One-Domain Approach for Heat Transfer At The Fluid-Porous Medium Inter-Region

Abstract: The modeling of transport phenomena in the zone of rapid changes between a fluid and a porous medium (i.e., the inter-region) can be carried out using two distinctive approaches. The first one, generally called the one-domain approach, describes transport phenomena in the whole fluid-porous system using averaged macroscopic conservation equations including spatially dependent effective properties. These coefficients reduce to their respective constant values in the homogeneous fluid and porous regions of the system. As an alternative, the two-domain approach uses the transport equations with constant coefficients in the entire domain of each region, including the zone of drastic changes. To overcome this approximation, jump conditions are introduced but their derivation requires the knowledge of the corresponding one-domain approach model. This work deals with the derivation of the governing macroscale equations for convective heat transfer in the inter-region using a volume averaging procedure. Under a one-domain formulation, local thermal equilibrium (TE) and non-local thermal equilibrium (NTE) models are explored. In both cases, the associated closure problems are derived and solved numerically. This allows the computation of the spatial variations of the associated effective transfer properties in the inter-region. Comparisons of the temperature fields obtained with direct numerical simulations evidence that the TE model is good enough for describing the abrupt heat transfer variations in the inter