Effective Heat Transfer Between a Porous Medium and a Fluid Layer: Homogenization and Simulation

We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a), where the solid part of the porous media is assumed to consist of disconnected inclusions and Case (b), where the solid matrix is assumed to be connected. For both scenarios, we consider a heat equation with convection where a small scale parameter epsilon characterizes the heterogeneity of the porous medium and conduct a limit process via two-scale convergence for the solutions of the epsilon-problems. In Case (a), we arrive at a one-temperature problem exhibiting a memory term and, in Case (b), at a two-phase mixture model. We compare and discuss these two limit models with several simulation studies both with and without convection.