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diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch5.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch5.ipynb new file mode 100644 index 00000000..77c2b9da --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch5.ipynb @@ -0,0 +1,431 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5 : free convection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1 Page No : 153" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The rate of heat loss is 267 W\n" + ] + } + ], + "source": [ + "# Variables\n", + "T1 = 65. \t\t\t#C, furnace temp.\n", + "T2 = 25. \t\t\t#C, ambient temp.\n", + "h = 1.5 \t\t\t#m, height of door\n", + "w = 1. \t\t\t#m, width of door\n", + "Tf = (T1+T2)/2 \t\t\t#c, average air film temp.\n", + "\n", + "# Calculations\n", + "Pr = 0.695 \t\t\t#Prandtl no.\n", + "mu = 1.85*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "beeta = 1/(Tf+273) \t\t\t#K**-1. coefficient of volumetric expension\n", + "k = 0.028 \t\t\t#W/m C, thermal conductivity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "Grl = g*beeta*(T1-T2)*h**3/(mu**2) \t\t\t#Grashof no.\n", + "Ral = Grl*Pr \t\t\t#Rayleigh no.\n", + "#Nusslet no.\n", + "Nul = (0.825+(0.387*(Ral)**(1./6))/(1+(0.492/Pr)**(9./16))**(8./27))**2 \n", + "hav = Nul*k/h \t\t\t#average heat transfer coefficient\n", + "Ad = h*w \t\t\t#m**2, door area\n", + "dt = T1-T2 \t\t\t#temp. driving force\n", + "q = hav*Ad*dt \t\t\t#W,rate of heat loss\n", + "\n", + "# Results\n", + "print \"The rate of heat loss is %.0f W\"%(q)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2 Page No : 154" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the steady state temp. of the plate is 61.6 C\n" + ] + } + ], + "source": [ + "# Variables\n", + "T1 = 60. \t\t\t#C, plate temp.\n", + "T2 = 25. \t\t\t#C, ambient temp.\n", + "h = 1.\n", + "w = 1. \t\t\t#m, width of door\n", + "q = 170. \t\t\t#W, rate of heat transfer\n", + "Tf = (T1+T2)/2 \t\t\t#c, average air film temp.\n", + "#Properties of air at Tf\n", + "Pr = 0.7 \t\t\t#Prandtl no.\n", + "mu = 1.85*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "beeta = 1./(Tf+273) \t\t\t#K**-1. coefficient of volumetric expension\n", + "k = 0.028 \t\t\t#W/m C, thermal conductivity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "\n", + "#Calculation\n", + "A = h*w \t\t\t#m**2, plate area\n", + "P = 2*(h+w) \t\t\t#m,perimeter of plate \n", + "L = A/P \t\t\t#m characteristic length\n", + "Grl = g*beeta*(T1-T2)*L**3/(mu**2) \t\t\t#Grashof no.\n", + "Ral = Grl*Pr \t\t\t#Rayleigh no.\n", + "#Nusslet no.\n", + "Nul = 0.54*(Ral)**(1./4) \t\t\t#Nusslet no.\n", + "hav = Nul*k/L \t\t\t#average heat transfer coefficient\n", + "Ts = q/(hav*A)+T2\n", + "\n", + "# Results\n", + "print \"the steady state temp. of the plate is %.1f C\"%(Ts)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3 Page No : 156" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The required time for cooling is 2.30 hr\n" + ] + } + ], + "source": [ + "import math \n", + "from scipy.integrate import quad \n", + "# Variables\n", + "d = 0.0254 \t\t\t#m, diameter of steel rod\n", + "l = 0.4 \t\t\t#m, length of rod\n", + "T1 = 80. \t\t\t#C, initial temp.\n", + "T2 = 30. \t\t\t#C, ambient temp.\n", + "T3 = 35. \t\t\t#c, temp. after cooling\n", + "rho = 7800. \t\t\t#kg/m**3 ,density of steel rod\n", + "cp = 0.473 \t\t\t#kj/kg C. specific heat\n", + "\n", + "#Calculation\n", + "m = math.pi/4*d**2*l*rho \t\t\t#kg. mass of cylinder\n", + "A = math.pi*d*l \t\t\t#m**2, area of cylinder\n", + "dt = T1-T2 \t\t\t#c, insmath.tanmath.taneous temp. difference\n", + "h = 1.32*(dt/d)**0.25 \t\t\t#W/m**2 C, heat transfer coefficient\n", + "\n", + "def f0(T): \n", + " return 1./(T**(5./4))\n", + "\n", + "i = quad(f0,5,50)[0]\n", + "\n", + "t = i/(3.306*A/(m*cp*10**3))\n", + "\n", + "# Results\n", + "print \"The required time for cooling is %.2f hr\"%(t/3600.