I would like to store store the change in temp in each node for each time step

So if you run the code. The temperature for each node is changing for the set time step. I would like to store the change of temp in each node for each time step. Could someone help out please.

Answer 1

[Alan Stevens]

I think the following does your desired calculations:

%Parameters
rho = 1; %density, kg/m^3
cp = 1; %specific heat, J/kgK
K = 1; %thermal conductivity, w/mK
h = 1; %heat transfer conefficient, W/(m^2K)
V = 3; %V, voltage
I = 1.5; %A, current
P = V*I; %W, power
%Domain and step
Lx = 7; %length, m

q_gen = P/Lx; %W/m, heat rate per length

A = K/rho/cp; %aplha

Nx = 51; Nt = 100;
dx = Lx/(Nx-1);

%Satisfy CFL condition 
c = 1;
C = 0.1; %CFL condition, C<1
dt = 0.5*dx^2;

%Field variables: rows = space, columns = time
Tn = zeros(Nx,Nt); %Temperature
x = linspace(0, Lx, Nx); %x distance

%Initial condition
Tn(:,1) = 25;    % Initial temperature at all values of x
Tn(1,:) = 0;     % Left-hand temperature for all time
Tn(end,:) = 90;  % Right-hand temperature for all time
Tc = Tn(:,1);         % initialise previous timestep temperatures
DeltaT = zeros(Nx,Nt-1); %For storing temperature changes
t = 0;           % Start time
%Loop
for n = 1:Nt
   
    t = t+dt;
    
    %New temperature
    for i = 2:Nx-1
    Tn(i, n+1) = Tc(i) + dt*A*((Tc(i+1) -2*Tc(i) + Tc(i-1)))/dx^2;
    end
    
    %Source term
    Sx = 2: 2: Nx;
    if (t<5)
    Tn(Sx,:) = Tn(Sx,:) + dt*q_gen/rho/cp;
    end
    DeltaT(:,n) = Tn(:,n) - Tc; % store temperature changes at each node
    Tc = Tn(:,n); %Save the previous timestep temperatures
    
    %Visualize
    plot(x, Tn(:,1:n)); set(gca, 'ylim', [0 100]);
    xlabel('Distance along rod'); ylabel('Temperature');
    title(sprintf('Time = %f seconds', t));
    pause(0.01)
end
ts = 20;  % look at change from timestep ts-1 to ts 
figure
plot(x,DeltaT(:,ts))

[purichmun low]

Thank you for your answer. I did not understand this part

Tn(i, n+1) = Tc(i) + dt*A*((Tc(i+1) -2*Tc(i) + Tc(i-1)))/dx^2;

Tn is a 51x100 matrix but Tc is a 51x1 matrix. How does it work as it doesnt have the same matrix size?

Lastly I did not understand these 2 lines of code. Could you perhaps explain more in depth and in a simpler way if possible.

DeltaT(:,n) = Tn(:,n) - Tc; % store temperature changes at each node
Tc = Tn(:,n); %Save the previous timestep temperatures      

[Alan Stevens]

Tn(i, n+1)

This selects the i'th row of the (n+1)'th column of matrix Tn, so is a single value.

Tc(i)

Selects the i'th row of the vector Tc, so is also a single value.

DeltaT(:,n) = Tn(:,n) - Tc; 

The colon (:) here means use all rows, so the RHS means select all the rows of the n'th column of matrix Tn, resulting in a 51x1 vector, then subtract, element by element, the values in Tc, which is also a 51x1 vector. The results are stored in the n'th column of the DeltaT matrix. I included this because you asked for a store for the temperature changes from one timestep to the next.

Tc = Tn(:,n);

The RHS selects elements from all the rows of the n'th column of matrix Tn and assigns them to vector Tc. Tc only ever stores the previous timestep value for use in the next timestep; it doesn't store all the previous values (which would be unnecessary as they are stored in Tn.

I hope this clarifies the situation for you.

[purichmun low]

Thank you for the clarification Alan! Appreciate it a lot.