diff options
Diffstat (limited to 'Principles_Of_Heat_Transfer_by_F_Kreith/5-Natural_Convection.ipynb')
| -rw-r--r-- | Principles_Of_Heat_Transfer_by_F_Kreith/5-Natural_Convection.ipynb | 479 |
1 files changed, 479 insertions, 0 deletions
diff --git a/Principles_Of_Heat_Transfer_by_F_Kreith/5-Natural_Convection.ipynb b/Principles_Of_Heat_Transfer_by_F_Kreith/5-Natural_Convection.ipynb new file mode 100644 index 0000000..0d55739 --- /dev/null +++ b/Principles_Of_Heat_Transfer_by_F_Kreith/5-Natural_Convection.ipynb @@ -0,0 +1,479 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Natural Convection" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: Convection_Heat_Loss_From_Room_Heater.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"// Display mode\n", +"mode(0);\n", +"\n", +"// Display warning for floating point exception\n", +"ieee(1);\n", +"\n", +"clc;\n", +"disp('Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.1 ');\n", +"\n", +"// ''Body temp in degree C''\n", +"Tb = 127;\n", +"//''Body temp in degree K''\n", +"TbK = Tb+273;\n", +"//''Ambient temp in degree C''\n", +"Ta = 27;\n", +"//''Ambient temp in degree K''\n", +"TaK = Ta+273;\n", +"//''Film temperature = (Body Temperature + Ambient Temperature)/2''\n", +"//''Film temp in degree K''\n", +"TfK = (TbK+TaK)/2;\n", +"//''Value of coefficient of expansion at this film temp in degree K inverse''\n", +"B = 1/TfK;\n", +"//''Value of Prandtl number at this film temp''\n", +"Pr = 0.71;\n", +"//''Value of kinematic viscosity at this film temp in m2/s''\n", +"v = 0.0000212;\n", +"//''Value of thermal conductivity at this film temp in W/m-K''\n", +"k = 0.0291;\n", +"//''acceleration due to gravity in m/s2''\n", +"g = 9.81;\n", +"//''temperature diff. between body and ambient in degree K''\n", +"deltaT = TbK-TaK;\n", +"//''diameter of heater wire in m''\n", +"d = 0.001;\n", +"//''Therefore using Rayleigh number = ((Pr*g*B*deltaT*d^3)/v^2)''\n", +"Ra = ((((Pr*g)*B)*deltaT)*(d^3))/(v^2);\n", +"\n", +"//''From Fig. 5.3 on Page 303, we get''\n", +"//''log(Nu) = 0.12, where Nu is nusselt number, therefore''\n", +"Nu = 1.32;\n", +"//''Using Nu = hc*d/k, we get heat transfer coefficient in W/m2-K''\n", +"hc = (Nu*k)/d;\n", +"disp('The rate of heat loss per meter length in air in W/m is given by hc*(A/l)*deltaT')\n", +"//heat loss per meter length in air in W/m\n", +"q = ((hc*deltaT)*%pi)*d\n", +"\n", +"//''For Co2, we evaluate the properties at film temperature''\n", +"//''Following are the values of dimensionless numbers so obtained''\n", +"//''Rayleigh number, Ra=16.90''\n", +"//''Nusselt number, Nu=1.62''\n", +"//''Using Nu = hc*d/k, we get''\n", +"//''hc = 33.2 W/m2-K''\n", +"disp('The rate of heat loss per meter length in CO2 is given by hc*(A/l)*deltaT')\n", +"disp('q = 10.4 W/m')\n", +"\n", +"disp(' Discussion - For same area and temperature difference: ')\n", +"disp(' Heat transfer by convection will be more, if heat transfer coeff. is high')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: Power_Requirement_of_Heater.