{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Chapter 07:Principles of forced convection"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.1:pg-296"
]
},
{
"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 7, Example 1\n",
"First we check from reynolds no. that the flow is laminar or tubulent\n",
"Reynold number is\n",
"Re= 20000.0\n",
"which is less than critical reynolds number,So the flow is laminar.\n",
"The average nusselt number over the entire length under the situation is given by NuL=0.664*Re**0.5*Pr**(1/3)\n",
"NuL= 93.9037805416\n",
"Heat flux in W/(m**2*K) is\n",
"h= 2.72320963571\n",
"The rate of heat transfer per unit width in W is\n",
"Q= 408.481445356\n"
]
}
],
"source": [
"import math \n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 1\"\n",
"#Engine oil at temprature,Tinf=60Â°C with a velocity of Uinf=1m/s flows over plate of length(L)=5m whose temprature(Tw)=30Â°C\n",
"Tw=30;\n",
"L=5;\n",
"Uinf=1;\n",
"Tinf=60;\n",
"#The properties at a film temprature of 45Â°C are as follows density(rho=870kg/m**3),Prandtl number(Pr=2850),conductivity(k=0.145W/(m*Â°C)),kinematic viscosity(nu=250*10**-6m**2/s).\n",
"rho=870;\n",
"Pr=2850;\n",
"k=0.145;\n",
"nu=250*10**-6;\n",
"print\"First we check from reynolds no. that the flow is laminar or tubulent\"\n",
"#Reynolds number is given by Re=(Uinf*L)/nu\n",
"print\"Reynold number is\"\n",
"Re=(Uinf*L)/nu\n",
"print\"Re=\",Re\n",
"print\"which is less than critical reynolds number,So the flow is laminar.\"\n",
"#NuL is the average nusselt number\n",
"print\"The average nusselt number over the entire length under the situation is given by NuL=0.664*Re**0.5*Pr**(1/3)\"\n",
"NuL=0.664*Re**0.5*Pr**(1/3)\n",
"print\"NuL=\",NuL\n",
"#Heat flux is given by h=(k/L)*NuL\n",
"print\"Heat flux in W/(m**2*K) is\"\n",
"h=(k/L)*NuL\n",
"print\"h=\",h\n",
"#The rate of heat transfer per unit width is Q=h*A*(Tinf-Tw)\n",
"#Since unit width is considerd so B=1\n",
"#Area(A)=L*B\n",
"B=1;\n",
"A=L*B;\n",
"print\"The rate of heat transfer per unit width in W is\"\n",
"Q=h*A*(Tinf-Tw)\n",
"print\"Q=\",Q"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.2:pg-298"
]
},
{
"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 7, Example 2\n",
"The location x in m where the transition occurs\n",
"x= 0.275\n",
"The average Nusselt number for the laminar zone is\n",
"Nux= 469.518902708\n",
"Heat flux in W/(m**2*K) is\n",
"h= 44.3908780742\n",
"The reynolds number at L=2m is\n",
"ReL= 3636363.63636\n",
"The average heat transfer coefficient over L=2m in W/(m**2*K)\n",
"hbarL= -11.322519\n",
"The rate of heat transfer per unit width in W is\n",
"Q= -2264.5038\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 2\"\n",
"#Atmospheric air at temprature,Tinf=300K and with a free stream Velocity Uinf=30m/s flows over a flat plate parallel to a side of length(L)=2m.\n",
"Tinf=300;\n",
"Uinf=30;\n",
"L=2;\n",
"#It is maintained at a uniform temprature of Tw=400K.\n",
"Tw=400;\n",
"#The properties of air at the film temprature of 350K are Prandtl number(Pr=0.705),conductivity(k=0.026W/(m*Â°C)),kinematic viscosity(nu=16.5*10**-6m**2/s)\n",
"Pr=0.705; \n",
"k=0.026;\n",
"nu=16.5*10**-6;\n",
"#We first find the location x(for reynolds number,Re=5*10**5) where the transition occurs\n",
"#Rex is reynolds number\n",
"print\"The location x in m where the transition occurs\"\n",
"Rex=5*10**5;\n",
"x=(nu*Rex)/Uinf\n",
"print\"x=\",x\n",
"#The average Nusselt number for the laminar zone is given by Nux=0.664*Re**0.5*Pr**(1/3)\n",
"print\"The average Nusselt number for the laminar zone is\"\n",
"Nux=0.664*Rex**0.5*Pr**(1/3)\n",
"print\"Nux=\",Nux\n",
"#Heat flux is given by h=(k/x)*Nux\n",
"print\"Heat flux in W/(m**2*K) is\"\n",
"h=(k/x)*Nux\n",
"print\"h=\",h\n",
