How to plot xy, yz and xz plane contour with integration matrix equation

I try to follw mt professor to plot contour plot of Rosenthal's equation, and here it my code

clear all
close all
clc

%Constant
rho = 4420;          %kg/m^3
Cp = 550;            %J/kg?K
T0 = 303.15;         %K
A = 0.5;             %[Absorbtivity] 
k = 7.2;             %W/m/K
alpha = 2.96*10^-6;  %m^2/s
D = alpha;
P = 100;             %W
v = 1;               %m/s
u = v;
Tm = 1933;        %K
d_laser = 0.01;      %mm
r_laser = d_laser/2; %mm
a = r_laser;
p = D/(u*a);

%Define
x = linspace(-0.005,0.025,100);
y = linspace(-0.0005,0.0005,100);
z = linspace(0,0.005,100);

%Normalized
x_nor = x/a;
y_nor = y/a;
z_nor = z/(D*a/u).^0.5;
[x_mesh, y_mesh] = meshgrid(x_nor, y_nor);
[x_mesh, z_mesh] = meshgrid(x_nor, z_nor);

%Calculation
r = (x_mesh.^2 + y_mesh.^2).^0.5;
Ts = A*P/(pi*rho*Cp*sqrt(D*u*a));
T2 = T0 + (A*P)./(2*pi*k*r).*exp(v.*(r+x_mesh)./(2*D));
q = (2*A*P/(pi*a^2))*exp(-2*r.^2/a^2);

syms t
fun = @(t) exp((-z_mesh.^2./(4*t))-((y_mesh.^2+(x_mesh-t).^2)./(4*p.*t+1)))./((4.*p.*t+1).*sqrt(t));
g = int(fun,t,[0 Inf]);

%Plot x'y' plane
figure
contourf(x_mesh, y_mesh, g, [303.15:100:2000])
colorbar
title('x\primey\prime plane')
xlabel('x\prime (m)')
ylabel('y\prime (m)')
xlim([-0.005 0.025])

%Plot y'z' plane
figure
contourf(x_mesh, z_mesh, g, [303.15:100:2000])
title('x\primez\prime plane')
xlabel('x\prime (m)')
ylabel('z\prime (m)')
xlim([-0.005 0.025])

[Torsten]

And what is your question ?

[Pannawat Pongsriassawin]

sorry, my question is 'how can I integrate the function and plot it into contour in xy, yz and xz plane like 2 images that I attached it' I don't know why it can't run or error cause of I'm new on MATLAB, Thank.

[Torsten]

So g should be a three-dimensional array where the first dimension refers to x, the second dimension refers to y and the third dimension refers to z ? Then, to plot in the xy plane, e.g., you want to choose a value "z(iz)" and plot g(:,:,iz) against the x- and y-array ? That's not what you do in your code.

[Pannawat Pongsriassawin]

yeah, actualy output (g) should be 100x100x100, but it is g(:,:,1), g(:,:,2), ..., g(:,:,100) then it can plot it into 2D plane contour. I don't know how to solve it. I think g(:,:,1) mean g(1:100,1:100,1) then it is g in z=1 plane? If it is, that what I desired.Actual it can't plot or Should I use aother command to plot it?

Answer 1

[Torsten]

clear all
close all
clc
%Constant
rho = 4420;          %kg/m^3
Cp = 550;            %J/kg?K
T0 = 303.15;         %K
A = 0.5;             %[Absorbtivity] 
k = 7.2;             %W/m/K
alpha = 2.96*10^-6;  %m^2/s
D = alpha;
P = 100;             %W
v = 1;               %m/s
u = v;
Tm = 1933;        %K
d_laser = 0.01;      %mm
r_laser = d_laser/2; %mm
a = r_laser;
p = D/(u*a);
%Define
x = linspace(-0.005,0.025,100);
y = linspace(-0.0005,0.0005,100);
z = linspace(0,0.005,100);
%Normalized
x_nor = x/a;
y_nor = y/a;
z_nor = z/(D*a/u).^0.5;
[x_mesh,y_mesh,z_mesh] = ndgrid(x_nor,y_nor,z_nor);
fun = @(t) exp((-z_mesh.^2./(4*t))-((y_mesh.^2+(x_mesh-t).^2)./(4*p.*t+1)))./((4.*p.*t+1).*sqrt(t));
g = integral(fun,0,Inf,'ArrayValued',true);
figure(1)
iz = 1;
contourf(y_nor,x_nor,squeeze(g(:,:,iz)))
colorbar

figure(2)
iy = 1;
contourf(z_nor,x_nor,squeeze(g(:,iy,:)))
colorbar

figure(3)
ix = 1;
contourf(z_nor,y_nor,squeeze(g(ix,:,:)))
colorbar

[Pannawat Pongsriassawin]

OK, thank you. I had adjust and chang some code, very kind of you to inspired me something.

Answer 2

[Sarthak]

Hello Pannawat,

You can plot the contour by using the meshgrid and surf functions which are available in MATLAB.

[X,Y] = meshgrid(x,y);  % Create a grid from x and y vectors
z = zeros(size(x, 1));  % Generate z data
surf(x, y, z);          % Plot the contour

You can also refer to the MATLAB Answer provided below for further information.

https://in.mathworks.com/matlabcentral/answers/101174-how-can-i-generate-a-plane-surface-in-matlab

Hope this helps!!