{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Chapter 09:Heat transfer in condensation and boiling"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex9.1:pg-392"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Introduction to heat transfer by S.K.Som, Chapter 9, Example 1\n",
"The properties of condensate(liquid water) are evaluated at the mean film temprature \n",
"The mean film temprature inÂ°C is\n",
"tf= 95\n",
"hfg= 2270000.0\n",
"The average heat transfer coefficient over length L in W/(m**2*K)\n",
"hbar= 0.745\n",
"The rate of heat transfer per unit width in W/m \n",
"Q= 3.772\n",
"The total rate of condensation in kg/(s*m)\n",
"mdotc= 1.66167400881e-06\n",
"We have to check whether the flow is laminar or not \n",
"Reynolds no. is\n",
"Therefore the flow is laminar and hence the use of the equation is justified\n",
"ReL= 0.0221556534508\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 9, Example 1\"\n",
"#A vertical cooling fin, Approximately a flat plate length,(L)=0.4m high is exposed to saturated steam(temprature,Tg=100Â°C) at atmospheric pressure.\n",
"L=0.4;\n",
"Tg=100;\n",
"#The fin is maintained at temprature,Tw=90Â°C by cooling water.\n",
"Tw=90;\n",
"print\"The properties of condensate(liquid water) are evaluated at the mean film temprature \"\n",
"#tf is mean film temprature\n",
"print\"The mean film temprature inÂ°C is\"\n",
"tf=(Tg+Tw)/2\n",
"print\"tf=\",tf\n",
"#The properties of condensate are density(rho=962kg/m**3),conductivity(k=0.677W/(m*K)),viscosity(mu=3*10**-4 kg/(m*s))\n",
"rho=962;\n",
"k=0.677;\n",
"mu=3*10**-4;\n",
"#The value rhov=0.598kg/m**3 and hfg=2.27*10**6J/kg at 100Â°C are found from steam table\n",
"#g is acceleration due to gravity =9.81m/s**2\n",
"g=9.81;\n",
"rhov=0.598;#rhov is vapour density\n",
"hfg=2.27*10**6;#hfg is enthalpy of vaporisation\n",
"print\"hfg=\",hfg\n",
"#The average heat transfer coefficient over length L is hbarL=0.943*((rho*(rho-rhov)*g*h*L**3)/(mu*k*(Tg-Tw)))**(1/4)\n",
"print\"The average heat transfer coefficient over length L in W/(m**2*K)\"\n",
"hbarL=0.943*((rho*(rho-rhov)*g*hfg*k**3)/(mu*L*(Tg-Tw)))**(1/4)\n",
"print\"hbar=\",hbar\n",
"#The rate of heat transfer per unit width is Q=hbarL*L*(Tg-Tw)\n",
"print\"The rate of heat transfer per unit width in W/m \"\n",
"Q=hbarL*L*(Tg-Tw)\n",
"print\"Q=\",Q\n",
"#The rate of condensation is given by mdotc=(Q/hfg)\n",
"print\"The total rate of condensation in kg/(s*m)\"\n",
"mdotc=(Q/hfg)\n",
"print\"mdotc=\",mdotc\n",
"print\"We have to check whether the flow is laminar or not \"\n",
"#Reynolds no is given by ReL=(4*mdotc)/(mu)\n",
"print\"Reynolds no. is\"\n",
"ReL=(4*mdotc)/(mu)\n",
"print\"Therefore the flow is laminar and hence the use of the equation is justified\"\n",
"print\"ReL=\",ReL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex9.2:pg-393"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Introduction to heat transfer by S.K.Som, Chapter 9, Example 2\n",
"The mean film temprature inÂ°C is\n",
"tf= 95\n",
"hfg= 2270000.0\n",
"The average heat transfer coefficient in W/(m**2*K)\n",