"#Reynolds number is given by ReL=(Uinf*L)/nu\n",
"print\"The reynolds number at L=2m is\"\n",
"ReL=(Uinf*L)/nu\n",
"print\"ReL=\",ReL\n",
"#The average heat transfer coefficient over L=2m is determined from hbarL=(k/L)*(0.037*(ReL)**(4/5)-871)*Pr**(1/3)\n",
"print\"The average heat transfer coefficient over L=2m in W/(m**2*K)\"\n",
"hbarL=(k/L)*(0.037*(ReL)**(4/5)-871)*Pr**(1/3)\n",
"print\"hbarL=\",hbarL\n",
"#The rate of heat transfer per unit width is Q=h*A*(Tinf-Tw)\n",
"#Since unit width is considerd so B=1\n",
"#Area(A)=L*B\n",
"B=1;\n",
"A=L*B;\n",
"print\"The rate of heat transfer per unit width in W is\"\n",
"Q=hbarL*A*(Tw-Tinf)\n",
"print\"Q=\",Q"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.3:pg-314"
]
},
{
"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 7, Example 3\n",
"(a)When the air flows parallel to the long side we have L=5 and the Reynolds no. becomes\n",
"ReL= 1250000.0\n",
"which is greater than critical Reynolds number.\n",
"The average heat transfer coefficient over L=5m in W/(m**2*K)\n",
"hbarL= -5.225778\n",
"The rate of heat transfer per unit width in W is\n",
"Q= -3135.4668\n",
"(b)When the air flow is parallel to the 1m side we have L=1 an the Reynolds no. becomes \n",
"which is less than critical Reynolds number.\n",
"ReL= 250000.0\n",
"Heat flux in W/(m**2*K) is\n",
"h= 9.96\n",
"The rate of heat transfer per unit width in W is\n",
"Q= 5976.0\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 3\"\n",
"#Air at a pressure of 101kPa and temprature,Tinf=20Â°C flows with a velocity(Uinf) of 5m/s over a flat plate whose temprature is kept constant at Tw=140Â°C.\n",
"Tw=140;\n",
"Tinf=20;\n",
"Uinf=5;\n",
"#The properties at the film temprature of 80Â°C are Prandtl number(Pr=0.706),Conductivity(k=0.03W/(m*Â°C)),kinematic viscosity(nu=2*10**-5m**2/s)\n",
"Pr=0.706;\n",
"k=0.03;\n",
"nu=2*10**-5;\n",
"#ReL is reynolds number and L is length of flat plate\n",
"print\"(a)When the air flows parallel to the long side we have L=5 and the Reynolds no. becomes\"\n",
"L=5;\n",
"ReL=(Uinf*L)/nu\n",
"print\"ReL=\",ReL\n",
"print\"which is greater than critical Reynolds number.\"\n",
"#Thus we have combined laminar and tubulent flow.\n",
"# So The average heat transfer coefficient over L=5m is determined from hbarL=(k/L)*(0.037*(ReL)**(4/5)-871)*Pr**(1/3)\n",
"print\"The average heat transfer coefficient over L=5m in W/(m**2*K)\"\n",
"hbarL=(k/L)*(0.037*(ReL)**(4/5)-871)*Pr**(1/3)\n",
"print\"hbarL=\",hbarL\n",
"#The rate of heat transfer per unit width is Q=h*A*(Tinf-Tw)\n",
"#Since width is 1m so B=1\n",
"#Area(A)=L*B\n",
"B=1;\n",
"A=L*B;\n",
"#Q is the rate of heat transfer\n",
"print\"The rate of heat transfer per unit width in W is\"\n",
"Q=hbarL*A*(Tw-Tinf)\n",
"print\"Q=\",Q\n",
"#When the air flow is parallel to the 1m side we have L=1\n",
"print\"(b)When the air flow is parallel to the 1m side we have L=1 an the Reynolds no. becomes \"\n",
"L=1;\n",
"ReL=(Uinf*L)/nu\n",
"print\"which is less than critical Reynolds number.\"\n",
"print\"ReL=\",ReL\n",
"#Thus we have laminar flow\n",
"#Heat flux is given by h=(k/L)*0.664*ReL**0.5*Pr**(1/3)\n",
"print\"Heat flux in W/(m**2*K) is\"\n",
"h=(k/L)*0.664*ReL**0.5*Pr**(1/3)\n",
"print\"h=\",h\n",
"#The rate of heat transfer per unit width is Q=h*A*(Tinf-Tw)\n",
"#Now width is 5m so B=5\n",
"#Area(A)=L*B\n",
"B=5;\n",
"A=L*B;\n",
"#Q is the rate of heat transfer\n",
"print\"The rate of heat transfer per unit width in W is\"\n",
"Q=h*A*(Tw-Tinf)\n",
"print\"Q=\",Q"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.4:pg-322"
]
},
{
"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 7, Example 4\n",
"(a)Reynolds number is\n",
"ReL= 6000.0\n",
"The boundary layer thickness in m is\n",
"delta= 0.387298334621\n",
"Prandtl no. is\n",
"Pr= 831.024930748\n",
