Heat Transfer in Porous Media: Second-Order Closure and Nonlinear Source Terms

Abstract

Heat transfer in multiscale materials is ubiquitous in natural and engineered systems. These materials are often modeled at a macroscopic scale, where microscopic details are filtered out to reduce numerical and physical complexity. Here, we use the method of volume averaging to upscale heat transfer equations for a saturated porous medium with non-linear bulk and surface sources. This approach leads to the development of a variety of macroscopic models, including a two-temperature model with a second order closure that extends previous results from Quintard and Whitaker [2000]. Effective properties are calculated for model unit-cells (1D, 2D and 3D) and also for a realistic pore-scale geometry obtained using X-ray tomography. The model further features a distribution coefficient that indicates the distribution of the surface heat between the two phases at the macroscale. By comparing computational results for the two-temperature model against direct numerical simulations, we show that this effective distribution coefficient captures well the partitioning of heat, even in the transient regime.