summaryrefslogtreecommitdiff
path: root/Introduction_to_Heat_Transfer_by_S._K._Som/Chapter8.ipynb
diff options
context:
space:
mode:
Diffstat (limited to 'Introduction_to_Heat_Transfer_by_S._K._Som/Chapter8.ipynb')
-rw-r--r--Introduction_to_Heat_Transfer_by_S._K._Som/Chapter8.ipynb893
1 files changed, 893 insertions, 0 deletions
diff --git a/Introduction_to_Heat_Transfer_by_S._K._Som/Chapter8.ipynb b/Introduction_to_Heat_Transfer_by_S._K._Som/Chapter8.ipynb
new file mode 100644
index 00000000..a6c237e4
--- /dev/null
+++ b/Introduction_to_Heat_Transfer_by_S._K._Som/Chapter8.ipynb
@@ -0,0 +1,893 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "# Chapter 08:Principles of free convection"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.1:pg-355"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 1\n",
+ "Grashoff number is\n",
+ "GrL= 2175146201.53\n",
+ "Rayleigh number is\n",
+ "RaL= 9440134514.65\n",
+ "Therefore the flow is turbulent\n",
+ "Now we use [(hbarL*L)/k]=0.10*(GrL*Pr)**(1/3)\n",
+ "The average heat transfer coefficient in W/(m**2*K) is\n",
+ "hbarL= 0.314\n",
+ "The rate of heat transfer in W is\n",
+ "q= 0.5024\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math \n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 8, Example 1\"\n",
+ "#Water is heated by a vertical flat plate length(L=200mm or .2m )by breadth(B=200mm) which is maintained at temprature,Tw=60°C\n",
+ "Tw=60;\n",
+ "L=.2;\n",
+ "B=.2;# in metre\n",
+ "#Area(A) is L*B \n",
+ "A=L*B;\n",
+ "#Water is at temprature,Tinf=20°C\n",
+ "Tinf=20;\n",
+ "#At mean film temprature 40°C The physical properties parameters can be taken as \n",
+ "#conductivity(k=0.0628W/(m*K)),Prandtl number(Pr=4.34),density(rho=994.59kg/m**3),kinematic viscosity(nu=0.658*10**-6m**2/s),volume expnasion coefficient(Beta=3*10**-4K**-1))\n",
+ "k=0.628;\n",
+ "Pr=4.34;\n",
+ "rho=994.59;\n",
+ "nu=0.658*10**-6;\n",
+ "Beta=3*10**-4;\n",
+ "#g is acceleration due to gravity =9.81m/s**2\n",
+ "g=9.81;\n",
+ "#Grashoff number is given by GrL=(g*beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"Grashoff number is\"\n",
+ "GrL=(g*Beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"GrL=\",GrL\n",
+ "#Rayleigh number is defined as RaL=GrL*Pr\n",
+ "print\"Rayleigh number is\"\n",
+ "RaL=GrL*Pr\n",
+ "print\"RaL=\",RaL\n",
+ "print\"Therefore the flow is turbulent\"\n",
+ "print\"Now we use [(hbarL*L)/k]=0.10*(GrL*Pr)**(1/3)\"\n",
+ "#hbarL is the average heat transfer coefficient\n",
+ "print\"The average heat transfer coefficient in W/(m**2*K) is\"\n",
+ "hbarL=(0.10*(GrL*Pr)**(1/3)*k)/L\n",
+ "print\"hbarL=\",hbarL\n",
+ "#The rate of heat transfer is given by q=hbarL*A*(Tw-Tinf)\n",
+ "print\"The rate of heat transfer in W is\"\n",
+ "q=hbarL*A*(Tw-Tinf)\n",
+ "print\"q=\",q\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.2:pg-357"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 2\n",
+ "The minimum spacing between the plates will be twice the thickness of the boundary layer at the trailing edge where x=0.09\n",