"The thermal boundary layer thickness in m is\n",
"deltaT= 0.387298334621\n",
"(b)Since the prandtl number is high So Nusselt no. is\n",
"NuL= 26.2588270873\n",
"Heat flux in W/(m**2*K) is\n",
"hL= 0.919058948055\n",
"hbarL in W/(m**2*K) is\n",
"hbarL= 1.83811789611\n",
"(c)The rate of heat transfer in W is\n",
"Q= 661.7224426\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 4\"\n",
"#Castor oil at temprature,Tinf=36Â°C flows over a heated plate of length,L=6m and breadth,B=1m at velocity,Uinf=0.06m/s\n",
"Tinf=36;\n",
"L=6;\n",
"B=1;\n",
"Uinf=0.06;\n",
"#For a surface temprature at Tw=96Â°C\n",
"Tw=96;\n",
"#The properties at film temprature 66Â°C conductivity(k=0.21W/(m*K)),kinematic viscosity(nu=6*10**-5m**2/s),Thermal diffusivity(alpha=7.22*10**-8 m**2/s)\n",
"nu=6*10**-5;\n",
"k=0.21;\n",
"alpha=7.22*10**-8;\n",
"#ReL is reynolds number\n",
"print\"(a)Reynolds number is\"\n",
"ReL=(Uinf*L)/nu\n",
"print\"ReL=\",ReL\n",
"#Therefore the boundary layer is laminar over the entire plate.\n",
"#delta is the boundary layer thickness\n",
"print\"The boundary layer thickness in m is\"\n",
"delta=(5*L)/(ReL)**0.5\n",
"print\"delta=\",delta\n",
"#Pr is prandtl number.\n",
"print\"Prandtl no. is\"\n",
"Pr=nu/alpha\n",
"print\"Pr=\",Pr\n",
"#deltaT is thermal boundary layer thickness\n",
"print\"The thermal boundary layer thickness in m is\"\n",
"deltaT=delta/(Pr**(1/3))#NOTE:Answer in the book is incorrect(calculation mistake)\n",
"print\"deltaT=\",deltaT\n",
"#NuL is the nusselt number\n",
"print\"(b)Since the prandtl number is high So Nusselt no. is\"\n",
"NuL=0.339*(ReL)**0.5*Pr**(1/3)\n",
"print\"NuL=\",NuL\n",
"#Heat flux is given by hL=(k/L)*NuL\n",
"print\"Heat flux in W/(m**2*K) is\"\n",
"hL=(k/L)*NuL\n",
"print\"hL=\",hL\n",
"#hbarL is the average heat flux over length L\n",
"print\"hbarL in W/(m**2*K) is\"\n",
"hbarL=2*hL\n",
"print\"hbarL=\",hbarL\n",
"#The rate of heat transfer is Q=h*A*(Tinf-Tw)\n",
"#Area(A)=L*B\n",
"A=L*B;\n",
"print\"(c)The rate of heat transfer in W is\"\n",
"Q=hbarL*A*(Tw-Tinf)\n",
"print\"Q=\",Q"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.5:pg-322"
]
},
{
"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 7, Example 5\n",
"Reynolds number is\n",
"ReL= 11181.8181818\n",
"Therefore the flow is turbulent over the module \n",
"The local heat transfer coefficient at L in W/(m**2*K)is\n",
"hL= 8.32911955901e+30\n",
"The required power generation in W/m**3 is\n",
"qm= 1.6658239118e+31\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 5\"\n",
"#A flat plate of width B=1m is maintained at a uniform surface temprtaure(Tw)=225Â°C\n",
"Tw=225;\n",
"B=1;\n",
"#Heating is done by rectangular modules of thickness t=10mm and length l=40mm.\n",
"t=10;\n",
"l=40;\n",
"#atmospheric air at temprature,Tinf=25Â°C flows over the plate at velocity(Uinf)=30m/s.\n",
"Tinf=25;\n",
"Uinf=30;\n",
"#The thermophysical properties of module are conductivity(km=5.2W/(m*K)),specific heat(cp=320J/(kg/K)),density(rho=2300kg/m**3).\n",
"km=5.2;\n",
"cp=320;\n",
"rho=2300;\n",
"#Assume the air properties at the film temprature of 125Â°C conductivity(ka=0.031W/(m*K)),kinematic viscosity(nu=22*10**-6m**2/s),Prandtl number(Pr=0.7)\n",
"ka=0.031;\n",
"nu=22*10**-6;\n",
"Pr=0.7;\n",
"#Module is placed at a distance of 800mm from the leading edge\n",
"#The distance from leading edge to the centre-line of the module,L=800+20=820mm.\n",
"L=0.0082;#in metre\n",
"#ReL is the reynolds number \n",
"print\"Reynolds number is\"\n",
"ReL=(Uinf*L)/nu\n",
"print\"ReL=\",ReL\n",
"print\"Therefore the flow is turbulent over the module \"\n",
"#The local heat transfer coefficient at L is calculated using hL=(k/L)*0.0296*(ReL)**(4/5)*(Pr)**(1/3)\n",
"print\"The local heat transfer coefficient at L in W/(m**2*K)is\"\n",