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4 Page No : 157" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat loss by free convection per meter length of pipe. is 107 W\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "id_ = 78.*10**-3 \t\t\t#m, internal diameter\n", + "od = 89.*10**-3 \t\t\t#m, outer diameter\n", + "Pg = 15. \t\t\t#kg/cm**2, gauge pressure\n", + "t = 2.*10**-2 \t\t\t#m, thickness of preformed mineral fibre\n", + "k = 0.05 \t\t\t#W/m C. thermal conductivity\n", + "Ta = 25. \t\t\t#C, ambient air temp.\n", + "Pr = 0.705 \t\t\t#Prandtl no.\n", + "#assume\n", + "Ts = 50. \t\t\t#C, skin temp.\n", + "l = 1. \t\t\t#m, length\n", + "Ti = 200.5 \t\t\t#C, initial temp.\n", + "rs = od/2+t \t\t\t#m, outer radius of insulation\n", + "ri = od/2 \t\t\t#m, inner radius of insulation\n", + "\n", + "# Calculations\n", + "Q = 2*math.pi*l*k*(Ti-Ts)/(math.log(rs/ri)) \t\t\t#W\n", + "#properties of air at taken at the mean film temp.\n", + "Tf = (Ta+Ts)/2 \t\t\t#C\n", + "mu = 1.76*10**-5 \t\t\t#m**2/s. vismath.cosity\n", + "beeta = (1/(Tf+273)) \t\t\t#K**-1, coefficient of volumetric expansion\n", + "k1 = 0.027 \t\t\t#W/m C, thermal conductivity\n", + "ds = 2*rs \t\t\t#m, outer dia. of insulated pipe\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "Grd = g*beeta*(Ts-Ta)*ds**3/(mu**2) \t\t\t#Grashof no.\n", + "Rad = Grd*Pr \t\t\t#Rayleigh no.\n", + "#from eq. 5.9\n", + "#Nusslet no. \n", + "Nu = (0.60+(0.387*(Rad)**(1./6))/(1+(0.559/Pr)**(9./16))**(8./27))**2 \n", + "hav = Nu*k1/ds \t\t\t#W/ m**2 C, average heat transfer coefficient\n", + "Ts = (Q/(math.pi*ds*l*hav))+Ta \t\t\t#C, skin temp.\n", + "#revised calculation by assuming\n", + "Ts1 = 70. \t\t\t#C, skin temp.\n", + "#Rate of heat transfer through insulation\n", + "Q1 = 2*math.pi*l*k*(Ti-Ts1)/(math.log(rs/ri))\n", + "Tf1 = (Ta+Ts1)/2 \t\t\t#C, average aie mean film temp.\n", + "mu1 = 1.8*10**-5 \t\t\t#m**2/s. vismath.cosity\n", + "beeta1 = (1/(Tf1+273)) \t\t\t#K**-1, coefficient of volumetric expansion\n", + "k1 = 0.0275 \t\t\t#W/m C, thermal conductivity\n", + "Pr1 = 0.703 \t\t\t#Prandtl no.\n", + "Grd1 = g*beeta1*(Ts1-Ta)*ds**3/(mu1**2) \t\t\t#Grashof no.\n", + "Rad = Grd1*Pr1 \t\t\t#Rayleigh no.\n", + "#from eq. 5.9\n", + "# average heat transfer coefficient, in \t\t\t#W/ m**2 C,\n", + "hav1 = (0.60+(0.387*(Rad)**(1./6))/(1+(0.559/Pr)**(9./16))**(8./27))**2*(k1/ds)\n", + "Ts2 = (Q1/(math.pi*ds*l*hav1))+Ta\n", + "#again assume skin temp. = 74\n", + "Ts2 = 74 \t\t\t#C, assumed skin temp.\n", + "Q3 = 2*math.pi*l*k*(Ti-Ts2)/(math.log(rs/ri))\n", + "\n", + "# Results\n", + "print \"the rate of heat loss by free convection per meter length of pipe. is %.0f W\"%(Q3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5 Page No : 159" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The required insulation thickness is 0.188 m\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve \n", + "import math \n", + "\n", + "# Variables\n", + "Ts = 65. \t\t\t#C, skin temp.\n", + "To = 30. \t\t\t#C, ambient temp.\n", + "Tw = 460. \t\t\t#C, wall temp.\n", + "Tf = (Ts+To)/2 \t\t\t#C,mean air film temp.\n", + "beeta = (1./(Tf+273)) \t\t\t#K**-1, coefficient of volumetric expansion\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "mu = 1.84*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "L = 10.5 \t\t\t#m, height of converter\n", + "di = 4. \t\t\t#m,diameter of converter\n", + "Pr = 0.705 \t\t\t#Prandtl no.\n", + "k = 0.0241 \t\t\t#kcal/h m C, thermal conductivity\n", + "\n", + "#Calculation\n", + "Grl = g*beeta*(Ts-To)*L**3/(mu**2) \t\t\t#Grashof no.