+ "Grashoff number is\n",
+ "GrL= 198210197.615\n",
+ "Rayleigh number is\n",
+ "RaL= 860232257.647\n",
+ "Since Ra<10**9,Therefore the flow is laminar\n",
+ "The thickness of the boundary layer in metre is\n",
+ "delta= 4.11168026839e-10\n",
+ "The minimum spacing in metre is\n",
+ "spac= 8.22336053678e-10\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "import math \n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 8, Example 2\"\n",
+ "#The thin plates are kept at temprature(Tw)=60°C while the temprature of water bath(Tinf)=20°C\n",
+ "Tw=60;\n",
+ "Tinf=20;\n",
+ "#The plates have length(L)=90mm or .09m\n",
+ "L=.09;\n",
+ "#The minimum spacing between the plates will be twice the thickness of the boundary layer at the trailing edge where x=0.09.\n",
+ "print\"The minimum spacing between the plates will be twice the thickness of the boundary layer at the trailing edge where x=0.09\"\n",
+ "x=.09;\n",
+ "#At mean film temprature 40°C The physical properties parameters can be taken as\n",
+ "# conducivity(k=0.0628W/(m*K)),Prandtl number(Pr=4.34),Density(rho=994.59kg/m**3),kinematic viscosity(nu=0.658*10**-6m**2/s),Volume expansion coefficient(Beta=3*10**-4K**-1)\n",
+ "k=0.628;\n",
+ "Pr=4.34;\n",
+ "rho=994.59;\n",
+ "nu=0.658*10**-6;\n",
+ "Beta=3*10**-4;\n",
+ "#g is acceleration due to gravity =9.81m/s**2\n",
+ "g=9.81;\n",
+ "#Grashoff number is given by GrL=(g*beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"Grashoff number is\"\n",
+ "GrL=(g*Beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"GrL=\",GrL\n",
+ "#Rayleigh number is defined as RaL=GrL*Pr\n",
+ "print\"Rayleigh number is\"\n",
+ "RaL=GrL*Pr\n",
+ "print\"RaL=\",RaL\n",
+ "print\"Since Ra<10**9,Therefore the flow is laminar\"\n",
+ "#delta is the thickness of the boundary layer\n",
+ "print\"The thickness of the boundary layer in metre is\"\n",
+ "delta=x*3.93*Pr**(-1/2)*(0.952+Pr)**(1/4)*GrL**(-1/4)\n",
+ "print\"delta=\",delta\n",
+ "#spac is the minimum spacing \n",
+ "print\"The minimum spacing in metre is\"\n",
+ "spac=2*delta\n",
+ "print\"spac=\",spac\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.3:pg-366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 3\n",
+ "Grashoff number is\n",
+ "Grx= 517025.52213\n",
+ "The boundary layer thickness in metre is\n",
+ "delta= 60304.3038858\n",
+ "The velocity at point x is ux in m/s is\n",
+ "ux= 3247798354.51\n",
+ "For maximum value of velocity,u\n",
+ "Maximum velocity in m/s is\n",
+ "Umax= 3.57089835848\n",
+ "Mass flow rate at x=0.8m,in kG is\n",
+ "mdot= 2.36830073295e+16\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "from scipy.integrate import quad\n",
+ "print \"Introduction to heat transfer by S.K.Som, Chapter 8, Example 3\"\n",
+ "#Considering question 5.7\n",
+ "#A wall is exposed to nitrogen at one atmospheric pressure and temprature,Tinf=4°C.\n",
+ "Tinf=4.0;\n",