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"// Display mode\n", +"mode(0);\n", +"\n", +"// Display warning for floating point exception\n", +"ieee(1);\n", +"\n", +"clc;\n", +"disp('Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.2 ');\n", +"\n", +"//''Surface temp in degree C''\n", +"TsC = 130;\n", +"//''Body temp in degree K''\n", +"Ts = TsC+273;\n", +"//''Ambient temp in degree C''\n", +"TinfinityC = 20;\n", +"//''Ambient temp in degree K''\n", +"Tinfinity = TinfinityC+273;\n", +"//''Film temperature = (Surface Temperature + Ambient Temperature)/2''\n", +"//''Film temp in degree K''\n", +"Tf = (Ts+Tinfinity)/2;\n", +"//''Height of plate in cms''\n", +"L = 15;\n", +"//''Width of plate in cms''\n", +"b = 10;\n", +"//''Value of Grashof number at this film temp is given by\n", +"//65(L^3)(Ts-Tinfinity)''\n", +"//Grashof number\n", +"Gr = (65*(L^3))*(Ts-Tinfinity);\n", +"//''Since the grashof number is less than 10^9, therefore flow is laminar''\n", +"//''For air at film temp = 75C (348K), Prandtl number is''\n", +"Pr = 0.71;\n", +"//''And the product Gr*Pr is''\n", +"//Prodect of Gr and Pr\n", +"GrPr = Gr*Pr;\n", +"//''From Fig 5.5 on page 305, at this value of GrPr, Nusselt number is''\n", +"Nu = 35.7;\n", +"//''Value of thermal conductivity at this film temp in W/m-K''\n", +"k = 0.029;\n", +"\n", +"//''Using Nu = hc*L/k, we get ''\n", +"//Heat transfer coefficient for convection in W/m2-K\n", +"hc = (Nu*k)/(L/100);\n", +"\n", +"//''Heat transfer coefficient for radiation, hr in W/m2-K''\n", +"hr = 8.5;\n", +"\n", +"//''Total area in m2 is given by 2*(b/100)*(L/100)''\n", +"A = (2*(b/100))*(L/100);\n", +"\n", +"\n", +"disp('Therefore total heat transfer in W is given by A*(hc+hr)*(Ts-Tinfinity)')\n", +"//total heat transfer in W\n", +"q = (A*(hc+hr))*(Ts-Tinfinity)\n", +"\n", +"//''For plate to be 450cm in height, Rayleigh number becomes 4.62*10^11''\n", +"//''which implies that the flow is turbulent''\n", +"//''From Fig 5.5 on page 305, at this value of GrPr, Nusselt number is 973''\n", +"//''Using Nu = hc*d/k, we get in W/m2-K, hc_bar=6.3''\n", +"//''New Total area in m2, A_bar=2*(0.1)*(4.5)''\n", +"\n", +"disp('Therefore in new case, total heat transfer in W is given by A_bar*(hc_bar+hr)*(Ts-Tinfinity)')\n", +"disp('we get q=1465W')\n", +"\n", +"\n", +"disp(' Discussion - For same temperature difference: ')\n", +"disp(' Heat transfer will be more, if area exposed for convection and radiation is more')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: Heat_Loss_From_Grill.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"// Display mode\n", +"mode(0);\n", +"\n", +"// Display warning for floating point exception\n", +"ieee(1);\n", +"\n", +"clc;\n", +"disp('Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.3 ')\n", +"\n", +"//''Surface temp in degree C''\n", +"TsC = 227;\n", +"//''Body temp in degree K'')\n", +"Ts = TsC+273;\n", +"//''Ambient temp in degree C''\n", +"TinfinityC = 27;\n", +"//''Ambient temp in degree K''\n", +"Tinfinity = TinfinityC+273;\n", +"//''Film temperature = (Surface Temperature + Ambient Temperature)/2''\n", +"//''Film temp in degree K'')\n", +"Tf = (Ts+Tinfinity)/2;\n", +"//''For a square plate, Height and width of plate in m''\n", +"L = 1;\n", +"b = 1;\n", +"//''For a square plate, characteristic length = surface area/parameter in m''\n", +"L_bar = (L*L)/(4*L);\n", +"//''Value of coefficient of expansion at this film temp in degree K inverse''\n", +"B = 1/Tf;\n", +"//''Value of Prandtl number at this film temp''\n", +"Pr = 0.71;\n", +"//''Value of thermal