Non-Fourier Dual-Phase-Lag thermal models using thermoelectric analogy

Abstract

This research presents the modelling of non-Fourier heat conduction using the Single and Dual-Phase-Lag (SPL/DPL) in the frequency domain. Thermal structures can be modelled using Foster, Cauer networks or their compact equivalents, using the analogy with electrical networks. The key aim of such modelling is to simplify the heat transfer processes of geometrically complex thermal structures composed of layers with different materials. In this paper, we propose the analytical solution of the heat transfer equation for a single-layer thermal object in the frequency domain. It is achieved by the transformation of Kirchhoff–Fourier equations into the multi-cell Cauer network that can be easily solved using the node potentials method. In the case of non-Fourier SPL and DPL models, the thermal conductivity is no longer a real value, but it varies with frequency. As a result, the spatially distributed thermal model can be presented as an electrical network consisting of thermal resistances, capacitances and inductances. It makes it possible to take into account diffusive, wave propagation and mixed conductive heat transfer. Such modelling allows confirming the non-Fourier heat transfer in porous-like materials and biostructures with a better understanding of the physical nature of heat transfer, which is still discussed in the scientific literature.