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

Abstract

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.

Keywords:

• Dual-phase-lag heat conduction
• thermal wave
• thermal stress
• numerical method

Acknowledgments

The authors are very grateful to the three anonymous referees for providing a number of comments on their manuscript, which are very useful for improving the quality and presentation of the final paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Science Foundation of China (Project No. 11502101), Jinling Institute of Technology Research Innovation Foundation (Project No. jit-b-201515) and Research Innovation Fund of Shenzhen City of China (Project No. JCYJ20170413104256729).