Natural Convection in a Square Cavity With Thin Porous Layers on Its Vertical Walls

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Abstract
Natural convection in a square cavity in which differentially heated vertical walls are covered with thin porous layers is studied by using a control volume formulation and a SIMPLER algorithm for pressure-velocity coupling. Comparisons with benchmark solutions for natural convection in fluid-filled cavities are first presented for Rayleigh numbers up to 108. The problem of the square cavity with thin porous layers on its vertical walls is then studied by using a modified form of the Navier-Stokes equations by addition of a Darcy term. It is shown that the main effect of the introduction of porous layers is to produce a large decrease of the overall Nusselt number when the permeability is reduced. The higher the Rayleigh number is, the stronger is the decrease, and obviously the decrease also increases with the layer thickness. Moreover, porous layers having a thickness of the order of the boundary layer thickness are sufficient, and taking thicker ones only induces a small decrease of the heat transfer. The main effect of porous layers is to reduce the upwind flow and then to decrease the convective heat transfer.

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