Please help as I am struggling to solve this homework problem.

An H-section copper conductor carries an overload current of 54000 A. Under steady state conditions, the surface temperature is 60°C.

The dimensions of the bar are given in Figure 1 overleaf, and you are asked to use a numerical method to produce a mesh plot of the temperature distribution and a graph of the temperature distribution along the line y = 0.

The electrical resistivity, ρ, of copper is 2 × 10-8 Ω m, and the thermal conductivity, κ, is 0.311 kW m-1 K-1.

The governing differential equation is ∂2T + ∂2T + g = 0 (1)

∂x2 ∂y2 κ where g is the (constant) generation rate of heat per unit volume:

g = i2ρ (2) and i is the current density.

Using an appropriate Numerical Technique:

Determine the temperature distribution to an accuracy of 4 significant figures

You are expected to hand in the following by the submission date:

Hints

The Gauss-Seidel technique used in Tutorial 9 can be adapted to the present problem by including the additional term g/κ in the finite difference equation. You can generate a mask array as in Tutorial 9 to specify the region of the array covered by the H cross- section.

Try calculating the solution over a square mesh for a range of step lengths h = 5 mm, 2.5 mm, 1.25 mm...

You can if you wish make use of the symmetry of the problem and model just one quarter of the conductor. However, the boundary conditions then become more difficult to apply.

The H section is of width 40mm, depth 30mm and cut outs on top and bottom of depth 10x width 20 mm

Any help would be most appreciated

Cheers

Sam

[José-Luis]

Who haz teh codez?

[Sven]

"You are expected to hand in the following by the submission date"

Uh oh...I think I skipped this lecture... where do we hand in your assignment?

http://www.mathworks.com/matlabcentral/answers/8626-how-do-i-get-help-on-homework-questions-on-matlab-answers

[Ryan]

What have you tried so far, Sam?

[Steven Lord]

Since this is a homework assignment, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

Answer 1

[Elizabeth]

Don't know if this is any assistance to you but--Here is my code for the Gauss-Seidel iterative method:

    function [ X, Ntot ] = gs( A, b, tol, nmax )
    %GS is a function that utilizes the Gauss-Seidel iterative method in order to 
    %   to formulate an approximation to the linear algebra problem Ax=b
    %Input
    % A is an NxN nonsingular matrix
    % b is an Nx1 matrix
    % tol is the tolerance for convergence
    % Nmax is the maximum number of iterations
    %Output
    % X is the Gauss-Seidel approximation to the soln of Ax=b
    % Ntot is the number of iterations it took to reach convergence
    N=length(b) ;
    p=zeros(N,1);
    tol=eps;
    for k=1:nmax %for each iteration
        for j=1:N %to solve for the unknown variable Xj
           if j==1
               X(1)=(b(1)-A(1,2:N)*p(2:N))/A(1,1); %x1 in terms other variables which are unknowns
           elseif j==N
               X(N)=(b(N)-A(N,1:N-1)*(X(1:N-1))')/A(N,N); %xN written in terms other variables
           else
               X(j)=(b(j)-A(j,1:j-1)*X(1:j-1)'-A(j,j+1:N)*p(j+1:N))/A(j,j); %xj written in terms of other variables
           end
        end
       p=X';
       r=max(abs(A*p-b));
       if r< tol
           X=p;
           Ntot=k;
           disp('The problem has converged to a soln');
       end
    end
    Ntot=k;
    if k>nmax
    disp('Warning: the solution did not converge.');
    end
    end

[Jan]

Thge convergence criterion is useless in your code, because the iteration is not stopped. A missing convergence is not detected, because for k=1:nmax will never set the value of k to nmax+1, such that the test if k>nmax will be FALSE in every case. Better:

converged = false;
while k <= nmax
  ...
  if r < tol
    converged = true;
    break;
  end
end

[Elizabeth]

Thanks for the check.