Fin heat transfer Matrix

I need help solving this matrix with the equations given to me:

For the first node: T_1 = T_b

for the internal nodes: (T_2,T_3,T_4) = -T_i-1 +(2+(mdeltax)^2)T_i - Ti+1 = (mdeltax)^2T_inf

for the 5th node: -T_4 + (1+((mdeltax)^2/2))T_5 = ((mdeltax)^2/2)T_inf

where m = sqrt((hp)/(KA_c))

T_inf = 900 degrees celsius

T_b = 400 degress celsius

also have to compare the matrix solution to:

T_analytic = (cosh(m(L-x))/cosh(mL))*(T_b-T_inf)+T_inf

I need some help with the matrix solution.

[Ive J]

Share with us what you've tried so far and clearly explain how do you want to solve this heat transfer equation in particular?

Answer 1

[Alan Stevens]

% Construct the matrix
% M = [ 1      0         0       0          0;
%      -1 (2+(m*dx)^2)  -1       0          0;
%       0      -1   (2+(m*dx)^2) -1         0;
%       0       0       -1   (2+(m*dx)^2)   -1;
%       0       0        0       -1    (2+(m*dx)^2)/2];
%
% and the column vector
% K = [T_b;
%     (m*dx)^2*T_inf; 
%     (m*dx)^2*T_inf; 
%     (m*dx)^2*T_inf; 
%      (m*dx)^2/2*T_inf];
%
% then you have the matrix equation  M*T = K
% where T is a column vector of values of T_1; T_2 ...T_5
% and you can solve for T using T = M\K  (notice the backslash
% not forward slash)