Numerical analysis of temperature field and thermal stress associated with dual-phase-lag heat conduction

A numerical method for generalized dual-phase-lag (DPL) heat conduction is proposed. Differential equations including the third-order derivative in time are obtained by using finite element space discretization and are solved by the finite difference method. The backward difference has less numerical oscillation but the central difference can better describe the sharp temperature change near the thermal wave front. In generality, the backward difference is an ideal method for the transient solution of the temperature field associated with the DPL model. However, the time step must be small enough so that the temperature field near the thermal wave front can be obtained accurately.