+ "#The wall is H=2.0m high and 2.5m wide and is maintained at temprature,Tw=56°C\n",
+ "Tw=56.0;\n",
+ "H=2.0;\n",
+ "B=2.5;\n",
+ "A=H*B;#Area of wall in m**2\n",
+ "#The properties of nitrogen at mean film temprature (56+4)/2=30°C are given as \n",
+ "#density(rho=1.142kg/m*3) ,conductivity(k=0.026W/(m*K)),kinematic viscosity(nu=15.630*10-6 m*2/s) ,prandtl number(Pr=0.713)\n",
+ "rho=1.142;\n",
+ "k=0.026;\n",
+ "nu=15.630*10**-6;\n",
+ "Pr=0.713;\n",
+ "Tf=30.0;#mean film temprature\n",
+ "Beta=1/(273.0+Tf);#volume expansion coefficient:unit K**-1\n",
+ "#Now Grashoff number is Grx=(g*Beta*(Tw-Tinf)*x*3)/nu*2\n",
+ "g=9.81;#acceleration due to gravity\n",
+ "print \"Grashoff number is\"\n",
+ "x=0.8;#distance from the bottom of wall\n",
+ "Grx=(g*Beta*(Tw-Tinf)*x*3)/nu*2\n",
+ "print\"Grx=\",Grx\n",
+ "#Using equation delta=x*Pr*(-0.5)(0.952+Pr)*(0.25)*Grx*(-0.25)\n",
+ "#delta is the boundary layer thickness\n",
+ "print \"The boundary layer thickness in metre is\"\n",
+ "delta=x*3.93*Pr*(-0.5)*(0.952+Pr)*(0.25)*Grx*(-0.25)\n",
+ "print\"delta=\",delta\n",
+ "#Now using equation ux=(g*Beta*delta*2(Tw-Tinf))/(4*nu)\n",
+ "#ux is the velocity at point x\n",
+ "print \"The velocity at point x is ux in m/s is\"\n",
+ "ux=(g*Beta*delta*2*(Tw-Tinf))/(4*nu)\n",
+ "print\"ux=\",ux\n",
+ "# (u/ux)=(y/delta)*(1-y/delta)**2\n",
+ "#Putting value of ux we get velovity function,u=465.9*(y-116*y*2+3341*y*3)\n",
+ "#For maximum value of u,du/dy=465.9*(1-232*y+10023*y**2)=0...this is a quadratic equation in which coefficients a=10023,b=232,c=1\n",
+ "a=10023;\n",
+ "b=232;\n",
+ "c=1;\n",
+ "#Solution for quadratic equation is given by y=(-b+-(b*2-4ac)*0.5)/2*a\n",
+ "print \"For maximum value of velocity,u\"\n",
+ "y=(b+(b*2-4*a*c)*0.5)/(2*a)#root of the quadratic equation\n",
+ "y=(b-(b*2-4*a*c)*0.5)/(2*a)#root of the quadratic equation\n",
+ "#The value of 0.0173 is at the edge of boundary layer,where u=0\n",
+ "#Therefore the maximum value occurs at y=0.00573m i.e Umax=465.9*y*(1-57.8*y)**2\n",
+ "y=0.00573;\n",
+ "#Umax is maximum velocity\n",
+ "print \"Maximum velocity in m/s is\"\n",
+ "Umax=465.9*y*(1-57.8*y)*2#NOTE:The answer given in the book is incorrect,in this expresssion they considered square on y only,however it is on whole expression (1-57.8*y)*2\n",
+ "#mdot is mass flow rate\n",
+ "print\"Umax=\",Umax\n",
+ "print \"Mass flow rate at x=0.8m,in kG is\"\n",
+ "I=quad(lambda y:465.9*(y-116*y*2+3341*y*3),0,delta)\n",
+ "mdot=rho*B*I[0]\n",
+ "print\"mdot=\",mdot\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.4:pg-369"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 4\n",
+ "Grashoff number is\n",
+ "Rayleigh number is\n",
+ "Hence,the flow is laminar\n",
+ "The thickness of the boundary layer in metre is\n",
+ "The average heat transfer coeficient in W/(m**2*K) is\n",
+ "0.101781170483\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "import math \n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 8, Example 4\"\n",
