Plotting of colormap for single value in x axis and multiple values in y axis

% Choose the time you want to visualize
desired_time = 2.5;  % Change this to the desired time in seconds

% Find the nearest time step to the desired time
[~, time_step_to_visualize] = min(abs(t - desired_time));

% Plot the temperature distribution as a color spectrum
figure;
imagesc(t(time_step_to_visualize), y, u(:, time_step_to_visualize));
colormap(jet);


% Get the temperature values at the specified time step
temperature_values = u(:, time_step_to_visualize);
% Set color axis limits to match the temperature variation at the specified time step
clim([min(temperature_values(:)), max(temperature_values(:))]);
% Create a color bar and adjust its position and size
colorbar;

xlabel('Time (seconds)');
ylabel('Thickness (meters)');
title(['Temperature Distribution at Time = ', num2str(t(time_step_to_visualize)), ' seconds']);
% Set axis limits 
xlim([t(time_step_to_visualize-1), t(time_step_to_visualize)]);
ylim([0, max(y)]);
% Invert the y-axis direction
set(gca, 'YDir', 'normal');

I have tried to plot the color map of temperature at t=''secs but I am getting the temperature distribution over the whole axis limit. Could someone please tell me how to change the code for temperature distribution only at time step t?

[Constantino Carlos Reyes-Aldasoro]

This is not completely clear. We cannot reproduce the code as we do not have time, nor we can see what exactly is the problem. Add figures to illustrate what you get and what you would like to have.

[Joydeep Bagchi]

Actually I cannot share the whole code due to some other issues

please find attached the screenshot

It is just the plotting of u(thickness, timestep) which is storing the temperature values

so I want to see the temperature distribution only at 8.49 seconds and the axis limits should be short

Answer 1

[Voss]

Something like this? The only change is to set xlim(t([1 end])), i.e., let the x-limits span the entire t vector.

t = 0:10;
y = 0:5;
u = rand(6,11);


% Choose the time you want to visualize
desired_time = 2.5;  % Change this to the desired time in seconds

% Find the nearest time step to the desired time
[~, time_step_to_visualize] = min(abs(t - desired_time));

% Plot the temperature distribution as a color spectrum
figure;
imagesc(t(time_step_to_visualize), y, u(:, time_step_to_visualize));
colormap(jet);

% Get the temperature values at the specified time step
temperature_values = u(:, time_step_to_visualize);
% Set color axis limits to match the temperature variation at the specified time step
clim([min(temperature_values(:)), max(temperature_values(:))]);
% Create a color bar and adjust its position and size
colorbar;

xlabel('Time (seconds)');
ylabel('Thickness (meters)');
title(['Temperature Distribution at Time = ', num2str(t(time_step_to_visualize)), ' seconds']);

% Set axis limits 
% xlim([t(time_step_to_visualize-1), t(time_step_to_visualize)]);
xlim(t([1 end]));

ylim([0, max(y)]);
% Invert the y-axis direction
set(gca, 'YDir', 'normal');

[Joydeep Bagchi]

Thankyou for the reply

can we reduce the axis limits for example in the screeshot I want the temperature distribution at 8.49 seconds only and I want to reduce the axis limits so if i reduce the axis limits, it is showing temperature distribution over the whole time range

[Voss]

You're welcome!

I'm not certain what you want to see. My answer sets the axes x-limits to the entire time range. Did you try that in your code? And does it do what you want?

You can always set the axes x-limits using the xlim function.

[Joydeep Bagchi]

yes, i have changed to xlim[t(timestep), t(end)] so now i have

[Voss]

Is that the desired result? If not, what is?

[Joydeep Bagchi]

i just have shifted the axis and in the color bar i have choosen the values to be integer

[Voss]

Is that the desired result? If not, what is?

Are we making progress here?

Answer 2

[Torsten]

Use a contour plot

https://uk.mathworks.com/help/matlab/ref/contourf.html

with time and thickness as axes and temperature for color.

To do this, add the lines

contourf(t,y,u)
colorbar

to your code under

https://uk.mathworks.com/matlabcentral/answers/2025792-which-boundary-condition-is-coorect-or-what-will-be-the-correct-alternative?s_tid=prof_contriblnk

[Joydeep Bagchi]

Thankyou for the reply. Could you please have a look on above comment , I want to do that part actually!

[Torsten]

If you want a plot of the temperature distribution over the web at a specific time, you should use plot(y,T(t)). Everything else would be confusing in my opinion:

% Constants
Ly = 0.001;        % Thickness of the sheet (meters)
T = 15;             % Total simulation time (seconds)
Ny = 20;            % Number of spatial grid points
Nt = 3000;           % Number of time steps
k1 = 0.15;           % Thermal conductivity of PVC W/m-K
rho = 1250;          % density in kg/m3
cp  = 1350 ;         % specific heat in J/kg-K
alpha = k1/(rho*cp);   % Thermal diffusivity (m^2/s)
T_ambient = 25;     % Ambient temperature (°C)
velocity_x = 0.1667; % Velocity in x-direction (m/s)
%contact with hot roller
k2 = 50;             %Thermal conductivity of steel roller W/m-K
h_roller = 500;      %convective heat transfer coefficient of roller W/m2-K
d_roller = 0.4;      %diameter of roller in m
contact_angle = 180; %in °
contact_length = pi*d_roller*contact_angle/360; %contact length with roller
T_roller = 100;      % Roller temperature
%Contact in air
distance_x = 0.5;   % Distance traveled in x-direction (meters)
h_air = 12;         % Convective heat transfer coefficient of air W/m2-K
%Contact in IR field
distance_ir = 0.3 ; % in m
radiative_flux = 50e3; %W/m2
absorption = 50; % in %
performance = 80; % in %
Net_radiative_intensity = radiative_flux*(absorption/100)*(performance/100);
%Contact with air again
distance_v = 1 ; % in m
%Naming the distance variables
y1 = contact_length;
y2 = contact_length + distance_x;
y3 = contact_length + distance_x+ distance_ir;
y4 = contact_length + distance_x+ distance_ir+distance_v;
% Discretization
dy = Ly / (Ny - 1);
dt = T / Nt;
y = linspace(0, Ly, Ny);
t = linspace(0, T, Nt);
% Initial temperature distribution
initial_temperature = 25;
distance_travelled = zeros(1,Nt); %initial distance travelled
% Initialize temperature matrix
u = zeros(Ny, Nt);
u(:, 1) = initial_temperature;
% Forward euler method
r = alpha * dt / (dy^2); % as 0 < r < 0.5
% Time-stepping loop (explicit method)
for n = 1:Nt - 1
    
