Numerical analysis of dynamic thermoelastic problem combined with non-Fourier heat transfer equation by finite-difference time-domain method

Heat transfer in media is generally characterized by the empirical heat conduction law which was proposed by Fourier. However, the application of this empirical law to the problem of fast transient heat transfer such as a pulsed laser heat is not available, which is an important engineering problem. A heat conduction equation that considers about the time delay in the heat flux has been proposed to overcome such problem. In addition, Load and Shulman attempted to extend the heat conduction equation coupled with thermoelastic deformation. In this study, a nonlinear partial differential equation for the coupled problem of heat waves and thermoelastic waves with time delay was derived. Furthermore, temperature and thermal stress analysis was performed on the one-dimensional bar problem based on the finite-difference time-domain method. As results obtained in this study, thermal wave split into two peaks and propagated along the bar by considering the coupled thermoelasticity effect in the heat conduction equation. The elastic wave caused by the thermoelasticity effect also propagated. However, it was found that the peak stress in elastic wave was relaxed as the coupling effect being stronger.