Numerical analysis of time-fractional non-Fourier heat conduction in porous media based on Caputo fractional derivative under short heating pulses

Abstract

In this research, the heat transport in porous media (sand particles and interstitial gas) under short heating pulses is examined, taking into account the non-Fourier effects. The time-fractional heat conduction equation based on the Caputo definition is proposed to examine the thermal response of porous media in short-time scales. The results of the time-fractional model are compared to experimental data, which proves the accuracy of this model as well as its capability to describe the fast transient thermal process, the local thermal nonequilibrium condition, and the energy exchange between the solid and gaseous phases. Additionally, the influence of variation in the different parameters, including the order of fractionality and heating pulse widths are investigated, and it has been proved that the gas-solid interactions in the fast transient process play a vital role in heat transfer mechanism of porous media, especially in the near-field locations to the heater with short pulse width.