matrix dimension must agree and the size is different on left and right side. I need to iterate to observe cooling. Please help !

R_in =[0.02;1.0]; %total E Resistance

Keff = 1.5e-3; % W/K

rho = 10e-6; % ohm.meter

Sab = 200e-6; % Volt per Kelvin

N = [75];

% Ti = 200; % intiial temp

% Hhx = 0.004; % heat transfer Coef forced Air circulation

Ta = [50;10] ; % cooling side or being pumped in Kelvin

alpha =220e-6;% V/Keff seebecKeff coeff

I_in = [2:30];

V_in = [2:30];

W = V_in.*I_in;

T_pump_cold = 200.15; % final required temperature

T_sink = 173.15;

Tb = 298.15; % hot side initial temperature

DT = T_pump_cold - T_sink;

dx = 0.04; % in m

Q_c = 2*N*((Sab*T_pump_cold.*I_in) - 2*N*((Keff*rho)./R_in)*(DT)-0.5*(I_in.^2).*R_in)

COP = Q_c/W;

A_cr = 0.00002; % in m2

t(1) =1;

T(1)=T_pump_cold ;

Time2=(1:t:12); hours

for j = (1:t:1000)

[T(j+1)] = ((dx.*Q_c)./Keff.*Time2.*A_cr)+T(j);

end

Answer 1

[Rushil]

Hello

While running the code, I encountered an error in the following line:

[T(j+1)] = ((dx.*Q_c)./Keff.*Time2.*A_cr)+T(j);

This happens because the size of “Q_c” is [2x29] and “Time2” is [1x12]. In the above line, the code attempts to multiply “Q_c” and “Time2”. This is not valid because their dimensions do not align for element-wise operations.

A possible way to treat this issue is to choose a fixed value of "Q_c" and model "T" in a slightly different way. Here is some code that shows you how it could be done (it iterates over the length of "Time2" instead):

Q_c_value = Q_c(1, 1); % example: using the first element

for j = 1:length(Time2)
    T(j+1) = ((dx * Q_c_value) ./ Keff * A_cr) * Time2(j) + T(j);
end

Hope you are able resolve the issue.