Application of Lumped-System Analysis to Layered Porous Cavities Heated from Below

摘要

Natural convection in layered porous cavities heated from below has been numerically examined in this study as an extension to several earlier studies. In addition, the present study has further examined the feasibility of using a lumped-system approach in the prediction of heat transfer results in layered porous cavities. For the present study, the discrepancy found between the actual results and those predicted by the lumped system in some cases is larger than those reported in the previous studies. This may be attributed to the nature of the problem presently considered, which is inherently more unstable than other heating conditions, and the flow and temperature fields of which are more susceptible to change with the Rayleigh number. However, it is observed that the Rayleigh numbers at which the discrepancy is a maximum fall outside the range of practical interest (Ra > 100). From this aspect, one can say with confidence that the lumped-system analysis is appropriate for most engineering applications involving layered porous media. In particular, the present study has further validated the basic principle in the determination of the effective permeability to be used in the lumped-system analysis. That is, for sublayers whose orientation is perpendicular to the primary heat flow, the effective permeability should be based on the harmonic average. On the other hand, for sublayers whose orientation is parallel to the primary heat flow, the effective permeability should be based on the arithmetic mean.