Natural convection in rectangular enclosures partially filled with a porous medium

Analysis is undertaken of steady-state natural convection heat transfer in rectangular enclosures, that are vertically divided into a region filled with a fluid and another filled with a fluid-saturated porous medium. The two are separated by an impermeable wall and the vertical and horizontal boundaries are considered to be isothermal and adiabatic, respectively. The objective is to establish the heat transfer characteristics for enclosures containing different amounts of porous material. The flow in the porous region is modelled by a modified Darcy's law where Brinkman's extension is incorporated to allow the no-slip condition to be satisfied. A finite-difference scheme was used to numerically solve the field equations in the two regions. It was found that there were situations where heat transfer could be minimized by partially filling instead of entirely filling an enclosure with a porous medium. Results obtained in this study are directly applicable to design of insulation systems, suggesting that a better optimized insulation usage is possible.