"hbar= 0.745\n",
"The total rate of condensation in kg/s\n",
"Check for reynolds no.\n",
"mdotc= 1.54657700017e-06\n",
"Reynolds number is\n",
"Re= 0.00343683777816\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 9, Example 2\"\n",
"#Steam is condensed at temprature(Tg=100Â°C) on the outer surafce of a horizontal tube of length(L=3m) and diameter(d)=50mm or .05m\n",
"Tg=100;\n",
"L=3;\n",
"D=0.05;\n",
"#The Tube surface is maintained at temprature,Tw=90Â°C \n",
"Tw=90;\n",
"#tf is mean film temprature\n",
"print\"The mean film temprature inÂ°C is\"\n",
"tf=(Tg+Tw)/2\n",
"print\"tf=\",tf\n",
"#The properties of condensate are density(rho=962kg/m**3),conductivity(k=0.677W/(m*K)),viscosity(mu=3*10**-4 kg/(m*s))\n",
"rho=962;\n",
"k=0.677;\n",
"mu=3*10**-4;\n",
"#The value rhov=0.598kg/m**3 and hfg=2.27*10**6J/kg at 100Â°C are found from steam table\n",
"#g is acceleration due to gravity =9.81m/s**2\n",
"g=9.81;\n",
"rhov=0.598;#vapour density\n",
"hfg=2.27*10**6;#enthalpy of vaporisation\n",
"print\"hfg=\",hfg\n",
"#The average heat transfer coefficient hbar=0.745*((rho*(rho-rhov)*g*hfg*k**3)/(mu*D*(Tg-Tw)))**(1/4)\n",
"print\"The average heat transfer coefficient in W/(m**2*K)\"\n",
"hbar=0.745*((rho*(rho-rhov)*g*hfg*k**3)/(mu*D*(Tg-Tw)))**(1/4)\n",
"print\"hbar=\",hbar\n",
"#The rate of condensation is given by mdotc=(hbar*(pi*D*L)*(Tg-Tw))/hfg\n",
"print\"The total rate of condensation in kg/s\"\n",
"mdotc=(hbar*(math.pi*D*L)*(Tg-Tw))/hfg\n",
"print\"Check for reynolds no.\"\n",
"print\"mdotc=\",mdotc\n",
"#For a horizontal tube having length,L,perimeter is P=2L\n",
"P=2*L;\n",
"#Re is reynolds number\n",
"print\"Reynolds number is\"\n",
"Re=(4*mdotc)/(mu*P)\n",
"print\"Re=\",Re"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex9.3:pg-394"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Introduction to heat transfer by S.K.Som, Chapter 9, Example 3\n",
"The mean film temprature inÂ°C is\n",
"tf= 80\n",
"The average heat transfer coefficient over length L in W/(m**2*K)\n",
"hbar= 0.943\n",
"The rate of heat transfer in kW \n",
"Q= 0.016974\n",
"(b)The film thickness at the trailing edges in m is\n",
"delta= 1.0\n",
"The total rate of condensation in kg/s\n",
"mdotc= 7.47753303965e-06\n",
"Hence the average flow velocity at the trailing edge in m/s is\n",
"v= 2.56431174199e-08\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 9, Example 3\"\n",
"#A vertical plate having length,(L)=1.5m is maintained at temprature(Tw) of 60Â°C in the presence of saturated steam(temprature,Tg=100Â°C) at atmospheric pressure.\n",
"L=1.5;\n",
"Tg=100;\n",
"Tw=60;\n",
"#Consider the width of plate to be (B)=0.3m\n",
"B=0.3;\n",
"#tf is the mean film temprature\n",
"print\"The mean film temprature inÂ°C is\"\n",
"tf=(Tg+Tw)/2\n",
"print\"tf=\",tf\n",
"#The relevant properties are desity(rho=972kg/m**3),conductivity(k=0.670W/(m*K)),viscosity(mu=3.54*10**-4 kg/(m*s))\n",
"#specific heat(cp=4.2J/(kg*K)),vapur density(rhov(100Â°C)=0.598k/m**3),Enthalpy of vaporisation(hfg(100Â°C)=2.27*10**6J/kg)\n",
