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Abstract

The problem of heat and fluid flow through a vertical thin porous medium located in an open square cavity is considered. This problem is analyzed using two approaches: the Pore Scale Method (PSM) and the Volume Average Method (VAM), for different Reynolds and Richardson numbers. The dimensional and dimensionless governing equations for both methods are presented. The velocity and temperature distributions obtained from the two approaches are compared to determine the range of Darcy numbers (i.e., the number of pores in the vertical direction) for which the results of the volume average approach can be validated. The obtained results indicated a good agreement between the velocity and temperature distributions of the two methods when the number of pores in vertical direction is approximately 20. However, decreasing the number of pores from 20 to 5 increases the discrepancy between the pore scale and volume average methods. Furthermore, for a cavity with a high Richardson number, where natural convection is dominant, a difference between the results of the two approaches is observed even for porous layer with 20 pores in vertical direction. This discrepancy is attributed to the influence of the transverse velocity component within the porous layer, which was neglected in this study.