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diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch11.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch11.ipynb new file mode 100644 index 00000000..b98ede25 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch11.ipynb @@ -0,0 +1,322 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11 : Boundary layer heat transfer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1 Page No : 478" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "i) Boundary layer thickness is 0.0033 m\n", + "Local drag coefficient is 8.72e-04 \n", + "total drag force is 0.615 N \n", + "Shear stress is 0.285 N/m**2\n" + ] + } + ], + "source": [ + "import math \n", + "#Variable\n", + "v = 1. \t\t\t#m/s\n", + "#temprature\n", + "T = 25. \t\t\t# degree celcius\n", + "#length of plate,l = 1m\n", + "l = 1. \t\t\t#m\n", + "#width of plate,w = 0.5m\n", + "w = 0.5 \t\t\t#m\n", + "#angle of incidence,theta = 0 degree\n", + "theta = 0. \t\t\t#degree\n", + "\n", + "#Calculation\n", + "#for water at 25 degree celcius ,momentum diffusivity,\n", + "MD = 8.63*(10**-7) \t\t\t# m**2/s\n", + "#local Reynold no.\n", + "x = 0.5 \t\t\t#m\n", + "Re = x*v/MD \n", + "#from Eq. 11.39,the boundary layer thickness is\n", + "t = 5*x/(Re**0.5)\n", + "\n", + "\n", + "#Results\n", + "print \"i) Boundary layer thickness is %.4f m\"%(t)\n", + "\n", + "#local drag coefficient\n", + "#CD = local drag force per unit area (F)/kinetic energy per unit volume(KE)\n", + "#F = 0.332*rho*v**2*Re**0.5 and KE = 0.5*rho*v**2\n", + "CD = 0.332*v**2*(Re**-0.5)/(0.5)*v**2\n", + "\n", + "print \"Local drag coefficient is %.2e \"%(CD)\n", + "\n", + "#From eq 11.44, the drag force acting on one side of the plate is\n", + "#kinetic viscocity\n", + "mu = 8.6*(10**-4)\n", + "fd = 0.664*mu*v*(l*v/MD)**0.5*w\n", + "#the total force acting on both sides of the plate\n", + "\n", + "tfd = 2*fd\n", + "print \"total drag force is %.3f N \"%(tfd)\n", + "\n", + "#shear stress at any point in the boundary layer\n", + "#at a point in the boundary layer,\n", + "x = 0.5 \t\t\t#m\n", + "y = t/2\n", + "# n = blasius dimensionless variable\n", + "n = y/(MD*x/v)**0.5\n", + "#From table 11.1, at n = 2.5,f\"(n) = 0.218\n", + "#shear stress = tau\n", + "fn = 0.218 \t\t\t#f\"(n) = fn\n", + "tau = (mu*v*(v/(MD*x))**0.5)*fn\n", + "print \"Shear stress is %.3f N/m**2\"%(tau)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2 Page No : 488" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Thermal boundary layer thickness is 8.7 mm \n", + "heat transfer coeff is 6.9 W/m**2 C\n" + ] + } + ], + "source": [ + "#Variable\n", + "Ts = 200. \t\t\t# C,temp. of air\n", + "Ta = 30. \t\t\t#C, temp .of surface\n", + "Va = 8. \t\t\t#m/s, velocity of air\n", + "d = 0.75 \t\t\t#m, dismath.tant from leading edge\n", + "\n", + "#Calculation and Results\n", + "Tm = (Ts+Ta)/2 \t\t\t#C, Mean temp. of boundary layer\n", + "mu = 2.5*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "P = 0.69 \t\t\t#prndatl no.\n", + "k = 0.036 \t\t\t#W/m c, thermal conductivity\n", + "Re = d*Va/mu \t\t\t#reynold no.\n", + "t = 5*d/(Re**0.5*P**(1./3)) \t\t\t#m, thermal boundary layer thickness\n", + "print \"Thermal boundary layer thickness is %.1f mm \"%(t*10**3)\n", + "\n", + "N = (0.332*Re**(0.5)*P**(1./3)) \t\t\t#Nusslet no.\n", + "h = k*N/d \t\t\t#heat transfer coefficent\n", + "print \"heat transfer coeff is %.1f W/m**2 C\"%(h)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3 Page No : 489" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Local rate of heat exchange is 235 W/m2\n", + "Plate temperature is :108 Celsius \n" + ] + } + ], + "source": [ + "# Variables\n", + "#Free strean velocity (v1) and temp.