Question

Project: 2D, S/S Heat Conduction in a Rectangle with Heat Generation Write a code in MATLAB that can calculate the temperature inside a thin, rectangular, metal plate, T(x, y) at some selected points as shown in the figure. The temperatures at the boundaries are constant and there is heat generation inside the plate. The problem is steady- state and k = 100 W/(m·K) with L = 1m and H = 0.5 m. The equation to be solved is, 50 °C H/2 0°C 0 °C L/2 100°C H 50 °C 100 °C

Answer 1

MATLAB COde:

T=ones(9,5)*5;

T(:,1)=0;T(:,H)=T1;

T(1,:)=0;T(l,:)=T2;

for j=1:5

jb=6-j;

fprintf('%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f\n',T(:,jb))

end

omega=1.3;

for n=1:T2

for i=2:8

for j=2:4

e(i,j) = 0.25*(T(i,j-1) + T(i,j+1) + T(i-1,j) + T(i+1,j)) - T(i,j);

T(i,j)=T(i,j)+omega*e(i,j);

end

end

if max(abs(e))<.01, break, end

end

fprintf('Number of iteration = %g\n',n)

for j=1:5

jb=6-j;

fprintf('%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f\n',T(:,jb))

end