+ "#A square plate length,L=0.2m by breadth,B=0.2m is suspended vertically in a quiescent atmospheric air at a temprature(Tinf)=300K\n",
+ "L=0.2;\n",
+ "B=0.2;\n",
+ "Tinf=300;\n",
+ "#The Temprature of plate(Tw) is maintained at 400K\n",
+ "Tw=400;\n",
+ "#The required property value of air at a film temprature(Tf)=350K,kinematic viscosity (nu=20.75*10**-6),Prandtl number(Pr=0.69),conductivity(k=0.03W/(m*K))\n",
+ "Tf=350;\n",
+ "nu=20.75*10**-6;\n",
+ "Pr=0.69;\n",
+ "k=0.03;\n",
+ "#volume expansion coefficient is Beta\n",
+ "Beta=(1/Tf);\n",
+ "#g is acceleration due to gravity =9.81m/s**2\n",
+ "g=9.81;\n",
+ "#Grashoff number is given by GrL=(g*beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"Grashoff number is\"\n",
+ "GrL=(g*Beta*(Tw-Tinf)*L**3)/(nu)**2 \n",
+ "print\"GrL=\",GrL\n",
+ "#Rayleigh number is defined as RaL=GrL*Pr\n",
+ "print\"Rayleigh number is\"\n",
+ "RaL=GrL*Pr\n",
+ "print\"Hence,the flow is laminar\"\n",
+ "print\"RaL=\",RaL\n",
+ "#delta is the thickness of the boundary layer\n",
+ "print\"The thickness of the boundary layer in metre is\"\n",
+ "x=0.2;#location of trailing edge of plate\n",
+ "delta=(x*3.93*(0.952+Pr)**(1/4))/(Pr**(1/2)*(GrL)**(1/4))#NOTE:The answer in the book is incorrect(calculation mistake)\n",
+ "print\"delta=\",delta\n",
+ "#hL and hbarL are local and average heat transfer coefficient respectively\n",
+ "print\"The average heat transfer coeficient in W/(m**2*K) is\"\n",
+ "hL=(2*k)/delta;\n",
+ "hbarL=(4.0/3)*(hL)#NOTE:The answer in the book is incorrect(calculation mistake)\n",
+ "print\"hL=\",hL\n",
+ "print\"hbarL=\",hbarL\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.5:pg-373"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 5\n",
+ "Grashoff number is\n",
+ "503958851.066\n",
+ "Rayleigh number is\n",
+ "357810784.257\n",
+ "Therefore the flow is laminar\n",
+ "Nusselt number is\n",
+ "75.3134665126\n",
+ "Average heat transfer coefficient(hbarL)in W/(m**2*°C)\n",
+ "The rate of heat transfer in W is \n",
+ "Now if we use NuL2=0.59*RaL**(1/4) with the value of C=0.59,n=(1/4)\n",
+ "Nusselt number is\n",
+ "Average heat transfer coefficient(hbarL)in W/(m**2*°C)\n",
+ "The rate of heat transfer in W is \n",
+ "49.9857347505\n",
+ "(b)For the horizontal plate facing up\n",
+ "Now RaL2=Gr*Pr*(Lc/L)**3\n",
+ "Rayleigh number is\n",
+ "Nusselt number is given by NuL3=C*(GrL*Pr)**n\n",
+ "Average heat transfer coefficient(hbarL)in W/(m**2*°C)\n",
+ "The rate of heat transfer in W is \n",
+ "64.6997833306\n",
+ "(c)When the hot surface faces is down\n",
+ "Nusselt number is given by NuL4=0.27*RaL2**(1/4)\n",
+ "13.1290144745\n",
+ "Average heat transfer coefficient(hbarL) in W/(m**2)\n",
+ "2.9408992423\n",
+ "The rate of heat transfer in W is \n",
+ "32.3498916653\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "import math \n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 8, Example 5\"\n",
+ "#A square plate of length(L)=0.5m by breadth,B=0.5m in a room at temprature,Tinf=30°C\n",
