Summary
Natural convection in a vertical slot filled with a fluid-saturated porous medium modeled by the Brinkman equation is considered. A continuum of solutions are found from capped to open ends in fully-developed two-dimensional flow. This brings to flow in a porous media some aspects of the Newtonian conduction regime results of Bühler (Heat Mass Transf 39: 631, 2003) and the convection regime results of Weidman (Heat Mass Transf 43: 103, 2006). The Brinkman model, valid for sufficiently large porosity and governed by parameter α, allows one to connect Bühler’s conduction regime flow at low α to a near-Darcy convection regime boundary-layer flow at high α.
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References
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Weidman, P.D., Medina, A. Porous media convection between vertical walls: continuum of solutions from capped to open ends. Acta Mech 199, 209–216 (2008). https://doi.org/10.1007/s00707-007-0533-x
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DOI: https://doi.org/10.1007/s00707-007-0533-x