Coupling a two-temperature model and a one-temperature model at a fluid-porous interface

We study a convective heat transfer problem in a fluid-porous domain in the case of the local thermal non-equilibrium assumption (LTNE). The issue of this study is to determine appropriate boundary conditions to model heat transfer, while using models with a different number of equations: a two-temperature model in the homogeneous porous region versus a one-temperature model in the free region. To proceed, a two-step up-scaling approach is used, which has the particularity to provide closed jump relations depending on intrinsic characteristic of the interface. Thus, the use of jump or continuity conditions depend only on the interface location inside the fluid-porous transition region. The pertinence of the approach is illustrated on a 2D convective heat transfer problem considering a solid heat source in the porous medium.