"hL=(ka/L)*0.0296*(ReL)**(4/0.5)*(Pr)**(1/0.3)\n",
"print\"hL=\",hL\n",
"#We consider that the local heat transfer coefficient at L=0.82m remains the same over the module which extends from L=0.80m to 0.84m \n",
"#If qm be the power generation in W/m**2 within the module ,we can write from energy balance qm*(t/0.1000)*(l/0.1000)*(B)=hbarL*(t/0.1000)*(B)*(Tw-Tinf)\n",
"print\"The required power generation in W/m**3 is\"\n",
"qm=(hL*(l/0.1000)*(B)*(Tw-Tinf))/((t/0.1000)*(l/0.1000)*(B))\n",
"print\"qm=\",qm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.6:pg-327"
]
},
{
"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 7, Example 6\n",
"Reynolds number is\n",
"ReL= 15000000.0\n",
"Since ReL>Rec(=5*10**5) the flow is approximated as turbulent over the entire surface of the wing \n",
"Nux= 0.0308\n",
"Nusselt number is \n",
"NubarL= 0.0308\n",
"Average heat transfer coefficient in W/(m**2*K) is\n",
"hbarL= 0.0003696\n",
"Surface temprature of wing in kelvin is\n",
"Tw= 1217800.46753\n"
]
}
],
"source": [
"import math\n",
"\n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 6\"\n",
"#An aircraft is moving at a velocity of Uinf=150m/s in air at an altitude where the pressure is 0.7bar and the temprature is Tinf=-5Â°C.\n",
"Tinf=-5;\n",
"Uinf=150;\n",
"#The top surface of the wing absorbs solar radiation at a rate of Qr=900W/m**2.\n",
"Qr=900;\n",
"#Considering the wing as a flat plate of length(L)=2m and to be of solid construction with a single uniform surface temprature .\n",
"L=2;\n",
"#The properties of air at 268K and 0.7 bar are conductivity(k=0.024W/(m*K)),kinematic viscosity(nu=2*10**-5m**2/s),Prandtl number(Pr=0.72)\n",
"k=0.024;\n",
"nu=2*10**-5;\n",
"Pr=0.72;\n",
"#ReL is reynolds number\n",
"print\"Reynolds number is\"\n",
"ReL=Uinf*L/nu\n",
"print\"ReL=\",ReL\n",
"#Rec is critical reynolds number\n",
"print\"Since ReL>Rec(=5*10**5) the flow is approximated as turbulent over the entire surface of the wing \"\n",
"#Nusselt number is given by Nux=0.0308*ReL**(4/5)*Pr**(1/3)\n",
"Nux=0.0308*ReL**(4/5)*Pr**(1/3);\n",
"print\"Nux=\",Nux\n",
"#NubarL is average nusselt number over length L\n",
"print\"Nusselt number is \"\n",
"NubarL=(5/4)*Nux\n",
"print\"NubarL=\",NubarL\n",
"#Average heat transfer coefficient is given by hbarL=(k/L)*NubarL\n",
"print\"Average heat transfer coefficient in W/(m**2*K) is\"\n",
"hbarL=(k/L)*NubarL\n",
"print\"hbarL=\",hbarL\n",
"#From an energy balance the airfoil at steady state,Qr*As=2*hbarL*As*(Tw-Tinf) where Qr=radiation flux,As=upper or lower surface area.\n",
"#Therefore we can write Surface temprature of wing, Tw=Tinf+(Qr/(2*hbarL))\n",
"print\"Surface temprature of wing in kelvin is\"\n",
"Tw=(273+Tinf)+(Qr/(2*hbarL))\n",
"print\"Tw=\",Tw"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.7:pg-331"
]
},
{
"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 7, Example 7\n",
"Reynolds number is\n",
"Re= 141.176470588\n",
"Nusselt number is\n",
"NuD= 6.85819682626\n",
"The average Heat transfer coefficient in W/(m**2*K) is\n",
"hbar= 4629.28285773\n",
"Heat transfer per unit length in W/m is\n",
"qL= 14.5433210172\n",
"If we use eq NuD=0.3+((0.62*Re**0.5*Pr**(1/3))/(1+(0.4/Pr**(2/3))**(1/4))*(1+(Re/282000)**(5/8))**(4/5)\n",
"NuD= 7.66669771975\n",
"The average Heat transfer coefficient in W/(m**2*K) is\n",
"hbar= 5175.02096083\n",
"Heat transfer per unit length in W/m is\n",
"qL= 16.2578078327\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 7\"\n",
"#A fine wire having a diameter(D)=0.04mm is placed in an air stream at temprature,Tinf=25Â°C having a flow velocity of Uinf=60m/s perpendicular to wire.\n",
"D=0.04;\n",
"Tinf=25;\n",
"Uinf=60;\n",
"#An electric current is passed through the wire ,raising its surface temprature to Tw=50Â°C\n",
"Tw=50;\n",
