Heat transfer Conduction question

Question

Ahmed Alhezab 2017-4-21

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/336599-heat-transfer-conduction-question

编辑： Sudarshan Kolar 2017-4-24

Can someone help me out in finding the other Temperature values. I am only getting the first two.

I am using Gauss-Siedel Method

    tinf=30+273;% deg K
    h=100; % W/m^2-K
    kcopper= 401;
    kbronze= 52; % W/m-k
    alpha=14e6; % m^2/s
    qdprime= 1e4; % w/m^2
  deltax=.02
  Nx = 3;
  Ny = 9;
  % initialize coefficient matrix and constant vector with zeros
  A = zeros(Nx*Ny);
  C = zeros(1:Nx*Ny,1);
  % initial 'guess' for temperature distribution
  T(Nx*Ny,1)=100;
  % Build coefficient matrix and constant vector
  % inner nodes
  for n = 2:(Nx-1)
  for m = 2:(Ny-1)
  i = (n-1)*Ny + m;
  A(i,i+Ny) = 1;
  A(i,i-Ny) = 1;
  A(i,i+1) = 1;
  A(i,i-1) = 1;
  A(i,i) = -4;
  end
  end
  % Edge nodes
  % bottom (Case 6)
  for m = 2:(Ny-1)
  %n = 1
  i = (Nx-1)*Ny + m;
  A(i,i-Ny) = 2;
  A(i,i+1) = 1;
  A(i,i-1) = 1;
  A(i,i) = -(2.*(2+((h.*deltax)./kcopper)));
  C(i) = -(((2.*h.*deltax)./kcopper).*tinf);
  end
  %top (Case3)
  for m = 2:(Nx-1)
  % n = Ny
  i = (1 -1)*Ny + m;
  A(i,i+Ny) = 2;
  A(i,i+1) = 1;
  A(i,i-1) = 1;
  A(i,i) = -(2.*(2+((h.*deltax)./kcopper)));
  C(i) = -(((2.*h.*deltax)./kcopper).*tinf);
  end
  %left (case 7)
  for n=2:(Nx-1)
  %m = 1
  i = (n-1)*Ny + 1;
  A(i,i+Ny) = 1;
  A(i,i+1) = 2;
  A(i,i-Ny) = 1;
  A(i,i) = -4;
  C(i) = -((2.*qdprime.*deltax)./kcopper);
  end
  %right (Case 8)
  for n=2:(Nx-1)
  %m = Nx
  i = (n-1)*Ny + Ny;
  A(i,i+Ny) = 1;
  A(i,i-1) = 2;
  A(i,i-Ny) = 1;
  A(i,i) = -(2.*(2+((h.*deltax)./kcopper)));
  C(i) = -(((2.*h.*deltax)./kcopper).*tinf);
  end
  % Corners
  %bottom left (Case 4):
  i=(Nx-1)*Ny + 1;
  A(i,i-Ny) = 1;
  A(i,i+1) = 1;
  A(i,i) =  -(((h.*deltax)./kcopper)+2);
  C(i) = -(((h.*deltax)./kcopper).*tinf)+((qdprime.*deltax)./kcopper);
  %bottom right (case 5)
  i = (Nx)*Ny;
  A(i,i-Ny) = 1;
  A(i,i-1) = 1;
  A(i,i) =  -(2.*(1+((h.*deltax)./kcopper)));
  C(i) = -(((2.*h.*deltax)./kcopper).*tinf);
  %top left (case 1)
  i = 1;
  A(i,i+1) = 1;
  A(i,i) = -(((h.*deltax)./kcopper)+2);   
  A(i,i+Ny) = 1;
  C(i) = -(((h.*deltax)./kcopper).*tinf)+((qdprime.*deltax)./kcopper);
  %top right (Case 2)
  i = Ny;
  A(i,i-1) = 1;
  A(i,i) = -(2.*(1+((h.*deltax)./kcopper)));
  A(i,i+Ny) = 1;
  C(i) = -(((2.*h.*deltax)./kcopper).*tinf);
  %Solve using Gauss-Seidel
  residual = 100;
  iterations = 0;
  while (residual > 0.001) % The residual criterion is 0.0001 
  % different values can be tested
  iterations = iterations+1;
  %Transfer the previously computed temperatures to an array Told
  Told = T;
  %Update estimate of the temperature distribution
  for n=1:Ny
  for m=1:Nx
  i = (n-1)*Nx + m;
  Told(i) = T(i);
  end
  end
  % iterate through all of the equations
  for n=1:Ny
  for m=1:Nx
  i = (n-1)*Nx + m;
  %sum the terms based on updated temperatures
  sum1 = 0;
  for j=1:i-1
  sum1 = sum1 + A(i,j)*T(j);
  end
  %sum the terms based on temperatures not yet updated
  sum2 = 0;
  for j=i+1:Nx*Ny
  sum2 = sum2 + A(i,j)*Told(j);
  end
  % update the temperature for the current node
  T(i) = (1/A(i,i)) * (C(i) - sum1 - sum2);
  end
  end
  residual = max(T(i) - Told(i));
  end
  %compute residual
  deltaT = abs(T - Told);
  residual = max(deltaT);
  iterations;

2 个评论
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John D'Errico 2017-4-21

Um, huh? What other temperature values? Be clear about your question.

Ahmed Alhezab 2017-4-21

This is output matrix I'm getting. I don't understand why it is only shown the first two.

here is a picture of the problem I am trying to solve.

Im trying to find the temp. at each node

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Answer 1

Sudarshan Kolar 2017-4-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/336599-heat-transfer-conduction-question#answer_264238

编辑：Sudarshan Kolar 2017-4-24

Hello Ahmed,

I understand that you are not able to see certain temperature values in your variable. The best approach here would be to step through your code and observe the values of the variable under consideration as you step through. Following documentations will help you with your debugging:

https://www.mathworks.com/help/matlab/matlab_prog/debugging-process-and-features.html

https://www.mathworks.com/help/matlab/matlab_prog/examine-values.html