Lumped-system analysis of a cavity with triangular porous layers

This paper numerically investigates the feasibility of using a simple lumped system approach in the heat transfer analysis of a square layered porous cavity. Instead of a detailed analysis of energy transport in the entire cavity, this approach is usually employed to expedite the heat transfer prediction for applications involving layered porous media. The cavity considered in this work is heated by the left vertical wall and cooled by the right vertical wall. The cavity consists of two triangular porous layers. These two configurations considered are: (a) the configuration A whose layer interface is 45° tilted to the right of the hot left surface, and (b) the configuration B whose layer interface is 45° tilted to the left of the cold right surface. Numerical calculations have been performed to cover a wide range of parameters (i.e., 10 < Ra1 < 104 and 10−2 ⩽ K1/K2 ⩽ 102). A correlation between the heat transfer results and the effective Rayleigh number has been successfully developed. The aforementioned effective Rayleigh number depends on the effective permeability, which can be accurately characterized based on the flow resistance concept analogous to the electric current. Current results show that the lumped system approach can provide a very good prediction in heat transfer if the permeability is correctly characterized even if the layers are no longer vertical or horizontal. Also found is that the effective permeability of a layered porous cavity is independent of the orientation of the layer interface.