"#For air at the film temprature of 37.5Â°C,conductivity(k=0.027 W/(m*K)),kinematic viscosity(nu=17*10**-6m**2/s) and Prandtl number(Pr=0.71)\n",
"k=0.027;\n",
"nu=17*10**-6;\n",
"Pr=0.71;\n",
"#Re is reynolds number\n",
"print\"Reynolds number is\"\n",
"Re=Uinf*(D*10**-3)/nu\n",
"print\"Re=\",Re\n",
"#C and n are constants\n",
"#The values of C and n are found for Re=141 are C=0.683 and n=0.466\n",
"#NuD is nusselt number\n",
"print\"Nusselt number is\"\n",
"NuD=(0.683)*Re**0.466*Pr**(1/3)\n",
"print\"NuD=\",NuD\n",
"#hbar is the average Heat transfer coefficient\n",
"print\"The average Heat transfer coefficient in W/(m**2*K) is\"\n",
"hbar=(k/(D*10**-3))*NuD\n",
"print\"hbar=\",hbar\n",
"#Heat transfer per unit length(qL) is given by pi*D*hbar*(Tw-Tinf)\n",
"print\"Heat transfer per unit length in W/m is\"\n",
"qL=math.pi*(D*10**-3)*hbar*(Tw-Tinf)\n",
"print\"qL=\",qL\n",
"#NuD is nusselt number\n",
"print\"If we use eq NuD=0.3+((0.62*Re**0.5*Pr**(1/3))/(1+(0.4/Pr**(2/3))**(1/4))*(1+(Re/282000)**(5/8))**(4/5)\"\n",
"NuD=0.3+((0.62*Re**0.5*Pr**(1/3))/(1+(0.4/Pr)**(2/3))**(1/4))*(1+(Re/282000)**(5/8))**(4/5)\n",
"print\"NuD=\",NuD\n",
"#hbar is the average Heat transfer coefficient\n",
"print\"The average Heat transfer coefficient in W/(m**2*K) is\"\n",
"hbar=(k/(D*10**-3))*NuD\n",
"print\"hbar=\",hbar\n",
"#Heat transfer per unit length(qL) is given by pi*D*hbar*(Tw-Tinf)\n",
"print\"Heat transfer per unit length in W/m is\"\n",
"qL=math.pi*(D*10**-3)*hbar*(Tw-Tinf)\n",
"print\"qL=\",qL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.8:pg-334"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
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"outputs": [
{
"name": "stdout",
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"text": [
"Introduction to heat transfer by S.K.Som, Chapter 7, Example 8\n",
"Reynolds number for mercury is\n",
"ReHg= 1000.0\n",
"Reynolds number for oil is\n",
"Reoil= 15.3846153846\n",
"The hydrodynamic entry length for mercury in m is\n",
"LeHg= 1.25\n",
"The hydrodynamic entry length for oil in m is\n",
"Leoil= 0.0192307692308\n",
"The thermal entry length for mercury in m is \n",
"LtHg= 0.02375\n",
"The thermal entry length for oil in m is\n",
"Ltoil= 1.63461538462\n"
]
}
],
"source": [
"import math\n",
"\n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 8\"\n",
"#Mercury and a light oil flowing at Uinf=4mm/s in a smooth tube having diameter(D)=25mm at a bulk temprature of 80Â°C.\n",
"Uinf=4*10**-3;#in metre\n",
"D=25*10**-3;#in metre\n",
"#The pertinent properties of the fluid at that temprature are kinematic viscosity of mercury(nuHg=1*10**-7m**2/s),kinematic viscosity of oil(nuoil=6.5*10**-6m**2/s)\n",
"#Prandtl number of mercury(PrHg=0.019),Prandtl number of oil(Proil=85).\n",
"nuHg=1*10**-7;\n",
"nuoil=6.5*10**-6;\n",
"PrHg=0.019;\n",
"Proil=85;\n",
"#ReHg is Reynolds number for mercury\n",
"print\"Reynolds number for mercury is\"\n",
"ReHg=Uinf*D/nuHg\n",
"print\"ReHg=\",ReHg\n",
"#Reoil is Reynolds number for oil\n",
"print\"Reynolds number for oil is\"\n",
"Reoil=Uinf*D/nuoil\n",
"print\"Reoil=\",Reoil\n",
"#The hydrodynamic length are given by L=0.05*Re*D\n",
"#LeHg is the hydrodynamic entry length for mercury\n",
"print\"The hydrodynamic entry length for mercury in m is\"\n",
"LeHg=0.05*ReHg*D\n",
"print\"LeHg=\",LeHg\n",
"#Leoil the hydrodynamic entry length for oil\n",
"print\"The hydrodynamic entry length for oil in m is\"\n",
"Leoil=0.05*Reoil*D\n",
"print\"Leoil=\",Leoil\n",
"#The thermal entry length are given by L=0.05*Re*Pr*D\n",
"#LtHg is the thermal entry length for mercury\n",
"print\"The thermal entry length for mercury in m is \"\n",
"LtHg=0.05*ReHg*PrHg*D\n",
"print\"LtHg=\",LtHg\n",
"#Ltoil is the thermal entry length for oil\n",
