Fourier and time-phase-lag heat conduction analysis of the functionally graded porosity media.

We performed numerical heat conduction analysis for the new proposed functionally graded porosity (FGP) media. Fourier, Cattaneo-Vernotte (C V), dual-phase lag (DPL) and time-fractional heat conduction responses for a porous solid-gas media are compared with the different flux pulse duration experimental results. Four configurations of the FGP domain in which the porosity gradations are controlled by the power-law volume fractions, are introduced. Accordingly, the porosity-dependent effective thermal properties of the domain are estimated and the temperature responses are discussed for different heat conduction models. Even a slight change in the porosity, leads to a different temperature-time history and its gradation affects the temperature distributions through the medium; therefore, by tuning the porosity gradations the desired temperature distributions can be achievable. Finally, the diffusion-like DPL and the classical Fourier models in descending configuration predict about 35% and 41% higher peak temperatures than the constant porosity ones, respectively. Furthermore, these models demonstrate the same temperature distributions in constant porosity; that is, in the case of graded porosity the maximum difference is less than 4% due to not taking into account the time laggings as the function of porosity gradations. • The transient and steady-like DPL model proves the highest accuracy in comparison with experimental data. • Four functionally graded porosity configurations have been proposed. • Fourier, C V, DPL temperature responses have been compared for the FGP media. • The diffusion-like DPL and Fourier models are identical for the constant porosity. [ABSTRACT FROM AUTHOR]