Analysis of heat conduction of functionally graded sphere in transient regime by chebyshev pseudospectral method

The functionally graded thick-walled hollow sphere is analyzed in transient regime using a hyperbolic heat conduction model. It is assumed that the material properties such as heat conduction coefficient, density and specific heat change exponentially in radial direction. Under these conditions, a partial differential equation whic is difficult to solve by conventional methods is obtained. By applying Laplace transform to this differential equation, time-independent linear ordinary differential equation is created in Laplace space. Then, the differential equation is solved numerically using Chebyshev Pseudospectral Method and the solution in time space is obtained by using the Modified Durbin Inverse Transformation Method. The dynamic reactions of heat and heat flux in the transient regime and their behavior against thermal relaxation, relative temperature parameters are investigated for a special material of metal-ceramic mixture and comparisons are made with homogeneous material. The solutions available in the literature are used to validate the results. The combined method used in this study is shown to be a well structured, simple and effective.