Convective heat transfer in a channel partially filled with a porous medium

In this work we solve effective-medium equations for modeling momentum and heat transfer in a parallel-plate channel partially filled with a porous insert. In order to avoid specifying the boundary conditions at the fluid–porous boundary, we solve equations involving position-dependent coefficients (i.e., a one-domain approach). The solution of the momentum-transport problem is carried out using implicit integral equation formulations based on Green’s functions, whereas the heat transfer problem was solved numerically using the finite element method. The simulations were performed in terms of several values of the porosity, the Péclet number, the size of porous insert and the thermal conductivities ratio. In agreement with previous works, it was found that the thermal performance is improved by either increasing the size of the porous insert or by favoring mixing inside the channel. A drawback of this approach is the high computational demand associated to modeling transport in the vicinity of the porous medium and the fluid. In this way, the extents and limitations about the use of a one-domain formulation are exposed in a practical application. The results from this work should serve as motivation for more experimental and theoretical research; in particular, the derivation and application of jump boundary conditions.