MATLAB: 2-D conduction in a aluminum plate

2-d conductionfinite difference

I have a large matrix from a 2-D heated plate with each point in the matrix giving a temperature. I want to use second order central finite difference method to numerically compute what the heat flux is at each point and then create a 2D contour plot. I am new to using finite difference method and how to take my equations and boundary conditions from paper and write the code in matlab to solve for the heat flux. Any help would be great.
Thanks

Best Answer

Your equation:
Can be re-written as (difference scheme):
You should express 
while 1                     % loop until tolerance
    for i = 2:m-1           % loop rows matrix
        for j = 2:n-1       % loop columns matrix
            T(i,j) = long_expression
        end
    end
    if tolerance < 0.1
        break;
    end
end
Found a mistake in your boundary conditions:
I also attached similar script for another scheme. Look
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