(9/16))**(8/27))**2\n", "#average convection coefficient\n", "hbar = NuLbar*k/L\n", "#the heat transfer by free convection between the firescreen and room air is\n", "q = hbar*L*w*(Ts - Tinf)\n", "\n", "#Results\n", "print \"the heat transfer by free convection between the firescreen and room air is\", round(q,0),\"W\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the heat transfer by free convection between the firescreen and room air is 1060.0 W\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.12, page: 443

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "Tinf = 300 #K\n", "Tsur = 300 #K\n", "Ts = 350 #K\n", "e = 0.25\n", "s1 = 1.2 #m\n", "s2 = 1.2 #m\n", "Tf = 325 #K\n", "g = 9.8 #m/s2\n", "sigma = 5.67E-8 #W/m2.K4\n", "\n", "#calculations:\n", "v = 18.4E-6 #m2/s\n", "k = 0.028 #W/m.K\n", "a = 26.2E-6 #m2/s\n", "# Area\n", "As = s1*s2\n", "#perimeter\n", "P = 4*s1\n", "#characteristic length\n", "L = As/P\n", "#Rayleigh num\n", "b = 1/Tf\n", "RaL = g*b*(Ts - Tinf)*L**3/v/a\n", "#avg conv coeff\n", "hbar = (0.15*RaL**(1/3))*k/L\n", "#allowable electrical power\n", "Pe = hbar*As*(Ts - Tinf) + e*As*sigma*(Ts**4 - Tsur**4)\n", "\n", "#Results\n", "print \"Maximum allowable electrical power dissipation is\", round(Pe,0),\"W\"\n", "#answer wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum allowable electrical power dissipation is 583.0 W\n" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.13, page: 445

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "D = 0.1 #m\n", "Tinf = 23 #degC\n", "Tsur = 23 #degC\n", "Ts = 165 #degC\n", "e = 0.85\n", "g = 9.8 #m/s2\n", "sigma = 5.67E-8 #W/m2.K4\n", "\n", "#calculations:\n", "k = 0.0313 #W/m.K\n", "v = 22.8E-6 #m2/s\n", "a = 32.8E-6 #m2/s\n", "Pr = 0.697\n", "b = 2.725E-3 #1/K\n", "#Rayleigh number\n", "RaD = g*b*(Ts - Tinf)*D**3/v/a\n", "#average convection coefficient\n", "hbar = (0.6 + 0.387*RaD**(1/6)/(1 + (0.559/Pr)**(9/16))**(8/27))**2*k/D\n", "#total heat transfer rate from the pipe is\n", "q1 = hbar*math.pi*D*(Ts - Tinf) + e*math.pi*D*sigma*((Ts + 273)**4 - (Tsur+273)**4)\n", "\n", "#Results\n", "print \"Heat transfer from the pipe per unit length is\", round(q1,0),\"W/m\"\n", "#anwer wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat transfer from the pipe per unit length is 763.0 W/m\n" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.14, page: 452

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "ho = 40 #W/m2.K\n", "Do = 0.045 #m\n", "Di = 0.025 #m\n", "Thi = 100 #degC\n", "mhdot = 0.1 #kg/s\n", "Tho = 60 #degC\n", "mcdot = 0.2 #kg/s\n", "Tci = 30 #degC\n", "\n", "#calculations:\n", "Cpc = 4178 #J/kg.K\n", "mu = 725E-6 #Ns/m2\n", "k = 0.625 #W/m.K\n", "Pr = 4.85\n", "Cph = 2131 #J/kg.K\n", "#heat transfer rate\n", "q = mhdot*Cph*(Thi - Tho)\n", "#water outlet temperature\n", "Tco = q/mcdot/Cpc + Tci\n", "#log mean temperature difference\n", "dTlm = ((Thi - Tco) - (Tho - Tci))/math.log((Thi-Tco)/(Tho-Tci))\n", "#reynolds num\n", "ReD = 4*mcdot/math.pi/Di/mu\n", "#conv coeff\n", "hi = (0.023*ReD**0.8*Pr**0.4)*k/Di\n", "#overall heat transfer coefficien\n", "U = 1/(1/hi + 1/ho)\n", "#the required length of the exchanger\n", "L = q/U/math.pi/Di/dTlm\n", "\n", "#Results\n", "print \"Tube length to achieve a desired hot fluid outlet temperature is\", round(L,1),\"m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Tube length to achieve a desired hot fluid outlet temperature is 63.9 m\n" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 17.15, page: 454

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "ho = 400 #W/m2.K\n", "n = 10\n", "D = 0.025 #m\n", "Thi = 160 #degC\n", "Tho = 100 #degC\n", "Tco = 85 #degC\n", "Tci = 15 #degC\n", "mcdot = 2.5 #kg/s\n", "\n", "#calculations:\n", "Cph = 2350 #J/kg.K\n", "Cpc = 4181 #J/kg.K\n", "mu = 548E-6 #Ns/m2\n", "k = 0.643 #W/m.K\n", "Pr = 3.56\n", "#heat transfer rate\n", "q = mcdot*Cpc*(Tco - Tci)\n", "#required flow rate\n", "mhdot = q/Cph/(Thi - Tho)\n", "#m1dot\n", "m1dot = mcdot/n\n", "#reynolds num\n", "ReD = 4*m1dot/math.pi/D/mu\n", "#conv coeff\n", "hi = (0.023*ReD**0.8*Pr**0.4)*k/D\n", "#overall Coeff\n", "U = 1/(1/ho + 1/hi)\n", "#\n", "R = (Thi - Tho)/(Tco - Tci)\n", "P = (Tco - Tci)/(Thi - Tci)\n", "F = 0.87\n", "#log mean temperature difference\n", "dTlm = ((Thi - Tco) - (Tho - Tci))/math.log((Thi-Tco)/(Tho-Tci))\n", "#the required tube length\n", "L = q/U/n/math.pi/D/F/dTlm\n", "\n", "#Results\n", "print \"Oil flow rate required is\", round(mhdot,2),\"kg/s\"\n", "print \"Tube length required is\", round(L,1),\"m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Oil flow rate required is 5.19 kg/s\n", "Tube length required is 37.9 m\n" ] } ], "prompt_number": 15 } ], "metadata": {} } ] }