Analysis of Non-Fourier Heat Conduction Using Hybrid Numerical Scheme

摘要

In this Paper non-Fourier heat conduction problem is analyzed using a hybrid scheme. Because of second order time derivative in the governing equation, application of conventional numerical schemes such as Newmark method leads to Strong oscillations of the results around discontinuities in solution domain. In this research to overcome this difficulty, a so-called hybrid method is employed. In this method, time derivatives are removed applying Laplace transform to the equation, and the transformed equation is solved using Galerkin finite element method. This method is more effective than temporal approximation methods such as Newmark. Several test case including one-dimensional and two-dimensional problems have been carried out to investigate the validation of the scheme. The first test case concerns a one-dimensional finite slab with no heat source. For this test case, the results of Newmark method and hybrid method are compared with the result of analytical solution. The second case is one-dimensional finite slab with a pulsed heat source, Newmark method is not able to solve this problem but the results of hybrid method are in good agreement with the results of analytical solution. The third case is a two dimensional heat conduction problem. This case is analyzed using the hybrid method and the results are compared with the result of a finite volume based hybrid scheme. The results show that the present hybrid method has better performance near boundaries.