+ "#One side of plate is kept a uniform temprature(Tw)=74°C\n",
+ "Tw=74;\n",
+ "L=0.5;\n",
+ "B=0.5;\n",
+ "Tinf=30.0;\n",
+ "#The required properties at the film temprature(Tf)=52°C are kinematic viscosity(nu=1.815*10**-5),Prandtl number(Pr=0.71),conductivity(k=0.028W/(m*°C))\n",
+ "Tf=52.0;\n",
+ "Pr=0.71;\n",
+ "nu=1.815*10**-5;\n",
+ "k=0.028;\n",
+ "#Area(A)=L*B m**2\n",
+ "A=L*B;\n",
+ "#Volume expansion coefficient is Beta\n",
+ "Beta=1/(273+Tf);\n",
+ "#g is acceleration due to gravity =9.81m/s**2\n",
+ "g=9.81;\n",
+ "#Grashoff number is given by GrL=(g*beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"Grashoff number is\"\n",
+ "GrL=(g*Beta*(Tw-Tinf)*L**3)/(nu)**2 \n",
+ "print GrL\n",
+ "#Rayleigh number is defined as RaL1=GrL*Pr\n",
+ "print\"Rayleigh number is\"\n",
+ "RaL1=GrL*Pr\n",
+ "print RaL1\n",
+ "print\"Therefore the flow is laminar\"\n",
+ "#We make use of following equation to find Nusselt number,NuL1=(4/3)*(0.508*Pr**(-1/2)*(0.952+Pr)**(-1/4)*Gr**(1/4))\n",
+ "print\"Nusselt number is\"\n",
+ "NuL1=(4.0/3)*(0.508*Pr**(1.0/2)*(0.952+Pr)**(-1.0/4)*GrL**(1.0/4))\n",
+ "#Average heat transfer coefficient(hbarL) is given by (NuL*k)/L\n",
+ "print NuL1\n",
+ "print\"Average heat transfer coefficient(hbarL)in W/(m**2*°C)\"\n",
+ "hbarL=(NuL1*k)/L\n",
+ "#The rate of heat transfer(Q) from the plate by free convection is given by Q=hbarL*A*(Tw-Tinf)\n",
+ "print\"The rate of heat transfer in W is \"\n",
+ "Q=hbarL*A*(Tw-Tinf)\n",
+ "print\"Now if we use NuL2=0.59*RaL**(1/4) with the value of C=0.59,n=(1/4)\"\n",
+ "print\"Nusselt number is\"\n",
+ "NuL2=0.59*RaL1**(1.0/4)\n",
+ "#Average heat transfer coefficient(hbarL) is given by (NuL*k)/L\n",
+ "print\"Average heat transfer coefficient(hbarL)in W/(m**2*°C)\"\n",
+ "hbarL=(NuL2*k)/L\n",
+ "#The rate of heat transfer(Q) from the plate by free convection is given by Q=hbarL*A*(Tw-Tinf)\n",
+ "print\"The rate of heat transfer in W is \"\n",
+ "Q=hbarL*A*(Tw-Tinf)\n",
+ "print Q\n",
+ "print\"(b)For the horizontal plate facing up\"\n",
+ "#Perimeter(P) for a square plate is P=4*L\n",
+ "P=4*L;\n",
+ "#Characterstic length(Lc)=A/P\n",
+ "Lc=A/P\n",
+ "print\"Now RaL2=Gr*Pr*(Lc/L)**3\"\n",
+ "print\"Rayleigh number is\"\n",
+ "RaL2=GrL*Pr*(Lc/L)**3\n",
+ "#The values of constants,C=0.54 and n=(1/4)\n",
+ "C=0.54;\n",
+ "n=(1.0/4);\n",
+ "print\"Nusselt number is given by NuL3=C*(GrL*Pr)**n\"\n",
+ "NuL3=C*(RaL2)**n\n",
+ "print\"Average heat transfer coefficient(hbarL)in W/(m**2*°C)\"\n",
+ "hbarL=(NuL3*k)/Lc\n",
+ "print\"The rate of heat transfer in W is \"\n",
+ "Q=hbarL*A*(Tw-Tinf)\n",
+ "print Q\n",
+ "print\"(c)When the hot surface faces is down\"\n",
+ "print\"Nusselt number is given by NuL4=0.27*RaL2**(1/4)\"\n",
+ "NuL4=0.27*RaL2**(1.0/4)\n",
+ "print NuL4\n",
+ "print\"Average heat transfer coefficient(hbarL) in W/(m**2)\"\n",
+ "hbarL=(NuL4*k)/Lc\n",
+ "print hbarL\n",
+ "print\"The rate of heat transfer in W is \"\n",
+ "Q=hbarL*A*(Tw-Tinf)\n",
