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

Strąkowska Maria, De Mey Gilbert, Więcek Bogusław

Archives of Electrical Engineering

2026

Vol. 75, nr 1

57--78

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.

Response of stiffness and viscosity on the energy ratios at piezo-visco-thermo-elastic medium

Kumar Sandeep, Kumari Neelam, Gupta Vipin, Barak M. S.

International Journal of Applied Mechanics and Engineering

2024

Vol. 29, no. 1

54--72

This article presents a mathematical framework that characterizes a transversely isotropic piezo-visco-thermo-elastic medium within the context of the dual-phase lags heat transfer law (PVID) applied to an elastic medium (ES). Specifically, the study investigates the propagation of plane waves within the elastic medium and their interaction with the imperfect interface of the ES/PVID media. This interaction results in two waves reflecting back into the elastic medium and four waves propagating through the piezo-visco-thermo-elastic medium. The research explores the distribution of energy between the reflected and transmitted waves by analyzing amplitude ratios at the boundary interfaces, considering factors such as phase delays, viscosity effects, and wave frequency. The study illustrates the influence of boundary stiffness and viscosity parameters on these energy ratios through graphical representations. The study's findings are consistent with the principles of the energy balance law, and the research also delves into specific cases of interest. Overall, this investigation provides insights into wave behavior within complex media and offers potential applications across various fields.