Elegant way to calculate heat flux for heat equation

Hi.

I want to calculate heat flux in two-diemnsional, uniform domain using Fourier equation:

I have four vectors: X - containg x coordinates of domain points, Y - containg y coordinates of domain points, T - containg temperatures in specific points, K - containg values of heat conductivity in specific points. Dimension of X,Y,T,K is [nx*ny , 1]. I did it this way:

[px,py] = gradient(reshape(T,[nx,ny]),dx,dy);

qx = -qx .* reshape(K,[nx,ny]);

qy = -qy .* reshape(K,[nx,ny]);

qx = qx(:);

qy = qy(:);

which I find not very elegant, I even did not use X,Y vectors. dx,dy are spacings of uniform domain and nx, ny are number of points in each direction. Do you have better idea?

Kind regards

[Bjorn Gustavsson]

Why do you find this not elegant?

If your coordinate matrices arent uniformly spaced you can use the first row-and column of X and Y in place of dx and dy. (in that case you might prefer to use a properly calculated central difference instead of the wonky one in gradient.)