+ "print Q\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.6:pg-375"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 6\n",
+ "Grashoff number is\n",
+ "GrL= 813719594.384\n",
+ "Rayleigh number is\n",
+ "RaL= 569603716.069\n",
+ "Therefore the flow is laminar\n",
+ "Now we use NuL=0.59*RaL**(1/4.0) with the value of constants C=0.59,n=(1/4.0)\n",
+ "Nusselt number is\n",
+ "NuL= 91.1475952489\n",
+ "Average heat transfer coefficient in W/(m**2*K)\n",
+ "hbarL1= 5.46885571493\n",
+ "Grashoff number GrD=GrL*(D/L)**3\n",
+ "GrD= 0.00650975675508\n",
+ "The correction factor is\n",
+ "F= 39.485281111\n",
+ "The correct value of Average heat transfer coefficient(hbarL2)=hbarL1*F in W/(m**2*K) is\n",
+ "hbarL2= 215.939305259\n",
+ "The ohmic loss in W is \n",
+ "q= 3.39196667512\n",
+ "The current flowing in the wire in Ampere is\n",
+ "I= 7.51882822777\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "import math \n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 8, Example 6\"\n",
+ "#A vertical wire of length(L)=0.5m and Dimeter(D)=0.1mm is maintained at temprature, Tw=400K\n",
+ "#The temprature of quicsent air is Tinf=300K\n",
+ "#Resistance(R) per meter length is 0.12ohm\n",
+ "R=0.12;\n",
+ "Tw=400.0;\n",
+ "L=0.5;\n",
+ "D=0.1*10**-3;#in metre\n",
+ "Tinf=300;\n",
+ "#The required properties at the film temprature(Tf)=350K are kinematic viscosity(nu=20.75*10**-6m**2/s),Prandtl number(Pr=0.70),conductivity(k=0.03W/(m*°C))\n",
+ "Tf=350.0;\n",
+ "Pr=0.70;\n",
+ "nu=20.75*10**-6;\n",
+ "k=0.03;\n",
+ "#Area(A)=L*B m**2\n",
+ "A=math.pi*D*L;\n",
+ "#Volume expansion Coefficient is Beta\n",
+ "Beta=1/(Tf);\n",
+ "#g is acceleration due to gravity =9.81m/s**2\n",
+ "g=9.81;\n",
+ "#Grashoff number is given by GrL=(g*beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"Grashoff number is\"\n",
+ "GrL=(g*Beta*(Tw-Tinf)*L**3)/(nu)**2 \n",
+ "print\"GrL=\",GrL\n",
+ "#Rayleigh number is defined as RaL=GrL*Pr\n",
+ "print\"Rayleigh number is\"\n",
+ "RaL=GrL*Pr\n",
+ "print\"RaL=\",RaL\n",
+ "print\"Therefore the flow is laminar\"\n",
+ "#NuL is nusselt number\n",
+ "#C and n are constants\n",
+ "print\"Now we use NuL=0.59*RaL**(1/4.0) with the value of constants C=0.59,n=(1/4.0)\"\n",
+ "print\"Nusselt number is\"\n",
+ "NuL=0.59*RaL**(1/4.0)\n",
+ "print\"NuL=\",NuL\n",
+ "#hbarL1 is the Average heat transfer coefficient\n",
+ "print\"Average heat transfer coefficient in W/(m**2*K)\"\n",
+ "hbarL1=(NuL*k)/L\n",
+ "print\"hbarL1=\",hbarL1\n",
+ "#Grashoff number GrD=GrL*(D/L)**3\n",
+ "print\"Grashoff number GrD=GrL*(D/L)**3\"\n",
+ "GrD=GrL*(D/L)**3\n",
+ "print\"GrD=\",GrD\n",
+ "#The correction factor is given By F=1.3*((L/D)/GrD)**(1/4.0)+1.0\n",
+ "print\"The correction factor is\"\n",
+ "F=1.3*((L/D)/GrD)**(1/4.0)+1.0\n",
+ "print\"F=\",F\n",
+ "print\"The correct value of Average heat transfer coefficient(hbarL2)=hbarL1*F in W/(m**2*K) is\"\n",
+ "hbarL2=hbarL1*F\n",
+ "print\"hbarL2=\",hbarL2\n",
