This research aims to carry out the fast-transient process of heat flow in a porous medium, proposing the Caputo-type fractional Cattaneo subdiffusion model to study the anomalous diffusion process in the temperature response of the two-phase system. It has been shown that during the short thermal disturbance of porous medium, the solid-fluid interactions in microscale, energy swap through the solid-glass spheres and air, the local non-equilibrium state, and also the fast transient process can be simulated by use of fractional calculus approach. The classical Fourier model fails to interpret such effects, because it is assumed that the thermal wave propagates with infinite speed, and also the thermal interactions between phases occur simultaneously. The energy equation has been developed upon the Caputo fractional derivative, then numerically solved and it has been observed that its results are comparable to the measured data, which reveals the accuracy of the time-fractional model proposed. The numerical results exactly follow the experimental data, which illustrates the applicability of fractional Cattaneo subdiffusion model for examining the transient process in a porous medium at the short temporal scales, and also its capability to interpret the solid-fluid interactions in microscale.

这项研究旨在在多孔介质中进行热流的快速瞬变过程，提出一种Caputo型分数阶Cattaneo亚扩散模型，以研究两相系统温度响应中的异常扩散过程。结果表明，在多孔介质短时热扰动过程中，可以模拟微尺度的固液相互作用，固体玻璃球和空气的能量交换，局部非平衡态以及快速瞬态过程。使用分数演算方法。经典的傅立叶模型无法解释这种影响，因为假设热波以无限的速度传播，而且相之间的热相互作用同时发生。能量方程是根据Caputo分数导数开发的，然后进行数值求解，并且观察到其结果与实测数据相当，这表明了所提出的时间分数模型的准确性。数值结果正好跟随实验数据，这说明了分数Cattaneo扩散模型适用于在短时间尺度上检查多孔介质中的瞬态过程，以及其在微观尺度上解释固液相互作用的能力。