INERTIA EFFECTS ON NATURAL CONVECTION IN A VERTICAL POROUS CAVITY

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Abstract
Inertia effects on buoyancy-driven flow and heat transfer in a vertical porous cavity are examined by using the Forchheimer-extended Darcy equation of motion for flow through porous media. A dimensional analysis indicates that in the inertial flow regime a new dimensionless parameter, the Forchheimer number Fs, which characterizes the porous matrix structure and its confinement, must be considered together with the Rayleigh and Prandtl numbers, Ra* and Pr*. Finite-difference numerical results obtained for a wide range of parameters indicate that the effect of Prandtl number and aspect ratio remains unchanged with an enhancement in the inertia effects, whereas the dependence on Grashof and Forchheimer numbers changes substantially. Indeed, for a Nusselt number correlation Nu = CGr*pPr*qFs−rA−s, q and s remain the same as those obtained for Darcy flow, but p and r change in such a way that p + r is always equal to the value of p in the Darcy regime. The criteria for the Darcy and inertial flow limits are also obtained, and it is shown that the boundary-layer flow structure does not exist when Fs/Pr* → ∞. Hence, the applicability of a boundary-layer solution in the inertial flow regime is highly restricted.