(t1) on side 1\n", + "v1 = 6. \t\t\t#m/s\n", + "t1 = 150. \t\t\t#degree celcius\n", + "#same on side 2\n", + "v2 = 3. \t\t\t#m/s\n", + "t2 = 50. \t\t\t#degree celcius\n", + "#dismath.tant\n", + "x = 0.7 \t\t\t#m\n", + "#The plate temp. is assumed to be equal to the mean of the bulk air temp on the two sides of the plates\n", + "T = 100. \t\t\t#degree celcius\n", + "\n", + "# Calculations\n", + "#Side 1\n", + "#mean air temp.\n", + "tm1 = (T+t1)/2\n", + "#From thermophysical properties:kinetic vismath.cosity (kv),Prandtl no.(P), thermal conductivity (k)\n", + "kv1 = 2.6*10**-5 \t\t\t#m**2/s\n", + "P1 = 0.69\n", + "k1 = 0.0336 \t\t\t#W/m degree celcius\n", + "#Reynold no.\n", + "Re1 = x*v1/kv1\n", + "#Nusslet no(N1)\n", + "a = 1/3.\n", + "N1 = 0.332*(Re1)**0.5*P1**a\n", + "h1 = k1*N1/x\n", + "#Side 2 of the plate\n", + "tm2 = (T+t2)/2\n", + "#Similarly\n", + "kv2 = 2.076*(10)**-5 \t\t\t#m**2/s\n", + "P2 = 0.70\n", + "k2 = 0.03 \t\t\t#W/m degree celcius\n", + "Re2 = x*v2/kv2\n", + "N2 = 0.332*(Re2)**0.5*P2**a\n", + "h2 = k2*N2/x\n", + "#overall heat transfer coeff. \n", + "U = h1*h2/(h1+h2)\n", + "#The local rate of heat exchange\n", + "RH = U*(t1-t2)\n", + "\n", + "# Results\n", + "print \"Local rate of heat exchange is %.0f W/m2\"%(RH)\n", + "#the plate temp is given by\n", + "TP = t2+(t1-t2)*U/h2\n", + "print \"Plate temperature is :%.0f Celsius \"%(TP)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.4 Page No : 490" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The temprature of plate after 1 hour is 82 C\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "T1 = 120. \t\t\t#C, initial temp.\n", + "T2 = 25. \t\t\t#C, Final temp.\n", + "Tm = (T1+T2)/2 \t\t\t#C, mean temp.\n", + "rho = 8880. \t\t\t#kg/m**3, density of plate\n", + "#Properties of air at mean temp.\n", + "mu = 2.07*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "Pr = 0.7 \t\t\t#Prandtl no.\n", + "k = 0.03 \t\t\t#W/m C, thermal conductivity\n", + "l = 0.4 \t\t\t#m, length of plate\n", + "w = 0.3 \t\t\t#m, width of plate\n", + "d = 0.0254 \t\t\t#m, thickness of plate\n", + "Vinf = 1. \t\t\t#m/s, air velocity\n", + "Re = l*Vinf/mu \t\t\t#REynold no.\n", + "\n", + "#from eq. 11.90 (b)\n", + "Nu = 0.664*(Re)**(1./2)*(Pr)**(1./3) \t\t\t#average Nusslet no.\n", + "#Nu = l*h/k\n", + "h = Nu*k/l \t\t\t#W/m**2 C, heat transfer coefficient\n", + "#Rate of change of temp. is given by\n", + "A = 2*l*w \t\t\t#m**2. area of plate\n", + "t = 1*3600. \t\t\t#s, time\n", + "cp = 0.385*10.**3 \t\t\t#j/kg K, specific heat\n", + "m = l*w*d*rho \t\t\t#kg, mass of plate\n", + "\n", + "#-d/dt(m*cp8dt) = A*hv*(T1-T2)\n", + "#appling the boundary condition \n", + "T = (T1-T2)*math.exp(-A*h*t/(m*cp))+T2\n", + "print \"The temprature of plate after 1 hour is %.0f C\"%(T)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.5 Page No : 508" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nusslet no is: 388 \n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "#Reynold no (Re),friction factor(f),Prandlt no. (P)\n", + "Re = 7.44*(10**4)\n", + "f = 0.00485\n", + "P = 5.12\n", + "x = P-1 \t\t\t#assume\n", + "\n", + "# Calculations\n", + "#according to Von Karmen anamath.logy\n", + "N = ((f/2)*Re*P)/(1+(5*math.sqrt(f/2))*(x+math.log(1+(5./6)*x)))\n", + "\n", + "# Results\n", + "print \"Nusslet no is: %.0f \"%(N)\n", + "\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 +} |