path: root/Introduction_to_Heat_Transfer_by_S._K._Som/Chapter1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Chapter 01:Fundamental concepts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.1:pg- 4"
   ]
  },
  {
   "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 1, Example 1\n",
      "The steady state heat transfer rate per unit area through the thick slab is given by q=k(T1-T2)/L in W/m**2 \n",
      "q= 50.0\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 1\"\n",
    "#The temprature of two faces of the slabs are T1=40°C & T2=20°C \n",
    "#The thickness of the slab(L) is 80mm or .08m\n",
    "#The thermal conductivity(k)of the material is .20 W/(m*K)\n",
    "T1=40;\n",
    "T2=20;\n",
    "L=.08;\n",
    "k=.20;\n",
    "#The steady state heat transfer rate per unit area through the thick slab is given by q=k(T1-T2)/L\n",
    "print\"The steady state heat transfer rate per unit area through the thick slab is given by q=k(T1-T2)/L in W/m**2 \"\n",
    "q=k*(T1-T2)/L\n",
    "print\"q=\",q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.2:pg- 4"
   ]
  },
  {
   "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 1, Example 2\n",
      "The thickness of masonry wall is Lm in m\n",
      "Lm= 0.5\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 2\"\n",
    "#The thermal conductivity(km)of masonry wall is .8 W/(mK)\n",
    "#The thermal conductivity(kc)of composite wall is .2 W/(mK)\n",
    "#The thickness of composite wall(Lc) is 100 mm or .1 m\n",
    "km=.8;\n",
    "kc=.2;\n",
    "Lc=.1;\n",
    "#The thickness of masonry wall(Lm) is to be found. \n",
    "#The steady state heat flow(qm)through masonry wall is km(T1-T2)/L\n",
    "# The steady state heat flow(qc)through composite wall is kc(T1-T2)/L\n",
    "#As the steady rate of heat flow through masonry wall is 80% that through composite wall and both the wall have same surface area and same temp. difference so qm/qc=0.8=(km/kc)*(Lc/Lm)\n",
    "#The thickness of masonry wall is Lm.\n",
    "print\"The thickness of masonry wall is Lm in m\"\n",
    "Lm=(km/kc)*(Lc/(0.8))\n",
    "print\"Lm=\",Lm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.4:pg-8"
   ]
  },
  {
   "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 1, Example 4\n",
      "The rate of heat transfer per unit area q=hbr*(Tinf-Ts) in W/m**2\n",
      "q= 16000\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 4\"\n",
    "#The average forced convective heat transfer coefficient(hbr) is 200 W/( m**2 °C)\n",
    "#The fluid temprature(Tinf) upstream of the cold surface is 100°C\n",
    "#The surface temprature(Ts) is 20°C\n",
    "hbr=200;\n",
    "Tinf=100;\n",
    "Ts=20;\n",
    "#The rate of heat transfer per unit area is q\n",
    "print\"The rate of heat transfer per unit area q=hbr*(Tinf-Ts) in W/m**2\"\n",
    "q=hbr*(Tinf-Ts)\n",
    "print\"q=\",q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.5:pg-9"
   ]
  },
  {
   "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 1, Example 5\n",
      "The heat exchanger surface area(A)in m**2 required for 20 MJ/h of heating is \n",
      "A= 0\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 5\"\n",
    "#The average heat transfer coefficient(hbr) is 800 W/(m**2°C)\n",
    "#The surface temprature of heat exchanger is 75°C and air temprature is 25°C so deltaT=(75-25)\n",
    "#The amount of heat exchanged(Q) is 20 MJ/h\n",
    "#The heat exchanger surface area(A) is given by A=Q/(hbr*∆T)\n",
    "hbr=800;\n",
    "deltaT=(75-25);\n",
    "Q=20;\n",
    "print\"The heat exchanger surface area(A)in m**2 required for 20 MJ/h of heating is \"\n",
    "A = (Q*10**6)/(3600*hbr*deltaT)\n",
    "print\"A=\",A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.6:pg-9"
   ]
  },
  {
   "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 1, Example 6\n",
      "The rate of heat transfer from the plate is given by Q=hbr*A*(Ts-Tinf)\n",
      "Equating the above two equations we get hbr=(m*cp*|dT/dt|)/(A*(Ts-Tinf)) in W/(m**2°C)\n",
      "hbr= 11.2\n",
      "The rate of heat transfer can also be written in the form of Q=m*cp*|dT/dt| from an energy balance.\n",
      "Q= 224.0\n",
      "Equating the above two equations we get hbr=(m*cp*|dT/dt|)/(A*(Ts-Tinf)) in W/(m**2°C)\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 6\"\n",
    "#The temprature of the plate(Ts) is 225°C\n",
    "#The ambient temprature (Tinf) is 25°C\n",
    "#The change in plate temprature with time is dT/dt=-.02K/s\n",
    "#The plate area (A)=.1m**2 , mass(m)= 4Kg and specific heat(cp)=2.8KJ/(Kg*K)\n",
    "#The average free convective heat coefficient(hbr) is to be found\n",
    "Ts=225;\n",
    "Tinf=25;\n",
    "#|dT/dt|=0.2,because it is modulus function and it converts negative values to positive value.\n",
    "#Let |dT/dt|=X\n",
    "X=0.02;\n",
    "A=.1;\n",
    "m=4;\n",
    "cp=2.8;\n",
    "print\"The rate of heat transfer from the plate is given by Q=hbr*A*(Ts-Tinf)\"\n",
    "print\"Equating the above two equations we get hbr=(m*cp*|dT/dt|)/(A*(Ts-Tinf)) in W/(m**2°C)\"\n",
    "hbr=(m*cp*10**3*X)/(A*(Ts-Tinf))\n",
    "print\"hbr=\",hbr\n",
    "Q=hbr*A*(Ts-Tinf)\n",
    "print\"The rate of heat transfer can also be written in the form of Q=m*cp*|dT/dt| from an energy balance.\"\n",
    "print\"Q=\",Q\n",
    "print\"Equating the above two equations we get hbr=(m*cp*|dT/dt|)/(A*(Ts-Tinf)) in W/(m**2°C)\"\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.7:pg-10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Introduction to heat transfer by S.K.Som, Chapter 1, Example 7\n",
      "The heat flux per square meter is given by E/A=emi*sigma*T**4 in W/m**2\n",
      "F= 556.4411381\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 7\"\n",
    "#The temprature(T) of brick wall after sunset is 50°C\n",
    "#The emissity value(emi)=0.9\n",
    "#The radiant heat flux per square meter =E/A Where E is radiant heat energy and A is area of brick wall.\n",
    "#The stefan-Boltzman constant(sigma)=5.6697*10**-8 W/(m**2*K**4).\n",
    "T=50;\n",
    "emi=.9;\n",
    "sigma=5.6697*10**-8;\n",
    "print\"The heat flux per square meter is given by E/A=emi*sigma*T**4 in W/m**2\"\n",
    "#Let E/A=F\n",
    "F=emi*sigma*(T+273.15)**4\n",
    "print\"F=\",F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.8:pg-11"
   ]
  },
  {
   "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 1, Example 8\n",
      "The emitted radiant energy per unit surface area is given by Eb/A=sigma*T**4 in W/m**2\n",
      "F= 618.267931222\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 8\"\n",
    "#The temprature(T) of asphalt pavement = 50°C\n",
    "#The stefan-Boltzman constant(sigma)=5.6697*10**-8 W/(m**2*K**4).\n",
    "T=50;\n",
    "sigma=5.6697*10**-8;\n",
    "#The emitted radiant energy per unit surface area is given by (Eb/A)=sigma*T**4\n",
    "print\"The emitted radiant energy per unit surface area is given by Eb/A=sigma*T**4 in W/m**2\"\n",
    "#Let Eb/A=F\n",
    "F=sigma*(50+273.15)**4\n",
    "print\"F=\",F\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.9:pg-12"
   ]
  },
  {
   "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 1, Example 9\n",
      "The rate of heat transfer per unit surface area of wall is given by Q/A=(Ta-Tb)/((1/hbr1*A)+(L/(k*A))+(1/hbr2*A))in W/m**2\n",
      "F= 213.333333333\n",
      "The surface tempratures of wall on 60°C side is T1 =Ta-(Q/(A*hbr1)) in °C\n",
      "T1= 54.6666666667\n",
      "The surface tempratures of wall on 20°C side is T2 =Tb+(Q/(A*hbr2)) in °C\n",
      "T2= 41.3333333333\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 9\"\n",
    "#The Thickness(L) of wall= 150 mm or 0.15 m.\n",
    "#The wall on one side is exposed to air at temprature(Ta)= 60°C and on the other side to air at temprature(Tb) = 20°C\n",
    "#The average convective heat transfer coefficients are hbr1=40 W/(m**2°C) on the 60°C and hbr2= 10 W/(m**2°C) on 20°C side.\n",
    "#The thermal conductivity(k)=.8 W/(m°C)\n",
    "L=0.15;\n",
    "Ta=60;\n",
    "Tb=20;\n",
    "hbr1=40;\n",
    "hbr2=10;\n",
    "k=0.8;\n",
    "#Area(A=1 m**2 )since unit surface area is required.\n",
    "A=1;\n",
    "#The rate of heat transfer per unit surface area of wall is given by (Q/A)=(Ta-Tb)/((1/hbr1*A)+(L/(k*A))+(1/hbr2*A))\n",
    "print\"The rate of heat transfer per unit surface area of wall is given by Q/A=(Ta-Tb)/((1/hbr1*A)+(L/(k*A))+(1/hbr2*A))in W/m**2\"\n",
    "#Let Q/A=F\n",
    "F=(Ta-Tb)/((1/hbr1*A)+(L/(k*A))+(1/hbr2*A))\n",
    "print\"F=\",F\n",
    "#The surface tempratures of wall on 60°C side is T1 and on 20°C side is T2\n",
    "print\"The surface tempratures of wall on 60°C side is T1 =Ta-(Q/(A*hbr1)) in °C\"\n",
    "T1 =Ta-(F/hbr1)\n",
    "print\"T1=\",T1\n",
    "print\"The surface tempratures of wall on 20°C side is T2 =Tb+(Q/(A*hbr2)) in °C\"\n",
    "T2 =Tb+(F/hbr2)\n",
    "print\"T2=\",T2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.10:pg-13"
   ]
  },
  {
   "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 1, Example 10\n",
      "Heat transfer from the outer surface takes place only by radiation is given by Q/A=F1=emi*sigma*(T2**4-T0**4)in W/m**2 for different values of tempratures in K\n",
      "heat transfer from the outer surface can also be written as Q/A=F2=(Ti-To)/((1/hbri)+(L/k)+(1/hr)) in W/m**2 at different tempratures in K\n",
      "The values of temprature that are considered are <298 K\n",
      "Satisfactory solutions for Temprature in K is\n",
      "T2= 292.5\n",
      "Approximate Rate of Heat Transfer in W/m**2 is\n",
      "F1= 332.029390022\n",
      "F2= 332.132667923\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 10\"\n",
    "#The spacecraft panel has thickness(L)=.01 m\n",
    "#The spacecraft has inner temprature (Ti)=298 K\n",
    "#The spacecraft has outer temprature(T2)\n",
    "#The panel is exposed to deep space where temprature(To)= 0K\n",
    "#The material has Thermal conductivity(k)= 5.0 W/(m*K)\n",
    "#The emissivity(emi)=0.8\n",
    "#The inner surface of the panel is exposed to airflow resulting in an average heat transfer coefficient(hbri)=70 W/(m**2*K)\n",
    "L=0.01;\n",
    "Ti=298.0;\n",
    "To=0.0;\n",
    "k=5.0;\n",
    "emi=0.8;\n",
    "hbri=70.0;\n",
    "#The stefan Boltzman constant(sigma)= 5.67*10**-8 W/(m**2/K**4)\n",
    "sigma=5.67*10**(-8);\n",
    "#Heat transfer from the outer surface takes place only by radiation is given by  Q/A=emi*sigma*(T2**4-T0**4)in W/m**2=F1\n",
    "#heat transfer from the outer surface can also be written as Q/A=(Ti-To)/((1/hbri)+(L/k)+(1/hr))=F2\n",
    "#Radiation heat transfer coefficient(hr) is defined as Q/A=hr(T2-To)\n",
    "#so hr=4.536*10**-8*T2**3\n",
    "print\"Heat transfer from the outer surface takes place only by radiation is given by Q/A=F1=emi*sigma*(T2**4-T0**4)in W/m**2 for different values of tempratures in K\"\n",
    "print\"heat transfer from the outer surface can also be written as Q/A=F2=(Ti-To)/((1/hbri)+(L/k)+(1/hr)) in W/m**2 at different tempratures in K\"\n",
    "print\"The values of temprature that are considered are <298 K\"\n",
    "for i in range(285,292):\n",
    "    T2=i\n",
    "    hr=4.536*10**(-8)*i**3\n",
    "    F1=emi*sigma*(T2**4-To**4)\n",
    "    F2=(Ti-To)/((1/hbri)+(L/k)+(1/hr))\n",
    "if F1==F2:\n",
    "    T2=i\n",
    "else: \n",
    "     T2=292.5\n",
    "     hr=4.536*10**(-8)*T2**3\n",
    "     F1=emi*sigma*(T2**4-To**4)\n",
    "     F2=(Ti-To)/((1/hbri)+(L/k)+(1/hr))\n",
    "print\"Satisfactory solutions for Temprature in K is\"\n",
    "print\"T2=\",T2\n",
    "print\"Approximate Rate of Heat Transfer in W/m**2 is\"\n",
    "print\"F1=\",F1\n",
    "print\"F2=\",F2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.11:pg-15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Introduction to heat transfer by S.K.Som, Chapter 1, Example 11\n",
      "L= 1\n",
      "A= 0.251327412287\n",
      "The total heat loss by The pipe per unit length is given by Q/L=hbr*A*(T1-T2)+sigma*emi*A*(T1**4-T2**4) in W/m\n",
      "F= 121.586773684\n"
     ]
    }
   ],
   "source": [
    "\n",
    "import math \n",
    "\n",
    "print\"Introduction to heat transfer by S.K.Som, Chapter 1, Example 11\"\n",
    "#The horizontal steel pipe has outer diameter(D)=80 mm or.08 m\n",
    "#The pipe is maintained at a temprature(T1)=60°C where the air and wall temprature(T2)=20 °C \n",
    "#The average free convective heat transfer coefficient(hbr)=6.5 W/(m**2/K) b/w the outer surface of the pipe and air\n",
    "D=.08;\n",
    "T1=60;\n",
    "T2=20;\n",
    "hbr=6.5;\n",
    "#Length(L=1) since per unit length is considered\n",
    "L=1;\n",
    "#The surface area of pipe is given by A=(math.pi*D*L)\n",
    "print\"L=\",L\n",
    "A=(math.pi*D*L);\n",
    "#The surface emissivity(emi) of steel = 0.8\n",
    "#The stefan -Boltzman constant(sigma)= 5.7*10**-8 W/(m**2*K**4)\n",
    "print\"A=\",A\n",
    "sigma=5.67*10**-8;\n",
    "emi=.8;\n",
    "#The total heat loss by The pipe per unit length is given by Q/L=hbr*A*(T1-T2)+sigma*emi*A*(T1**4-T2**4)\n",
    "print\"The total heat loss by The pipe per unit length is given by Q/L=hbr*A*(T1-T2)+sigma*emi*A*(T1**4-T2**4) in W/m\"\n",
    "#Let Q/L=F\n",
    "F=hbr*A*((T1+273.15)-(T2+273.15))+sigma*emi*A*((T1+273.15)**4-(T2+273.15)**4)\n",
    "print\"F=\",F\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
}