# Fin heat transfer Matrix

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Yogesh Bhambhwani on 16 Dec 2020
Edited: Alan Stevens on 17 Dec 2020
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 on 17 Dec 2020
Share with us what you've tried so far and clearly explain how do you want to solve this heat transfer equation in particular?

Alan Stevens on 17 Dec 2020
Edited: Alan Stevens on 17 Dec 2020
% 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)