Error while contour plotting an integral.

I am trying to plot this temperature equation like a simulation. The temperature should be a function of x and z with t as varying time step. We are getting this error: Input arguments must be numeric or objects which can be converted to double.

I have written the following code. Can someone please help in this?

% Material Properties
P= 50;
eta= 0.3;
rho=4429;
D=2.89*10^(-6);
Cp=553;
T0=300;
v=0.1;
%function% Define the range of x and z values
x_range = linspace(-10, 10, 100); % Adjust the range and number of points as needed
z_range = linspace(-10, 10, 100); % Adjust the range and number of points as needed
fun = exp(-((z - z1).^2 + (t/10 - t1/10 - x + x1).^2)./((6823819567746637*t)./590295810358705651712 - (6823819567746637*t1)./590295810358705651712))./(t - t1).^(3/2);
% Create a grid of x and z values
[X, Z] = meshgrid(x_range, z_range);
% Define the number of time steps
num_time_steps = 10; % Adjust as needed
% Initialize a cell array to store the integral results for each time step
integral_results = cell(num_time_steps, 1);
% Calculate the integral result for each time step
for t_step = 1:num_time_steps
    t = t_step * 0.1; % Adjust the time step as needed
    
    % Initialize a matrix for this time step
    integral_result = zeros(length(x_range), length(z_range));
    
    for x_index = 1:length(x_range)
        for z_index = 1:length(z_range)
            x = x_range(x_index);
            z = z_range(z_index);
            
            % Numerical integration using quad
            fun_numeric = @(t1) double(subs(fun, {x, z, t, x1, z1}, {x, z, t, x, z}));
            integral_result(x_index, z_index) = integral(fun_numeric, 0, t);
        end
    end
    
    % Store the result in the cell array
    integral_results{t_step} = integral_result;
end
% Create contour plots for each time step
for t_step = 1:num_time_steps
    t = t_step * 0.1; % Adjust the time step as needed
    
    figure;
    contourf(X, Z, integral_results{t_step}, 20); % Adjust the number of contour levels as needed
    colorbar;
    xlabel('x');
    ylabel('z');
    title(['Contour Plot at t = ' num2str(t)]);
end

[Star Strider]

I do not understand what you want to do.

That aside, this runs, however you will likely need to make changes to it (specifically the arguments to ‘fun’) to get the desired result —

% Material Properties
P= 50;
eta= 0.3;
rho=4429;
D=2.89*10^(-6);
Cp=553;
T0=300;
v=0.1;
%function% Define the range of x and z values
x_range = linspace(-10, 10, 100); % Adjust the range and number of points as needed
z_range = linspace(-10, 10, 100); % Adjust the range and number of points as needed
fun = @(x,z,t,x1,z1,t1) exp(-((z - z1).^2 + (t/10 - t1/10 - x + x1).^2)./((6823819567746637*t)./590295810358705651712 - (6823819567746637*t1)./590295810358705651712))./(t - t1).^(3/2);
% Create a grid of x and z values
[X, Z] = meshgrid(x_range, z_range);
% Define the number of time steps
num_time_steps = 10; % Adjust as needed
% Initialize a cell array to store the integral results for each time step
integral_results = cell(num_time_steps, 1);
% Calculate the integral result for each time step
for t_step = 1:num_time_steps
    t = t_step * 0.1; % Adjust the time step as needed
    
    % Initialize a matrix for this time step
    integral_result = zeros(length(x_range), length(z_range));
    
    for x_index = 1:length(x_range)
        for z_index = 1:length(z_range)
            x = x_range(x_index);
            z = z_range(z_index);
            
            % Numerical integration using quad
            % fun_numeric = fun(x,z,t,x,z)
            % fun_numeric = @(t1) double(subs(fun, {x, z, t, x1, z1}, {x, z, t, x, z}));
            integral_result(x_index, z_index) = integral(@(t)fun(x,z,t,x,z,t_step), 0, t);
        end
    end
    
    % Store the result in the cell array
    integral_results{t_step} = integral_result;
end
% Create contour plots for each time step
for t_step = 1:num_time_steps
    t = t_step * 0.1; % Adjust the time step as needed
    
    figure;
    contourf(X, Z, integral_results{t_step}, 20); % Adjust the number of contour levels as needed
    colorbar;
    xlabel('x');
    ylabel('z');
    title(['Contour Plot at t = ' num2str(t)]);
end

I am not running the code here because it takes longer than the allotted 55 seconds. Running it would simply show that it timed out.

The ‘fun_numeric’ assignment is not required. Create ‘fun’ as a function that does what you want, provide the correct arguments to it, and the code should do what you want.

.

[Walter Roberson]

            fun_numeric = @(t1) double(subs(fun, {x, z, t, x1, z1}, {x, z, t, x, z}));

Most of the time if you are wanting a numeric result from a symbolic calculation, you should use matlabFunction

You could probably do that outside some of the existing loops

[AD]

Thanks for your answer @Star Strider. However, I am getting a warning as infinity or nan value encountered. I tried to solve this error by changing the limit of t, but it is not working. I just want to run a simulation of the temperature field as a function of x and z from the equation given. Can you please help in this matter?

[Star Strider]

Did you use my revision of your code, or something else?

If you changed it, please post the new code.

When I ran it, the code I posted runs without error, although it takes forever, so I stopped it before it finished.

[Pooja Kumari]

Can you tell what is y and y' in the image attached above?

Answer 1

[Pooja Kumari]

Dear AD,

I understand that you are facing issue with contour plot of this integral function provided in the temperature function below:

These are some troubleshooting steps which you can follow:

• Convert the variables to symbolic scalar variables using “syms” function in MATLAB. You can refer to the below documentation for more information: Create symbolic scalar variables and functions, and matrix variables and functions - MATLAB syms - MathWorks India

Here is a sample code for reference:

 syms x z t x1 z1 t1;

• “matlabFunction” can be used to convert symbolic function to numeric function handle specifying the “Vars” as [x,z,t,x1,z1,t1]. You can refer to the below documentation for more information on matlabFunction: Convert symbolic expression to function handle or file - MATLAB matlabFunction - MathWorks India
• In the numerical integration using “integral” function, you can use “t1” which will resolve the “Warning: Inf or NaN value encountered.”

Here is a sample code for reference:

  q = integral(@(t1) fun(t1,5),0,2);
  

You can refer to the below documentation for more information on contour plot:

Filled 2-D contour plot - MATLAB contourf - MathWorks India

Regards,

Pooja Kumari