2-D conduction in a aluminum plate

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

[darova]

• how to take my equations and boundary conditions from paper

Where are they?

[Layne Christensen]

Answer 1

[darova]

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