Determination of Time-Delay Parameters in the Dual-Phase Lagging Heat Conduction Model

Abstract

The study of thermal transport based on the dual-phase lagging model involves not only the well known thermal properties but also two additional time parameters. Those parameters permit to take into account the thermal inertia and the microstructural interactions of the media in such a way that they establish the nonsimultaneity between temperature changes and heat flux. In the dual-phase lagging model, heat transport phenomena are extremely sensitive not only to the size of each time parameter but also to the relative size of them. In order to obtain useful and reliable results, it is important to develop methodologies for the determination of those time parameters. Additionally it is necessary to count with tools that allow evaluating easily the sensitivity of the temperature and heat to the changes in those time parameters. In this work, a system formed by a semi-infinite layer in thermal contact with a finite one, which is excited by a modulated heat flux, is studied. When the thermal effusivities of the layers are quite different, it is shown that a frequency range can be found in which the normalized amplitude and phase of the spatial component of the oscillatory surface temperature show strong oscillations. This behavior is used to obtain explicit formulas for determining simultaneously the time parameters as well as additional thermal properties of the finite layer, under the framework of the dual-phase lagging model of heat conduction. The limits of the corresponding equations for single-phase lagging models of heat conduction are also discussed.