Thermal Wave Reflection and Transmission in a Multilayer Slab with Imperfect Contact Using the Dual-Phase-Lag Model

Abstract

Heat transfer in layered thin films is of crucial importance for the proper design and operation of micro-devices. Layered thin films are used in many engineering systems such as micro-electronic devices, thin film superconductors, fins, reactor walls, and metal oxide semiconductors. In this study, thermal wave transmission and reflection phenomena induced by a pulsed boundary heat flux in a two-layer slab with imperfect interface are studied numerically using the dual-phase-lag heat conduction model. The results presented illustrate the strong dependence of the thermal wave behavior on both the thermal contact resistance, and the phase lag ratios of the two layers. When the thermal pulse propagates from a lower phase lag ratio layer to a higher phase lag ratio layer, the interface reflects a negative followed by a positive wave if the contact resistance is below a certain value, and it reflects a positive wave only if this value is exceeded. For a given thermal contact resistance, the interface reflects a negative followed by a positive wave if the phase lag ratio of layer 1 to that of layer 2 is below a certain value, and it reflects only a positive wave if this value is exceeded. On the other hand, when the pulsed boundary heat flux propagates from a layer with higher phase lag ratio to a layer with a lower phase lag ratio the imperfect interface always reflects a positive wave, and the strength of the reflected wave increases with increasing the contact resistance. The interface always transmits a positive wave with increasing strength as the contact resistance decreases. In the limit when the thermal contact resistance approaches infinity, the interface behaves as a perfect insulator with no energy transport through it.