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

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Pannawat Pongsriassawin
评论： Pannawat Pongsriassawin 2023-7-17
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])
  4 个评论
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Torsten
Torsten 2023-6-26
编辑：Torsten 2023-6-26
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
Pannawat Pongsriassawin 2023-6-26
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?

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采纳的回答

Torsten
Torsten 2023-6-26
编辑：Torsten 2023-6-26
Ran in:
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

更多回答（1 个）

Sarthak
Sarthak 2023-6-27
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!!

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