2D Heat Transfer Problem Not Yielding Plot

Question

Nickolai Serebriakov 2019-10-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/485776-2d-heat-transfer-problem-not-yielding-plot

回答： Anurag Pratap Singh 2020-6-24

Hi everyone, I am attempting to build a 4x4 grid and plot the temperature distribution, however my code is not yielding a graph. There are no errors in the code as far as matlab says. If someone could please point out the problem or help me fix it, I would greatly appreciate it.

%%
function [A,B,T,Temp]=FinDiffFourbyFour 
Ttop=1000; %K
Tleft=500; %K
Tright=500; %K
Tbottom=500; %K
w=0.01; %10 cm
l=0.01; %10 cm 
xsteps=4;
ysteps=4;
dx=l/(xsteps-1);
dy=w/(ysteps-1);
x=(0:dx:l);
y=(0:dy:w);
A=zeros(xsteps*ysteps,xsteps*ysteps);
B=zeros(xsteps*ysteps,1);
%Top
A(1,1)=1;
B(1)=Ttop;
A(2,2)=1;
B(2)=Ttop;
A(3,3)=1;
B(3)=Ttop;
A(4,4)=1;
B(4)=Ttop;
%Left 
A(5,5)=1;
B(5)=Tleft;
A(9,9)=1;
B(9)=Tleft;
%Right
A(8,8)=1;
B(8)=Tright;
A(12,12)=1;
B(12)=Tright;
%Interior 
A(6,6)=4;
A(6,2)=-1;
A(6,5)=-1;
A(6,7)=-1;
A(6,10)=-1;
B(6)=0;
A(7,7)=4;
A(7,1)=-1;
A(7,3)=-1;
A(7,6)=-1;
A(7,8)=-1;
B(7)=0;
A(10,10)=4;
A(10,6)=-1;
A(10,9)=-1;
A(10,11)=-1;
A(10,14)=-1;
B(10)=0;
A(11,11)=4;
A(11,7)=-1;
A(11,12)=-1;
A(11,15)=-1;
B(11)=0;
%Bottom 
A(13,13)=1;
B(13)=Tbottom;
A(14,13)=1;
B(14)=Tbottom;
A(15,15)=1;
B(15)=Tbottom;
A(16,16)=1;
B(16)=Tbottom;
T=inv(A*B);
%turn back into matrix
for i=1:ysteps
    for j=1:xsteps
        Temp(i,j)=T(xsteps*ysteps-xsteps*i+j);
    end 
end
[C,h]=contour(x,y,T); %plot contour
clabel(C,h); %label contour levels
colorbar
xlabel('x-axis')
ylabel('y-axis')
zlabel('Temperature(K)')
title('4x4 Finite Difference Solution')

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

darova 2019-10-17

在 MATLAB Online 中打开

Can you please explain this?

A(16,16)=1;
B(16)=Tbottom;
T=inv(A*B);        % A - 2D matrix, B - vector

x,y - are vector of 1x4 size

[C,h]=contour(x,y,T); %plot contour

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Anurag Pratap Singh 2020-6-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/485776-2d-heat-transfer-problem-not-yielding-plot#answer_456163

Hi Nickolai

I understand that you are facing problem in plotting the temperature distribution as a contour

I looked at your code and found you have not created matrices of x and y that will define you grid in the x,y plane.I suggest you could use meshgrid for that purpose.

Please refer to the https://www.mathworks.com/help/matlab/ref/contour.html#:~:text=contour(%20Z%20)%20creates%20a%20contour,coordinates%20in%20the%20plane%2C%20respectively.

documentation for making the contour for more information