    % Update position in x-direction
    distance_travelled(n+1) = distance_travelled(n) + velocity_x * dt;
    
    % Check if the total distance is within the contact length
    if distance_travelled(n) <= y1
        for i = 2:Ny - 1
            u(i, n + 1) = u(i, n) + r * (u(i + 1, n) - 2 * u(i, n) + u(i - 1, n));
        end
            % Apply boundary conditions for contact with the roller
        %u(1, n + 1) = ((h_roller * T_roller * dy) + (k1 * u(2, n))) / (k1 + h_roller * dy);
        %u(Ny, n + 1) = ((h_air * T_ambient * dy) + (k1 * u(Ny - 1, n))) / (k1 + h_air * dy);
        u(1, n + 1) = u(1,n) + dt*(alpha*(u(2,n)-u(1,n))/dy - h_roller/(rho*cp)*(u(1,n)-T_roller))/(dy/2);
        u(Ny, n + 1) = u(Ny,n) + dt*(-h_air/(rho*cp)*(u(Ny, n)-T_ambient)-alpha*(u(Ny,n)-u(Ny-1,n))/dy)/(dy/2);
        
        % For the next part in contact with air 
    elseif distance_travelled(n) <= y2
        for i = 2:Ny - 1
            u(i, n + 1) = u(i, n) + r * (u(i + 1, n) - 2 * u(i, n) + u(i - 1, n));
        end
        % Apply boundary conditions for contact with air
        %u(1, n + 1) = ((h_air * T_ambient * dy) + (k1 * u(2, n + 1))) / (k1 + h_air * dy);
        %u(Ny, n + 1) = ((h_air * T_ambient * dy) + (k1 * u(Ny - 1, n + 1))) / (k1 + h_air * dy);
        u(1, n + 1) = u(1,n) + dt*(alpha*(u(2,n)-u(1,n))/dy - h_air/(rho*cp)*(u(1,n)-T_ambient))/(dy/2);
        u(Ny, n + 1) = u(Ny,n) + dt*(-h_air/(rho*cp)*(u(Ny, n)-T_ambient)-alpha*(u(Ny,n)-u(Ny-1,n))/dy)/(dy/2);        
        %In contact with IR field radiation
    elseif distance_travelled(n) <= y3
        for i = 2:Ny - 1
            u(i, n + 1) = u(i, n) + r * (u(i + 1, n) - 2 * u(i, n) + u(i - 1, n));
        end
        % Apply boundary conditions for contact with IR field
        %u(1, n + 1) = ((h_air * T_ambient * dy) + (k1 * u(2, n + 1))) / (k1 + h_air * dy);
        %u(Ny, n + 1) = u(Ny - 1, n + 1) + ((Net_radiative_intensity * dy) / k1);
        u(1, n + 1) = u(1,n) + dt*(alpha*(u(2,n)-u(1,n))/dy - h_air/(rho*cp)*(u(1,n)-T_ambient))/(dy/2);
        u(Ny, n + 1) = u(Ny,n) + dt*(Net_radiative_intensity/(rho*cp)-alpha*(u(Ny,n)-u(Ny-1,n))/dy)/(dy/2);
        
        % Distance in contact with air again
    else
        for i = 2:Ny - 1
            u(i, n + 1) = u(i, n) + r * (u(i + 1, n) - 2 * u(i, n) + u(i - 1, n));
        end
        % Apply boundary conditions for contact with air
        %u(1, n + 1) = ((h_air * T_ambient * dy) + (k1 * u(2, n + 1))) / (k1 + h_air * dy);
        %u(Ny, n + 1) = ((h_air * T_ambient * dy) + (k1 * u(Ny - 1, n + 1))) / (k1 + h_air * dy);
        u(1, n + 1) = u(1,n) + dt*(alpha*(u(2,n)-u(1,n))/dy - h_air/(rho*cp)*(u(1,n)-T_ambient))/(dy/2);
        u(Ny, n + 1) = u(Ny,n) + dt*(-h_air/(rho*cp)*(u(Ny, n)-T_ambient)-alpha*(u(Ny,n)-u(Ny-1,n))/dy)/(dy/2);          
        
        
    end    
    
    % Break the loop when the total distance is reached
    if distance_travelled(n + 1) >= y4
        break;
    end
end

for i = 1:numel(y)
  tempcut(i) = interp1(t,u(i,:),8.49);
end
plot(y,tempcut)
xlabel('Thickness [m]')
ylabel('Temperature [°C]')
title('Temperature Distribution at Time = 8.49 s')

[Joydeep Bagchi]

Ok, thankyou torsten for your reply but I have implemented other option