Numerical simulation of anisotropic heat transfer problem by pseudospectral Chebyshev method

The two-dimensional steady-state heat transfer problem is analyzed under the most general boundary conditions in a heterogeneous medium with heat transfer coefficient and heat generation parameters depending on the space variable in two directions. The governing equation of the system is solved numerically by using the pseudospektral Chebyshev method with high accuracy In order to test the accuracy of the numerical method, both the closed form analytical solution and the numerical solution of the differential equation are obtained for the simple heat transfer coefficient and heat heat generation parameters depending on the space variable. It has been shown that the results overlap under high sensitivity. As a result, it is shown that this method is simple and effective and can be easily applied to such problems.