+ "#The ohmic power loss is given by energy balance I**2*R=q=hbar2*A*(Tw-Tinf)\n",
+ "#q is the ohmic power loss\n",
+ "print\"The ohmic loss in W is \"\n",
+ "q=hbarL2*A*(Tw-Tinf)\n",
+ "print\"q=\",q\n",
+ "#The current flowing in the wire I=(q/(R*L)**(1/2.0)\n",
+ "print\"The current flowing in the wire in Ampere is\"\n",
+ "I=(q/(R*L))**(1/2.0)\n",
+ "print\"I=\",I\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.7:pg-378"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 7\n",
+ "Grashoff number is\n",
+ "GrD= 53311595.6796\n",
+ "Rayleigh number is\n",
+ "RaD= 37318116.9757\n",
+ "The flow is laminar over the entire cylinder\n",
+ "we use following equation to find Nusselt number NuD=(0.60+((0.387*RaD**(1/6))/(1+(0.559/Pr**(9/16)))**(8/27)))**2\n",
+ "NuD= 0.974169\n",
+ "Average heat transfer coefficient in W/(m**2*K)\n",
+ "hbar= 0.14612535\n",
+ "The heat loss per meter length in W is\n",
+ "q= 9.64039284733\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "import math \n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 8, Example 7\"\n",
+ "#A long horizontal pressurized hot water of diameter(D)=200mm passes through a room where the air temprature is Tinf=25°C\n",
+ "D=.2;\n",
+ "Tinf=25;\n",
+ "#Length(L)=1m ,since the unit length is considered\n",
+ "L=1;\n",
+ "#Area(A)=pi*L*D\n",
+ "A=math.pi*L*D;\n",
+ "#The pipe surface temprature is Tw=130°C\n",
+ "Tw=130;\n",
+ "#The properties of air at the film temprature Tf=77.5°C are kinematic viscosity(nu=21*10**-6m**2/s),Prandtl number(Pr=0.70),Conductivity(k=0.03W/(m*K))\n",
+ "Tf=77.5;\n",
+ "nu=21*10**-6;\n",
+ "k=0.03;\n",
+ "Beta=(1/(273+Tf));#Volume expansion coefficient in k**-1)\n",
+ "Pr=0.70;\n",
+ "#g is acceleration due to gravity =9.81m/s**2\n",
+ "g=9.81;\n",
+ "#Grashoff number is given by GrD=(g*beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"Grashoff number is\"\n",
+ "GrD=(g*Beta*(Tw-Tinf)*D**3)/(nu)**2 \n",
+ "print\"GrD=\",GrD\n",
+ "#Rayleigh number is defined as RaD=GrD*Pr\n",
+ "print\"Rayleigh number is\"\n",
+ "RaD=GrD*Pr\n",
+ "print\"RaD=\",RaD\n",
+ "print\"The flow is laminar over the entire cylinder\"\n",
+ "#NuD is the nusselt number\n",
+ "print\"we use following equation to find Nusselt number NuD=(0.60+((0.387*RaD**(1/6))/(1+(0.559/Pr**(9/16)))**(8/27)))**2\"\n",
+ "NuD=(0.60+((0.387*RaD**(1/6))/(1+(0.559/Pr**(9/16)))**(8/27)))**2\n",
+ "print\"NuD=\",NuD\n",
+ "#hbar is the avearge heat transfer coefficient\n",
+ "print\"Average heat transfer coefficient in W/(m**2*K)\"\n",
+ "hbar=(NuD*k)/D\n",
+ "print\"hbar=\",hbar\n",
+ "#The heat loss per meter length is given by q=hbar*A*(Tw-Tinf)\n",
+ "print\"The heat loss per meter length in W is\"\n",
+ "q=hbar*A*(Tw-Tinf)\n",
+ "print\"q=\",q\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.8:pg-381"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Introduction to heat transfer by S.K.Som, Chapter 8, Example 8\n",
+ "Let us take first trial Tw=64°C\n",
+ "Grashoff number is\n",
+ "GrD= 226303.67232\n",