conductivity at this film temp in W/m-K''\n", +"k = 0.032;\n", +"//''Value of kinematic viscosity at this film temp in m2/s''\n", +"v = 0.000027;\n", +"//''acceleration due to gravity in m/s2''\n", +"g = 9.81;\n", +"//''temperature diff. between body and ambient in degree K''\n", +"deltaT = Ts-Tinfinity;\n", +"//''Therefore using Rayleigh number = ((Pr*g*B*deltaT*(L_bar)^3)/v^2)''\n", +"//Rayleigh number\n", +"Ra = ((((Pr*g)*B)*deltaT)*(L_bar^3))/(v^2);\n", +"\n", +"\n", +"//''From eq. 5.17 on page 311, we have nusselt number for bottom plate as 0.27*Pr^0.25''\n", +"NuBottom = 25.2;\n", +"//''From eq. 5.16 on page 311, we have nusselt number for top plate as 0.27*Pr^0.25''\n", +"NuTop = 63.4;\n", +"//''And therefore corresponding heat transfer coeeficients are in W/m2-K''\n", +"hcBottom = (NuBottom*k)/L_bar; //heat transfer coeeficients are in W/m2-K at bottom \n", +"hcTop = (NuTop*k)/L_bar; //heat transfer coeeficients are in W/m2-K at top\n", +"\n", +"\n", +"disp('Therefore total heat transfer in W is given by A*(hcTop+hcBottom)*(deltaT)')\n", +"//heat transfer in W\n", +"q = ((L*b)*(hcTop+hcBottom))*deltaT" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: Transition_to_Turbulent_Flow_in_Pipe.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"// Display mode\n", +"mode(0);\n", +"\n", +"// Display warning for floating point exception\n", +"ieee(1);\n", +"\n", +"clc;\n", +"disp('Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.4 ');\n", +"\n", +"//''Ambient temp in degree C''\n", +"TinfinityC = 27;\n", +"//''Ambient temp in degree K''\n", +"Tinfinity = TinfinityC+273;\n", +"//''The criterion for transition is rayleigh number to be 10^9''\n", +"\n", +"\n", +"//''Value of coefficient of expansion at this temp in degree K inverse''\n", +"B = 1/Tinfinity;\n", +"//''Value of Prandtl number at this ambient temp''\n", +"Pr = 0.71;\n", +"//''Diameter of pipe in m''\n", +"D = 1;\n", +"//''Value of kinematic viscosity at this temp in m2/s''\n", +"v = 0.0000164;\n", +"//''acceleration due to gravity in m/s2''\n", +"g = 9.81;\n", +"\n", +"//''Therefore using Rayleigh number = ((Pr*g*B*deltaT*(D)^3)/v^2) = 10^9''\n", +"//''we get the temperature difference in centrigrade to be''\n", +"deltaT = 12;\n", +"disp('therefore the temperature of pipe in C is')\n", +"// temperature of pipe in C\n", +"Tpipe = TinfinityC+deltaT\n", +"\n", +"\n", +"//''From table 13 in Appendix 2, for the case of water and using the same procedure we get''\n", +"// temperature difference in C\n", +"deltaTw = 0.05;\n", +"disp('therefore the temperature of pipe in C is')\n", +"// temperature of pipe in C\n", +"Tpipew = TinfinityC+deltaTw\n", +"\n", +"disp(' Discussion - For air and water: ')\n", +"disp(' Temperature required to induce turbulence is higher in air')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: Rate_of_Heat_Transfer_From_Burner.