"print\"The thermal entry length for oil in m is\"\n",
"Ltoil=0.05*Reoil*Proil*D\n",
"print\"Ltoil=\",Ltoil"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.9:pg-336"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Introduction to heat transfer by S.K.Som, Chapter 7, Example 9\n",
"Reynold number is\n",
"Re= 348.623853211\n",
"Therefore the flow is laminar.The hydrodynamic entrance length in m is\n",
"Leh= 0.0697247706422\n",
"The thermal entrance length in m is\n",
"Let= 0.0488073394495\n",
"The heat transfer coefficient in W/(m**2*K) is \n",
"h= 32.7\n",
"The mass flow rate of air in kg/s is\n",
"mdot= 2.38761041673e-05\n",
"Therefore the constant surface heat flux qw in W/m**2 is\n",
"qw= 95.95\n",
"The tube surface temprature at the exit plane in Â°C is \n",
"Twe= 127.934250765\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 9\"\n",
"#Air at one atmospheric pressure and temprature(Tbi=75Â°C) enters a tube of internal diameter(D)=4.0mm with average velocity(U)=2m/s\n",
"Tbi=75;\n",
"D=4*10**-3;#in metre\n",
"U=2;\n",
"#The tube length is L=1.0m and a constant heat flux is imposed by the tube surface on the air over the entire length.\n",
"L=1;\n",
"#An exit bulk mean temprature(Tbo)=125Â°C is required.\n",
"Tbo=125;\n",
"#The properties of air 100Â°C are density(rho=0.95kg/m**3),Prandtl number(Pr=0.70),conductivity(k=0.03W/(m*K)),viscosity(mu=2.18*10**-5kg/(m*s)),specific heat(cp=1.01kJ/(kg/K))\n",
"rho=0.95;\n",
"Pr=0.70;\n",
"k=0.03;\n",
"mu=2.18*10**-5;\n",
"cp=1.01*10**3;\n",
"#Re is reynolds number\n",
"print\"Reynold number is\"\n",
"Re=rho*U*D/mu\n",
"print\"Re=\",Re\n",
"#Leh is the hydrodynamic entrance length\n",
"print\"Therefore the flow is laminar.The hydrodynamic entrance length in m is\"\n",
"Leh=0.05*Re*D\n",
"print\"Leh=\",Leh\n",
"#Let is the thermal entrance length\n",
"print\"The thermal entrance length in m is\"\n",
"Let=0.05*Re*Pr*D\n",
"print\"Let=\",Let\n",
"#The length of tube is given as 1m.A reasonable approach is to consider the flow to be fully developed for both velocity and tempratures over the entire profile lengths.\n",
"#For a fully developed flow with constant surface heat flux,Nusselt number is Nu=4.36\n",
"Nu=4.36;\n",
"#h is the heat transfer coefficient\n",
"print\"The heat transfer coefficient in W/(m**2*K) is \"\n",
"h=Nu*(k/D)\n",
"print\"h=\",h\n",
"#Here h=hL Since the heat transfer coefficient is constant over the entire length of tube.\n",
"#hL is the local heat transfer coefficient\n",
"hL=h;\n",
"#from an energy balance qw*pi*D*L=mdot*cp*(Tbo-Tbi)\n",
"#mdot is mass flow rate\n",
"print\"The mass flow rate of air in kg/s is\"\n",
"mdot=rho*(math.pi/4)*D**2*U\n",
"print\"mdot=\",mdot\n",
"#qw is the constant surface heat flux\n",
"print\"Therefore the constant surface heat flux qw in W/m**2 is\"\n",
"qw=(mdot*cp*(Tbo-Tbi))/(math.pi*D*L)\n",
"print\"qw=\",qw\n",
"#Let Twe be the surface temprature at the exit plane.Then we can write hL*(Twe-Tbo)=qw\n",
"print\"The tube surface temprature at the exit plane in Â°C is \"\n",
"Twe=Tbo+(qw/hL)\n",
"print\"Twe=\",Twe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.10:pg-338"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Introduction to heat transfer by S.K.Som, Chapter 7, Example 10\n",
"Reynold number is\n",
"Re= 348.623853211\n",
"Therefore the flow is laminar.The hydrodynamic entrance length in m is\n",
"Leh= 0.0697247706422\n",
"The thermal entrance length in m is\n",
"Let= 0.0488073394495\n",
"The thermal entrance length is greater than the tube length Therefore the flow is hydrodynamically developed but not thermally developed\n",
"The inverse of graetz number Gr_1 is\n",
"Gr_1= 0.040977443609\n",
"Therefore the local heat transfer coefficient in W/(m**2*K) is\n",
"hL= 35.25\n",
"The mass flow rate of air in kg/s is\n",