"#g is acceleration due to gravity =9.81m/s**2\n",
"g=9.81;\n",
"rho=972;\n",
"k=0.670;\n",
"mu=3.54*10**-4;\n",
"cp=4.2;\n",
"rhov=0.598;\n",
"hfg=2.27*10**6;\n",
"#The average heat transfer coefficient over length L is hbar=0.943*((rho*(rho-rhov)*g*h*L**3)/(mu*k*(Tg-Tw)))**(1/4)\n",
"print\"The average heat transfer coefficient over length L in W/(m**2*K)\"\n",
"hbar=0.943*((rho*(rho-rhov)*g*hfg*k**3)/(mu*L*(Tg-Tw)))**(1/4)\n",
"print\"hbar=\",hbar\n",
"#The rate of heat transfer Q=hbarL*A*(Tg-Tw)\n",
"#Area(A)=L*B\n",
"A=L*B;\n",
"print\"The rate of heat transfer in kW \"\n",
"Q=(hbar*A*(Tg-Tw))/1000\n",
"print\"Q=\",Q\n",
"#The film thickness at the trailing edges is found out by delta=((4*mu*k*x*(Tg-Tw))/(g*hfg*rho*(rho-rhov)))**(1/4)\n",
"print\"(b)The film thickness at the trailing edges in m is\"\n",
"#at trailing edges x=1.5m\n",
"x=1.5;\n",
"delta=((4*mu*k*x*(Tg-Tw))/(g*hfg*rho*(rho-rhov)))**(1/4)\n",
"print\"delta=\",delta\n",
"#The rate of condensation is given by mdotc=(Q/hfg)\n",
"print\"The total rate of condensation in kg/s\"\n",
"mdotc=((Q*1000)/hfg)\n",
"print\"mdotc=\",mdotc\n",
"#v is the average flow velocity\n",
"print\"Hence the average flow velocity at the trailing edge in m/s is\"\n",
"v=(mdotc)/(rho*delta*B)\n",
"print\"v=\",v"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex9.4:pg-396"
]
},
{
"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 9, Example 4\n",
"The mean film temprature inÂ°C is\n",
"tf= 30\n",
" Modified enthalpy in J/kg is\n",
"hfgdash= 131330.0\n",
"The average heat transfer coefficient over length L in W/(m**2*K)\n",
"hbar= 0.555\n",
"The total rate of condensation in kg/hr\n",
"mdotc= 0.00716923260703\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 9, Example 4\"\n",
"#Saturated freon-012 at Temprature(Tg)=35Â°C is condensed horizontal tube of diameter(D)=15mm or.015m at a lower vapour velocity.\n",
"#length,L=1m,Since per meter of tube is considered.\n",
"L=1;\n",
"Tg=35;\n",
"D=0.015;\n",
"#The tube wall is maintained at temprature(Tw)=25Â°C\n",
"Tw=25;\n",
"#For freon-12 at 35Â°C,enthalpy of vaporisation(hfg=131.33kJ/kg) and vapour density(rhov=42.68kg/m**3)\n",
"hfg=131.33*10**3;\n",
"rhov=42.68;\n",
"#tf is mean film temprature\n",
"print\"The mean film temprature inÂ°C is\"\n",
"tf=(Tg+Tw)/2\n",
"print\"tf=\",tf\n",
"#The relevant properties at 30Â°C are density(rho=1.29*10**3kg/m**3),conductivity(k=0.071W/(mK)),viscosity(mu=2.50*10**-4kg/(m*s)),specific heat(cp=983J/(kg*Â°C))\n",
"rho=1.29*10**3;\n",
"k=0.071;\n",
"mu=2.50*10**-4;\n",
"cp=983;\n",
"#g is acceleration due to gravity =9.81m/s**2\n",
"g=9.81;\n",
"#we found the modified enthalpy by using following equation hfgdash=hfg+(3/8)*cp*(Tg-Tw)\n",
"print\" Modified enthalpy in J/kg is\"\n",
"hfgdash=hfg+((3/8)*cp*(Tg-Tw))\n",
"print\"hfgdash=\",hfgdash\n",
"#The average heat transfer coefficient over length L is hbar=0.555*((rho*(rho-rhov)*g*hfgdash*k**3)/(mu*D*(Tg-Tw)))**(1/4)\n",
"print\"The average heat transfer coefficient over length L in W/(m**2*K)\"\n",
