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clear;
clc;
printf('FUNDAMENTALS OF HEAT AND MASS TRANSFER \n Incropera / Dewitt / Bergman / Lavine \n EXAMPLE 13.7 Page 841 \n')// Example 13.7
// Rate at which heat must be supplied
// Temperature of the insulated surface
T1 = 1000 ;//[K] Temperature of Heated Surface
e1 = .8 ;// emissivity of Heated Surface
e2 = .8 ; // emissivity of Insulated Surface
r = .02 ;//[m] Radius of surface
Tm = 400 ;//[K] Temperature of surrounding air
m = .01 ;//[kg/s] Flow rate of surrounding air
p = 101325 ;//[Pa] Pressure of surrounding air
stfncnstt = 5.670*10^-8 ;//[W/m^2.K^4] Stefan Boltzman Constant
//Table A.4 Air Properties at 1 atm, 400 K
k = .0338 ;//[W/m.K] conductivity
u = 230*10^-7 ;//[kg/s.m] Viscosity
cp = 1014 ;//[J/kg] Specific heat
Pr = .69 ;// Prandtl Number
//Hydraulic Diameter
Dh = 2*%pi*r/(%pi+2) ;//[m]
//Reynolds number
Re = m*Dh/(%pi*r^2/2)/u;
//View Factor
F12 = 1 ;
printf("\n As Reynolds Number is %i, Hence it is Turbulent flow inside a cylinder. Hence we will use Dittus-Boelter Equation",Re);
//From Dittus-Boelter Equation
Nu = .023*Re^.8*Pr^.4;
h = Nu*k/Dh; //[W/m^2.K]
//From Equation 13.18 Heat Energy balance
//Newton Raphson
T2=600; //Initial Assumption
while(1>0)
f=(stfncnstt*(T1^4 - T2^4)/((1-e1)/(e1*2*r)+1/(2*r*F12)+(1-e2)/(e2*%pi*r)) - h*%pi*r*(T2-Tm));
fd=(4*stfncnstt*( - T2^3)/((1-e1)/(e1*2*r)+1/(2*r*F12)+(1-e2)/(e2*%pi*r)) - h*%pi*r*(T2));
T2n=T2-f/fd;
if(stfncnstt*(T1^4 - T2n^4)/((1-e1)/(e1*2*r)+1/(2*r*F12)+(1-e2)/(e2*%pi*r)) - h*%pi*r*(T2n-Tm))<=.01
break;
end;
T2=T2n;
end
//From energy Balance
q = h*%pi*r*(T2-Tm) + h*2*r*(T1-Tm) ;//[W/m]
printf('\n Rate at which heat must be supplied per unit length of duct = %.2f W/m & Temperature of the insulated surface = %i K',q,T2);
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