Application of the hybrid method to transient heat conduction in one-dimensional composite layers

The hybrid application of the Laplace transform technique and the finite element method to the transient temperature response of multilayered composites is no longer restricted to linear boundary conditions, but is extended to include nonlinear radiation boundary conditions. In the hybrid method, the time-dependent terms are removed from the problem by the application of the Laplace transform and then the transformed system is solved using the finite element method. The transformed temperature is inverted numerically to obtain the result in the physical quantity. It is found that the temperature distribution of the multilayered slabs at a specific time can be obtained for the most general type of linear or nonlinear boundary conditions. The present solutions show a good accuracy. It is noteworthy that the present method can improve the drawback that the inversion of the Laplace transform is very involved for problems of composite slabs with more than two layers.