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clear;
clc;
printf('FUNDAMENTALS OF HEAT AND MASS TRANSFER \n Incropera / Dewitt / Bergman / Lavine \n EXAMPLE 4.4 Page 230 \n'); //Example 4.4
// Temperature Field and Rate of Heat Transfer
//Operating Conditions
ho = 1000; //[W/m^2.K] Heat Convection coefficient
hi = 200; //[W/m^2.K] Heat Convection coefficient
Ti = 400; //[K] Temp of Air
Tg = 1700; //[K] Temp of Gas
h = 10 ; //[W/m^2.K] Heat Convection coefficient
A = 2*6*10^-6 ; //[m^2] Cross section of each Channel
x = .004 ; //[m] Spacing between joints
t = .006; //[m] Thickness
k = 25; //[W/m.K] Thermal Conductivity of Blade
delx = .001 ; //[m]
dely = .001 ; //[m]
//Applying Eqn 4.42 and 4.48
A = [-(2+ho*delx/k) 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
1 -2*(2+ho*delx/k) 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 1 -2*(2+ho*delx/k) 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 1 -2*(2+ho*delx/k) 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 1 -2*(2+ho*delx/k) 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 1 -(2+ho*delx/k) 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0;
1 0 0 0 0 0 -4 2 0 0 0 0 1 0 0 0 0 0 0 0 0;
0 1 0 0 0 0 1 -4 1 0 0 0 0 1 0 0 0 0 0 0 0;
0 0 1 0 0 0 0 1 -4 1 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 1 0 0 0 0 1 -4 1 0 0 0 0 1 0 0 0 0 0;
0 0 0 0 1 0 0 0 0 1 -4 1 0 0 0 0 1 0 0 0 0;
0 0 0 0 0 1 0 0 0 0 2 -4 0 0 0 0 0 1 0 0 0;
0 0 0 0 0 0 1 0 0 0 0 0 -4 2 0 0 0 0 1 0 0;
0 0 0 0 0 0 0 1 0 0 0 0 1 -4 1 0 0 0 0 1 0;
0 0 0 0 0 0 0 0 2 0 0 0 0 2 -2*(3+hi*delx/k) 1 0 0 0 0 1;
0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 -2*(2+hi*delx/k) 1 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 -2*(2+hi*delx/k) 1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 -(2+hi*delx/k) 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -2 1 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 -4 1;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 -(2+hi*delx/k)];
C = [-ho*delx*Tg/k;
-2*ho*delx*Tg/k;
-2*ho*delx*Tg/k;
-2*ho*delx*Tg/k;
-2*ho*delx*Tg/k;
-ho*delx*Tg/k;
0;
0;
0;
0;
0;
0;
0;
0;
-2*hi*delx*Ti/k;
-2*hi*delx*Ti/k;
-2*hi*delx*Ti/k;
-hi*delx*Ti/k;
0;
0;
-hi*delx*Ti/k];
T = inv(A)*C;
printf("\n Temp Distribution = ");
printf("\n %.1f K ", T);
q = 4*ho*[(delx/2)*(Tg-T(1))+delx*(Tg-T(2))+delx*(Tg-T(3))+ delx*(Tg-T(4))+delx*(Tg-T(5))+delx*(Tg-T(6))/2];
printf("\n\n Heat rate Transfer %.1f W/m ", q);
//END
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