+ "Rayleigh number is\n",
+ "The flow is laminar \n",
+ "RaD= 941423.276851\n",
+ "we use following equation to find Nusselt number NuD=(0.60+((0.387*RaD**(1/6))/(1+(0.559/Pr**(9/16)))**(8/27)))**2\n",
+ "NuD= 0.974169\n",
+ "Average heat transfer coefficient in W/(m**2*K)\n",
+ "hbarD= 77.20289325\n",
+ "Hence,steady state Surface temprature in °C is\n",
+ "Hence we see that our guess is in excellent agreement with the calculated value\n",
+ "Tw= 793.068225127\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "import math \n",
+ " \n",
+ "print\"Introduction to heat transfer by S.K.Som, Chapter 8, Example 8\"\n",
+ "#An electric immersion heater diameter(D)=8mm and length(L)=300mm is rated at power input,P=450W\n",
+ "P=450;\n",
+ "L=0.3;#in metre\n",
+ "D=0.008;#in metre\n",
+ "#If the heater is horizontally positioned in a large tank of stationery water at temprature,Tinf=20°C\n",
+ "Tinf=20;\n",
+ "#At steady state ,The electrical power input(P)=(Q)Heat loss from the heater\n",
+ "#P=Q\n",
+ "#Q=hbarD*(pi*D)*L*(Tw-Tinf)\n",
+ "#This gives Tw(surface temprature)=Tinf+(P/(hbarD*pi*D*L))\n",
+ "#So we need to find Average heat transfer coefficient,hbarD.\n",
+ "#In this problem we need to take guess of steady state surface temprature(Tw) and iterate the solution for Tw till a desired convergence is achieved.\n",
+ "print\"Let us take first trial Tw=64°C\"\n",
+ "Tw=64;\n",
+ "Tf=(Tw+Tinf)/2;#mean film temprature\n",
+ "#At this temprature of 42°C,The required properties of water kinematic viscosity(nu=6.25*10**-7m**2/s),Prandtl number(Pr=4.16),Conductivity(k=0.634W/(m*K)),Beta=4*10**-4K**-1\n",
+ "Beta=4*10**-4;#Volume expansion coefficient\n",
+ "nu=6.25*10**-7;\n",
+ "Pr=4.16;\n",
+ "k=0.634;\n",
+ "#g is acceleration due to gravity =9.81m/s**2\n",
+ "g=9.81;\n",
+ "#Grashoff number is given by GrD=(g*beta*(Tw-Tinf)*L**3)/(nu)**2\n",
+ "print\"Grashoff number is\"\n",
+ "GrD=(g*Beta*(Tw-Tinf)*D**3)/(nu)**2 \n",
+ "print\"GrD=\",GrD\n",
+ "#Rayleigh number is defined as RaD=GrD*Pr\n",
+ "print\"Rayleigh number is\"\n",
+ "RaD=GrD*Pr\n",
+ "print\"The flow is laminar \"\n",
+ "print\"RaD=\",RaD\n",
+ "#/NuD is nusselt number\n",
+ "#hbarD is Average heat transfer coefficient\n",
+ "print\"we use following equation to find Nusselt number NuD=(0.60+((0.387*RaD**(1/6))/(1+(0.559/Pr**(9/16)))**(8/27)))**2\"\n",
+ "NuD=(0.60+((0.387*RaD**(1/6))/(1+(0.559/Pr**(9/16)))**(8/27)))**2\n",
+ "print\"NuD=\",NuD\n",
+ "print\"Average heat transfer coefficient in W/(m**2*K)\"\n",
+ "hbarD=(NuD*k)/D\n",
+ "print\"hbarD=\",hbarD\n",
+ "print\"Hence,steady state Surface temprature in °C is\"\n",
+ "Tw=Tinf+(P/(hbarD*math.pi*D*L))\n",
+ "print\"Hence we see that our guess is in excellent agreement with the calculated value\"\n",
+ "print\"Tw=\",Tw\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\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": "2.7.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2024-12-20 11:16:36 +0000