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"// Display mode\n", +"mode(0);\n", +"\n", +"// Display warning for floating point exception\n", +"ieee(1);\n", +"\n", +"clc;\n", +"disp('Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.5 ');\n", +"\n", +"//''Top surface temp in degree C''\n", +"Tt = 20;\n", +"//''Body temp in degree K''\n", +"TtK = Tt+273;\n", +"//''Bottom temp in degree C''\n", +"Tb = 100;\n", +"//''Ambient temp in degree K''\n", +"TbK = Tb+273;\n", +"//''Average temp = (Bottom Temperature + top Temperature)/2''\n", +"//''average temp in degree K''\n", +"T = (TbK+TtK)/2;\n", +"//''Value of coefficient of expansion at this temp in degree K inverse''\n", +"B = 0.000518;\n", +"//''Value of Prandtl number at this temp''\n", +"Pr = 3.02;\n", +"//''Value of kinematic viscosity at this temp in m2/s''\n", +"v = 0.000000478;\n", +"//''acceleration due to gravity in m/s2''\n", +"g = 9.8;\n", +"//''temperature diff. between body and ambient in degree K''\n", +"deltaT = TbK-TtK;\n", +"//''depth of water in m''\n", +"h = 0.08;\n", +"//''Therefore using Rayleigh number = ((Pr*g*B*deltaT*h^3)/v^2)''\n", +"Ra = ((((Pr*g)*B)*deltaT)*(h^3))/(v^2);\n", +"\n", +"//''From Eq. (5.30b) on page 318, we find''\n", +"//Nusselt number\n", +"Nu = 79.3;\n", +"//''Value of thermal conductivity at this film temp in W/m-K''\n", +"k = 0.657;\n", +"//''Using Nu = hc*d/k, we get heat transfer coefficient in W/m2-K''\n", +"hc = (Nu*k)/h;\n", +"//''diameter of pan in m''\n", +"d = 0.15;\n", +"//''area = pi*d*d/4''\n", +"a = ((%pi*d)*d)/4;\n", +"disp('The rate of heat loss in W is given by hc*(A)*deltaT')\n", +"//heat loss in W\n", +"q = (hc*deltaT)*a" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: Convection_Heat_Transfer_From_Shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"\n", +"// Display mode\n", +"mode(0);\n", +"\n", +"// Display warning for floating point exception\n", +"ieee(1);\n", +"\n", +"clc;\n", +"disp('Principles of Heat Transfer, 7th Ed. Frank Kreith et. al Chapter - 5 Example # 5.6 ');\n", +"\n", +"//''RPM of shaft''\n", +"N = 3;\n", +"//''Angular velocity, omega=2*pi*N/60 in rad/s''\n", +"omega = 0.31;\n", +"//''Ambient temp in degree C''\n", +"Ta = 20;\n", +"//''Ambient temp in degree K''\n", +"TaK = Ta+273;\n", +"//''Shaft temp in degree C''\n", +"Ts = 100;\n", +"//''Shaft temp in degree K''\n", +"TsK = Ts+273;\n", +"//''Film temperature = (Shaft Temperature + Ambient Temperature)/2''\n", +"//''Film temp in degree K''\n", +"TfK = (TsK+TaK)/2;\n", +"//''diameter of shaft in m''\n", +"d = 0.2;\n", +"//''Value of kinematic viscosity at this film temp in m2/s''\n", +"v = 0.0000194;\n", +"//''Value of reynolds number''\n", +"Re = (((%pi*d)*d)*omega)/v;\n", +"\n", +"\n", +"//''acceleration due to gravity in m/s2''\n", +"g = 9.81;\n", +"//''temperature diff. between body and ambient in degree K''\n", +"deltaT = TsK-TaK;\n", +"//''Value of Prandtl number at this film temp''\n", +"Pr = 0.71;\n", +"//''Value of coefficient of expansion at this film temp in degree K inverse''\n", +"B = 1/TfK;\n", +"//''Therefore using Rayleigh number = ((Pr*g*B*deltaT*d^3)/v^2)''\n", +"//Rayleigh number\n", +"Ra = ((((Pr*g)*B)*deltaT)*(d^3))/(v^2);\n", +"\n", +"//''From Eq. 5.35 on Page 322, we get''\n", +"//Nusselt number\n", +"Nu = 49.2;\n", +"//''Value of thermal conductivity at this film temp in W/m-K''\n", +"k = 0.0279;\n", +"//''Using Nu = hc*d/k, we get in W/m2-K''\n", +"hc = (Nu*k)/d;\n", +"//''let the length exposed to heat transfer is l=1m''\n", +"//''then area in m2 = pi*d*l''\n", +"a = %pi*d;\n", +"disp('The rate of heat loss in air in W is given by hc*(a)*deltaT')\n", +"//heat loss in air in W\n", +"q = (hc*deltaT)*a" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |