Temperature distribution changes analysis based on Gr¨unwald-Letnikov space derivative

Abstract

In this paper, the numerical approximation of the Dual-Phase-Lag (DPL) model has been presented. The approximation scheme is based on the Gr¨unwald-Letnikov (GL) definition of fractional derivatives. Moreover, that definition has been applied to the space derivative of the temperature in Fourier-Kirchhoff (FK) model. Then, the Dual-Phase-Lag model has been approximated based on the prepared modification of FK model, which has been called the space GL FK model. Furthermore, the finite difference method methodology for the approximation of the considered thermal model has also been employed. All mathematical formulas obtained during the determination of the approximation scheme are presented in the paper. Numerical examples of temperature distributions obtained in the case of new space GL FK model are also included in the paper. Moreover, the behavior of the model based on order parameter values has also been investigated.