"hbar=0.555*((rho*(rho-rhov)*g*hfgdash*k**3)/(mu*D*(Tg-Tw)))**(1/4)\n",
"print\"hbar=\",hbar\n",
"#The rate of condensation is given by mdotc=(hbar*(pi*D*L)*(Tg-Tw))/hfg\n",
"print\"The total rate of condensation in kg/hr\"\n",
"mdotc=((hbar*(math.pi*D*L)*(Tg-Tw))/hfg)*3600\n",
"print\"mdotc=\",mdotc"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex9.5:pg-397"
]
},
{
"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 9, Example 5\n",
"Heat transfer coefficient in W/m**2 is\n",
"h= 105042.262441\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 9, Example 5\"\n",
"#A nickel wire of length(L)=0.1m,Diameter(D)=1mm or .001m \n",
"#Submerged horizontally in water at pressure=1 atm(101kPa) requires current,I=150A at voltage ,E=2.2V to maintain wire at temprature(T1)=110Â°C\n",
"L=0.1;\n",
"T1=110;\n",
"D=0.001;\n",
"I=150;\n",
"E=2.2;\n",
"#Area(A)=(math.pi*D*L)\n",
"A=math.pi*D*L;\n",
"#The saturation temprature of water at one atmospheric pressure(101kPa) is T2=100Â°C.\n",
"T2=100;\n",
"#We can write from energy balance E*I=h*A*(T1-T2),we can find heat transfer coefficient from it.\n",
"#h is heat transfer coefficient\n",
"print\"Heat transfer coefficient in W/m**2 is\"\n",
"h=(E*I)/(A*(T1-T2))\n",
"print\"h=\",h"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex9.6:pg-398"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Introduction to heat transfer by S.K.Som, Chapter 9, Example 6\n",
"Critical Heat flux in W/m**2 is\n",
"qc= 202044.0\n",
"The burn out voltage in Volts is \n",
"E= 1.90421983831\n"
]
}
],
"source": [
"import math\n",
" \n",
"print\"Introduction to heat transfer by S.K.Som, Chapter 9, Example 6\"\n",
"#In a laboratory experiment,A current(I)=100A burns out a nickel wire having Diameter(D)=1mm or 0.001mm,length(L)=0.3m\n",
"I=100;\n",
"D=.001;\n",
"L=0.3;\n",
"#It is submerged horizontally in water at one atmospheric pressure.\n",
"#For saturated water at one atmospheric pressure,density(rhol=960kg/m**3),vapour density(rhov=0.60kg/m**3),enthalpy of vaporisation(hfg=2.26*10**6J/kg),surface tension(sigma=0.055N/m).\n",
"rhol=960;\n",
"rhov=0.60;\n",
"hfg=2.26*10**6;\n",
"sigma=0.055;\n",
"#Area(A)=(pi*D*L)\n",
"A=math.pi*D*L;\n",
"#g is acceleration due to gravity =9.81m/s**2\n",
"g=9.81;\n",
"#The wire is burnt out when heat reaches its peak\n",
"#We use following expression to determine critical heat flux qc=0.149*hfg*rhov*((sigma*g*(rhol-rhov))/rhov**2)**(1/4)*((rhol+rhov)/rhol)**(1/2) \n",
"print\"Critical Heat flux in W/m**2 is\"\n",
"qc=0.149*hfg*rhov*((sigma*g*(rhol-rhov))/rhov**2)**(1/4)*((rhol+rhov)/rhol)**(1/2) \n",
"print\"qc=\",qc\n",
"#From the energy balance E*I=qc*A\n",
"#E is the burn out voltage\n",
"print\"The burn out voltage in Volts is \"\n",
"E=(qc*A)/I\n",
"print\"E=\",E"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex9.7:pg-399"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Introduction to heat transfer by S.K.Som, Chapter 9, Example 7\n",
"Heat flux q in W/m**2 is\n",
"The peak heat flux for water at one atmospheric pressure is qc=1.24*10**6(found in example 9.6).Since q