\n", + "x = di/L \t\t\t#assume di/l = x\n", + "y = 35/(Grl)**(1./4) \t\t\t#assume 35/(Grl)**(3/4) = y\n", + "#for a verticla flat plate, from eq. 5.3\n", + "Ral = Grl*Pr \t\t\t#Rayleigh no.\n", + "#nusslet no.\n", + "Nu = (0.825+(0.387*(Ral)**(1./6))/(1+(0.496/Pr)**(9./16))**(8./27))**2\n", + "hav = Nu*k/L \t\t\t#kcal/h m**2 C, average heat transfer coefficient\n", + "#w = poly(0,\"w\")\n", + "#Dav = (4+(4+2*w))/2 \t\t\t#average diameter\n", + "#Aav = math.pi*Dav*L \t\t\t#average heat transfer area\n", + "#Qi = math.pi*Dav*L*0.0602*(Tw-Ts)/w \t\t\t#Rate of heat transfer through insulation\n", + "#rate of heat transfer from the outer surface of the insulation by free convection\n", + "#Qc = hav*math.pi*Dav*L*(Ts-To) \n", + "#Qi = Qc\n", + "def f(w): \n", + " return math.pi*(4+w)*L*0.0602*(Tw-Ts)/w-hav*math.pi*(4+2*w)*L*(Ts-To)\n", + "w = fsolve(f,0.1)\n", + "\n", + "# Results\n", + "print \"The required insulation thickness is %.3f m\"%(w)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6 Page No : 162" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat transfer is 13.4 W\n" + ] + } + ], + "source": [ + "# Variables\n", + "L = 1.6 \t\t\t#m,height of enclosure\n", + "w = 0.04 \t\t\t#m, width of enclosure\n", + "b = 0.8 \t\t\t#m, breath\n", + "T1 = 22. \t\t\t#C,surface temp.\n", + "T2 = 30. \t\t\t#C, wall temp.\n", + "Tm = (T1+T2)/2 \t\t\t#C, Mean air temp.\n", + "Pr = 0.7 \t\t\t#Prandtl no.\n", + "\n", + "# Calculations\n", + "#fpr air at 26 C\n", + "beeta = 1./(Tm+273) \t\t\t#K**-1. coefficient of volumetric expension\n", + "mu = 1.684*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "k = 0.026 \t\t\t#W/m C, thermal conductivity\n", + "alpha = 2.21*10**-5 \t\t\t#m**2/s, thermal diffusity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "Raw = g*beeta*(T2-T1)*w**3/(mu*alpha) \t\t\t#Rayleigh no.\n", + "Nuw = 0.42*(Raw)**0.25*Pr**0.012*(L/w)**-0.3 \t\t\t#Nusslet no.\n", + "h = Nuw*k/w \t\t\t#kcal/h m**2 C, heat transfer coefficient\n", + "q = h*(T2-T1)*(L*b) \t\t\t#W,the rate of heat transfer\n", + "\n", + "# Results\n", + "print \"the rate of heat transfer is %.1f W\"%(q)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7 Page No : 163" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat loss per meter length is 39.7 kcal/h\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "Ts = 60. \t\t\t#C, surface temp\n", + "To = 30. \t\t\t#C, bulk temp.\n", + "d = 0.06 \t\t\t#m, diameter of pipe\n", + "l = 1. \t\t\t#m, length\n", + "Tm = (Ts+To)/2\n", + "#for air at Tm\n", + "rho = 1.105 \t\t\t#kg/m**3, density\n", + "cp = 0.24 \t\t\t#kcal/kg C. specific heat\n", + "mu = 1.95*10**-5 \t\t\t#kg/m s. vismath.cosity\n", + "P = 0.7 \t\t\t#Prandtl no. \n", + "kv = 1.85*10**-5 \t\t\t#m**2/s, kinetic vismath.cosity\n", + "k = 0.0241 \t\t\t#kcal/f m C, thermal conductivity\n", + "beeta = (1./(Tm+273)) \t\t\t#K**-1. coefficient of volumetric expension\n", + "V = 0.3 \t\t\t#m/s, velocity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "\n", + "#Calculation\n", + "Rad = g*beeta*(Ts-To)*d**3*P/(kv**2) \t\t\t#Rayleigh no.\n", + "#from eq. 5.9\n", + "Nufree = (0.60+(0.387*Rad**(1./6))/(1+(0.559/P)**(9./16))**(8./27))**2\n", + "#calculation of forced convection nusslet no.\n", + "#from eq. 4.19\n", + "Re = d*V/(kv)\n", + "Nuforced = 0.3+(0.62*Re**(1./2)*P**(1./3)/(1+(0.4/P)**(2./3))**(1./4))*(1.+(Re/(2.82*10**5))**(5./8))**(4./5)\n", + "Nu = (Nuforced**3+Nufree**3)**(1./3) \t\t\t#nusslet no. for mixed convection\n", + "#Nu = h*d/k\n", + "h = Nu*k/d \t\t\t#kcal/h m**2 C, heat transfer corfficient\n", + "q = h*math.pi*d*l*(Ts-To)\n", + "\n", + "# Results\n", + "print \"the rate of heat loss per meter length is %.1f kcal/h\"%(q)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |