{
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 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 5: Natural Convection"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 5.1: Convection_Heat_Loss_From_Room_Heater.sce"
		   ]
		  },
  {
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"\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
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"\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')"
   ]
   }
,
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		   "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"
   ]
   }
,
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		   "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": [],
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"\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"
   ]
   }
,
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 5.6: Convection_Heat_Transfer_From_Shaft.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
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"\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"
   ]
   }
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			 "text": "MetaKernel Magics",
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