Coding an equation (with summation within equation) with nested for Loops

Hello,

I am attempting to code the following equation in matlab using three for loops:

However, my initial values are incorrect and I believe my issue is related to how I am handling the the summation inside the equation. I would appreciate any suggestions on how to alter my for loop.

for i=1:length(x)
     for j=1:length(Temp(:,1))
         for n=1:20
 T_xt(i,j,n)= T_amb2 + (q_p./k).*(((exp(m.*(x(i)-2.*L))+...
 exp(-m.*x(i)))/(m.*(1-exp(-2.*m.*L))))-...
 ((2.*exp(-m^2.*a.*t(j)))*(1./(2.*m.^2*L)+...
(L.*((cos((n.*pi.*x(i))./L).*...
exp((-n.^2.*pi.^2.*a.*t(j))./L.^2))./(m.^2.*L.^2 + n.^2*pi^2))))));
         end
     end
end

Answer 1

[Walter Roberson]

You are probably summing T_xt(:,:,:) over the third dimension to get T(x,t) . However, when you do that, you would be adding T_amb2 once for each n value, which is not correct.

You can meaningfully create T_xt(i,j,n) but it should only be the cos*exp/sum term. Then you would sum those along the third dimension, multiply by 2*exp(-m^2*alpha*t), subtract from the [] and so on.

[AbeSal]

Thank you for the suggestion. After updating my code my plot looked better but there was an issue at t=0. Are there additionally changes you might suggest I make to the code?

S(1)=0;
for i=1:length(x)
     for j=1:length(Temp(:,1))
         T_xt(i,j)= T_amb + (q_p./k).*(((exp(m.*(x(i)-2.*L))+...
             exp(-m.*x(i)))/(m.*(1-exp(-2.*m.*L))))-...
             ((2.*exp(-m^2.*a.*t(j)))*(1./(2.*m.^2*L)+...
             (L.*S(end)))));
         for n = 1:20
         S(n+1) = S(n)+(cos((n.*pi.*x(i))./L).*...
             exp((-n.^2.*pi.^2.*a.*t(j))./L.^2))./(m.^2*L.^2 + n.^2.*pi.^2);
         end
     end
end