Solving Heat Equation With Spatially Varying Thermal Conductivity

I was following this tutorial on how to solve the steady state heat diffusion or transfer problem and so far its been helpful.

http://www.mathworks.com/help/pde/examples/solving-a-heat-transfer-problem-with-temperature-dependent-properties.html

However, I was wondering how would one solve the same problem when the thermal conductivity varies with either the x or y coordinate. In this they have a varying thermal conductivity but it only varies with temperature and not space. So I hope some one could explain how to do the same for a spatial varying thermal conductivity or direct me to something that could explain it. Thanks.

[Sitong Wu]

Hi, I am facing the exactly same problem as you did 6 years ago.

Did you find the way to solve it?

:D

Answer 1

[Alan Weiss]

The documentation describes how to include coefficients as string expressions. In brief, use 'x' and 'y' as strings representing the x and y coordinates. For example, if your k coefficient is 0.3 + x*y/20, then use

 k = '0.3+x.*y/20';

Alan Weiss

MATLAB mathematical toolbox documentation