"mdot= 2.38761041673e-05\n",
"Therefore surafce heat flux qw in W/m**2 is\n",
"qw= 2398.75\n",
"The tube surface temprature at the exit plane in Â°C is \n",
"Twe= 193.04964539\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 10\"\n",
"#Air at one atmospheric pressure and temprature(Tbi=75Â°C) enters a tube of internal diameter(D)=4.0mm with average velocity(U)=2m/s\n",
"Tbi=75;\n",
"D=4*10**-3;\n",
"U=2;\n",
"#The heated tube length is L=0.04m and a constant heat flux is imposed by the tube surface on the air over the entire length.\n",
"L=0.04;\n",
"#An exit bulk mean temprature(Tbo)=125Â°C is required.\n",
"Tbo=125;\n",
"#The properties of air 100Â°C are density(rho=0.95kg/m**3),Prandtl number(Pr=0.70),conductivity(k=0.03W/(m*K)),viscosity(mu=2.18*10**-5kg/(m*s)),specific heat(cp=1.01kJ/(kg/K))\n",
"rho=0.95;\n",
"Pr=0.70;\n",
"k=0.03;\n",
"mu=2.18*10**-5;\n",
"cp=1.01*10**3;\n",
"#Re is the reynolds number \n",
"print\"Reynold number is\"\n",
"Re=rho*U*D/mu\n",
"print\"Re=\",Re\n",
"#Leh is the hydrodynamic entrance length\n",
"print\"Therefore the flow is laminar.The hydrodynamic entrance length in m is\"\n",
"Leh=0.05*Re*D\n",
"print\"Leh=\",Leh\n",
"#Let is thermal entrance length\n",
"print\"The thermal entrance length in m is\"\n",
"Let=0.05*Re*Pr*D\n",
"print\"Let=\",Let\n",
"print\"The thermal entrance length is greater than the tube length Therefore the flow is hydrodynamically developed but not thermally developed\" \n",
"#We calculate the inverse graetz number at x=L=0.04m\n",
"x=0.04;\n",
"#Gr_1 is inverse of graetz number\n",
"print\"The inverse of graetz number Gr_1 is\"\n",
"Gr_1=(x/D)*(1/(Re*Pr))\n",
"print\"Gr_1=\",Gr_1\n",
"#For constant surface heat flux nusselt number is Nu=4.7 and Graetz number is Gr=4.1*10**-2\n",
"Nu=4.7;\n",
"Gr=4.1*10**-2;\n",
"#hL is the local heat transfer coefficient\n",
"print\"Therefore the local heat transfer coefficient in W/(m**2*K) is\"\n",
"hL=Nu*(k/D)\n",
"print\"hL=\",hL\n",
"#from an energy balance qw*pi*D*L=mdot*cp*(Tbo-Tbi)\n",
"#mdot is the mass flow rate\n",
"print\"The mass flow rate of air in kg/s is\"\n",
"mdot=rho*(math.pi/4)*D**2*U\n",
"print\"mdot=\",mdot\n",
"#qw is the surface heat flux\n",
"print\"Therefore surafce heat flux qw in W/m**2 is\"\n",
"qw=(mdot*cp*(Tbo-Tbi))/(math.pi*D*L)\n",
"print\"qw=\",qw\n",
"#Let Twe be the surface temprature at the exit plane.Then we can write hL*(Twe-Tbo)=qw\n",
"print\"The tube surface temprature at the exit plane in Â°C is \"\n",
"Twe=Tbo+(qw/hL)\n",
"print\"Twe=\",Twe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.11:pg-339"
]
},
{
"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 7, Example 11\n",
"Reynold number is\n",
"Re1= 13541.3214942\n",
"Nusselt number is\n",
"Nubar1= 56.808608087\n",
"The heat transfer transfer coefficient in W/(m**2*Â°C) \n",
"hbar1= 522.6391944\n",
"Outlet fluid temprature in first iteration is Tbo2 in Â°C is\n",
"Tb2 in Â°C is\n",
"Tb2= -30.4912413164\n",
"Reynold number is\n",
"Re2= 13938.8493187\n",
"Nusselt number is\n",
"The heat transfer transfer coefficient in W/(m**2*Â°C) \n",
"hbar2= 784.03829067\n",
"Outlet fluid temprature in second iteration is Tbo3 in Â°C is\n",
"Tbo3= -16.646852652\n",
"Tb3 in Â°C is\n",
"The Exit fluid temprature after second iteration is obtained as Tbo=-16.67Â°C\n",
"Tb3= -28.323426326\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 7, Example 11\"\n",
"#Liquid sulphur di oxide in a saturated state flows inside a L=5m long tube and D=25mm internal diameter with a mass flow rate(mdot) of 0.15 kg/s.\n",
"#The tube is heated at a constant surface temprature(Tw) of -10Â°C and the inlet fluid temprature is Tbi=-40Â°C\n",
"Tw=-10;\n",
"Tbi=-40;\n",
"mdot=0.15;\n",
"D=0.025;#in metre\n",
"L=5;\n",
