Semi analytical solution of hyperbolic heat conduction of a semi-infinite functionally graded body with a time dependentlaser heat source

In this study, the hyperbolic heat conduction of a semi-infinite functionally graded body isolated under the effect of a time dependent laser heat source is solved semi-analytically. Except for the thermal relaxation parameter, which is considered to be constant, it is assumed that the material properties of the body change with the force rule in the axial direction. These conditions produce a linear non-homogeneous partial differential equation. It is converted into ordinary differential equation by removing the dependence of the problem in the direction of time with Laplace transform. Then, after this ordinary differential equation is solved analytically in Laplace space, the values of the final results in time space are obtained using the modified Durbin method. To test the accuracy of the solution obtained, the same problem is solved and compared with the Pseudospectral Chebyshev Method. For three different laser heat sources: constant strength source, instantaneous source and laser pulse, temperature distributions of functional graded and homogeneous material are discussed on graphs.