Plot change in heat for a x y position as a function of time

Hello,

I recently created a code to solve 2-d transient conduction for a plate with length = 1 and width = 1. To do so I created a 3-d matrix to account for x and y spatial steps as well as temporal timesteps. I now want to plot temperature as a function of time for a specific x y position, as a 2-d plot, so I can see how temperature varies across time for a specific position on the plate. I've tried using certain functions including the plot3 function:

 plot3(Temp_new(.3,.3,:))

but I get the following error message:Not enough input arguments. Since the plate is 1x1 the locations will also be non-integers. Is there a function that will allow me to plot my data and deal with the non-integer issue? I've inlcuded the code i used to generate the data I wish to plot.

clc
clear

%Declare the domain
Lx=1; %plate length
Ly=1; %plate width
x_nodes=10;
y_nodes=10;
dx=Lx/x_nodes;%x direction step 0.1
dy=Ly/y_nodes;%y direction step 0.1
t_total=1000;
t_nodes=1000;
dt=t_total/t_nodes; % time step 0.1 seconds

%delcare constants and define alpha and fourier number
k=385;
C=377; 
d=8960; 
alpha=(k/(d*C)); %alpha= 1.139754642e-4
F=(alpha*dt)/(dx*dy); %stability criterion 1-4*F>0 , F<.25


%Initialize temperature
Temp=zeros(x_nodes+1,y_nodes+1,t_nodes+1);
Temp_new=zeros(x_nodes+1,y_nodes+1,t_nodes+1);

%Initial condition- Temperature
Temp(:,:,1)=225;
Temp_new(:,:,1)=225;

%Declare the boundary condition
T_bot = 500;
T_top = 0;
T_left = 0;
T_right = 0;


%top
Temp(x_nodes+1,:,:)=T_top; 
Temp_new(x_nodes+1,:,:)=T_top;

%left
Temp(:,1,:)=T_left;
Temp_new(:,1,:)=T_left;

%right 
Temp(:,y_nodes+1,:)=T_right; 
Temp_new(:,y_nodes+1,:)=T_right;

%bottom
Temp(1,:,:)=T_bot; 
Temp_new(1,:,:)=T_bot;

%Declare other variables
p=1; %counter
tolerence=0.001;
MaxError(p)=1;
MinError(p)=1;

while MaxError(p)>=tolerence || MinError(p)>=tolerence
    for i=2:x_nodes % looping
        for j=2:y_nodes
            for n=1:t_total
               Temp_new(i,j,n+1)=(F*(Temp(i+1,j,n)+Temp(i-1,j,n)+Temp(i,j+1,n)+Temp(i,j-1,n)))+((1-4*F)*Temp(i,j,n));
            end
        end
    end
   p=p+1; % update p

   % calculate error
  MaxError(p)=max(abs(Temp_new(:)-Temp(:)));
  MinError(p)=min(abs(Temp_new(:)-Temp(:)));
   
    Temp=Temp_new; % update T
end


figure(1)
contourf(Temp_new(:,:,10))
xlabel('X')
ylabel('Y')
zlabel('t')
h = colorbar;
set(get(h,'title'),'string','Temperature (C))');
hold on

figure(2)
contourf(Temp_new(:,:,100))
xlabel('X')
ylabel('Y')
zlabel('t')
h = colorbar;
set(get(h,'title'),'string','Temperature (C))');
hold on

figure(4)
contourf(Temp_new(:,:,500))
xlabel('X')
ylabel('Y')
zlabel('t')
h = colorbar;
set(get(h,'title'),'string','Temperature (C))');
hold on

figure(5)
contourf(Temp_new(:,:,1000))
xlabel('X')
ylabel('Y')
zlabel('t')
h = colorbar;
set(get(h,'title'),'string','Temperature (C))');
figure(7)
plot3(Temp_new(4,4,:))
hold on

%set(gca, 'YDir','reverse')
% xlabel('X')
% ylabel('Y')
% zlabel('t')
% h = colorbar;
% set(get(h,'title'),'string','Temperature (C))');

figure(6)
semilogx(MaxError)
hold on
semilogx(MinError)
xlabel('Iterations')
ylabel('Error')

[KALYAN ACHARJYA]

Yes, get the indexes on non-integer values, and plot accordingly

[AbeSal]

Is anyone able to provide the appropriate function and guidance on how to set it up in Matlab?

[darova]

Please attach orginal equation and the difference scheme you used

Answer 1

[Sindar]

Look at your Temp variable:

Temp=zeros(x_nodes+1,y_nodes+1,t_nodes+1);

if you want to know the temperature for a specific location, you can extract it easily (here, the bottom left):

temp00 = Temp(1,1,:);

you also need the time:

t=dt*[0:t_nodes-1];

then, to plot it, simply use plot():

plot(t,temp00)

does that give you the desired plot?

[AbeSal]

Unfortunately, it returns the following error message:

Error using plot. 
Data cannot have more than 2 dimensions.

I read some literature regarding the squeeze function and entered the following into matlab:

plot(squeeze(Temp_new(3,3,:)))

It allowed me to create a 2d plot form a 3d matrix, but I'm curious to confirm if this is the appropriate choice to resolve my issue.

[Sindar]

Ah, yes, sorry I always forget the need to squeeze until I get that error. That is the correct usage. You could add that either to my definition of temp00, or to the final plot. If you want to plot vs actual time (you're currently plotting vs index), just add t:

t=dt*[0:t_nodes-1];
plot(t,squeeze(Temp_new(3,3,:)))