"#The properties to be used shoud be estimated at a temprature which is arithmetic mean of Tbi and Tbo.\n",
"#Since (outlet fluid temprature Tbo) is not known a priori,the solution has to be based on an iterative method starting with a guess value of Tb1=(Tbi+Tbo)/2\n",
"#Here we denote bulk mean temprature as Tb.The superscript refers to the no. of trials\n",
"#For first trial,guess Tbo1=-20Â°C;so Tb1=-30Â°C\n",
"#We have the property values as follows at a temprature of -30Â°C.\n",
"rhob1=1520.64;#density in kg/m**3\n",
"nub1=0.371*10**-6;#kinematic viscosity in m**2/s\n",
"kb1=0.23;#conductivity in W/(m*Â°C)\n",
"Prb1=3.31;#Prandtl number\n",
"mub1=nub1*rhob1;#viscosity in kg/(m*s)\n",
"cpb1=1361.6;#specific heat in J/(kg*K)\n",
"#muw=nuw*rhow at Tw=10Â°C\n",
"nuw=0.288*10**-6;#kinematic viscosity at Tw in m**2/s\n",
"rhow=1463.61;#density at Tw in kg/m**3\n",
"muw=nuw*rhow;#viscosity at Tw in kg/(m*s)\n",
"#The reynolds number is found as Re1=(4*mdot)/(math.pi*D*mub1)\n",
"print\"Reynold number is\"\n",
"Re1=(4*mdot)/(math.pi*D*mub1)\n",
"print\"Re1=\",Re1\n",
"#Hence the flow is turbulent\n",
"#Now using equation, nusselt number is,Nubar1=0.027*(Re1)**0.8*Prb1**(1/3)*(mub1/muw)**0.14\n",
"print\"Nusselt number is\"\n",
"Nubar1=0.027*(Re1)**0.8*Prb1**(1/3)*(mub1/muw)**0.14\n",
"print\"Nubar1=\",Nubar1\n",
"#The heat transfer transfer coefficient hbar1=(kb1/D)*Nubar1\n",
"print\"The heat transfer transfer coefficient in W/(m**2*Â°C) \"\n",
"hbar1=(kb1/D)*Nubar1\n",
"print\"hbar1=\",hbar1\n",
"#The outlet fluid temprature can be found by making use of eqn Tbo2=Tw-(Tw-Tbi)*math.e((-math.pi*D*L*hbar1)/(mdot*cpb1))\n",
"print\"Outlet fluid temprature in first iteration is Tbo2 in Â°C is\"\n",
"Tbo2=Tw-(Tw-Tbi)*math.e**((-math.pi*D*L*hbar1)/(mdot*cpb1))\n",
"#Tb2 is the bulk mean temprature.\n",
"print\"Tb2 in Â°C is\"\n",
"Tb2=(Tbi+Tbo2)/2\n",
"print\"Tb2=\",Tb2\n",
"#Since the value differs from the assumed value of Tb1=-30Â°C,WE require furtheriteration,Therfore we start second trial with Tb2=-28.36Â°C\n",
"#We have the property value at a temprature of -28.36Â°C as follows\n",
"rhob2=1514;#density in kg/m**3\n",
"nub2=0.362*10**-6;#kinematic viscosity in m**2/s\n",
"kb2=0.229;#conductivity in W/(m*Â°C)\n",
"Prb2=3.23;#Prandtl number\n",
"mub2=nub2*rhob2;#viscosity in kg/(m*s)\n",
"cpb2=1362;#specific heat in J/(kg*K)\n",
"#muw=nuw*rhow at Tw=10Â°C\n",
"nuw=0.288*10**-6;#viscosity at Tw in m**2/s\n",
"rhow=1463.61;#density at Tw in kg/m**3\n",
"muw=nuw*rhow;#kinematic viscosity at Tw in kg/(m*s)\n",
"#The reynolds number is found as Re2=(4*mdot)/(math.pi*D*mub2)\n",
"print\"Reynold number is\"\n",
"Re2=(4*mdot)/(math.pi*D*mub2)\n",
"print\"Re2=\",Re2\n",
"#Now using equation, nusselt number is,Nubar2=0.027*(Re2)**0.8*Prb2**(1/3.0)*(mub2/muw)**0.14\n",
"print\"Nusselt number is\"\n",
"Nubar2=0.027*(Re2)**0.8*Prb2**(1/3.0)*(mub2/muw)**0.14\n",
"#The heat transfer transfer coefficient hbar2=(kb2/D)*Nubar2\n",
"print\"The heat transfer transfer coefficient in W/(m**2*Â°C) \"\n",
"hbar2=(kb2/D)*Nubar2\n",
"print\"hbar2=\",hbar2\n",
"#The outlet fluid temprature can be found by making use of eqn Tbo3=Tw-(Tw-Tbi)*math.e((-math.pi*D*L*hbar2)/(mdot*cpb2))\n",
"print\"Outlet fluid temprature in second iteration is Tbo3 in Â°C is\"\n",
"Tbo3=Tw-(Tw-Tbi)*math.e**((-math.pi*D*L*hbar2)/(mdot*cpb2))\n",
"print\"Tbo3=\",Tbo3\n",
"#Tb3 is the bulk mean temprature.\n",
"print\"Tb3 in Â°C is\"\n",
"Tb3=(Tbi+Tbo3)/2\n",
"#We see that difference between Tbo2 and Tbo3 and that between Tb2 and Tb3 is marginal.Therfore we can stop iteration and present the result as Tbo=-16.67Â°C\n",
"print\"The Exit fluid temprature after second iteration is obtained as Tbo=-16.67Â°C\"\n",
"print\"Tb3=\",Tb3"
]
}
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