Natural convection from a discrete heater in a square cavity filled with a porous medium.

*(English)*Zbl 1159.76382Summary: A numerical study of the natural convection in a square porous cavity with one of its vertical walls heated differentially is carried out in the present paper. It is assumed that an isoflux or isothermal discrete heater is mounted on one of the vertical walls and the other vertical wall is at constant temperature, while the horizontal walls are adiabatic. The finite-volume method is used to solve the non-dimensional governing equations. The effect of location of the discrete heater is investigated for values of Rayleigh number (\(Ra\)) in the range \(10 \leq Ra \leq 10^3\) and heater length \(0.1-0.5\) of the cavity height. It is shown that the location of the discrete heater has important influence on the flow and heat transfer characteristics. It is also found that the maximum average Nusselt number takes place when the heater is placed near the bottom of the vertical wall for high values of \(Ra\) and relatively higher location for relatively low values of \(Ra\) for both isoflux and isothermal discrete heaters. The average Nusselt number increases with increasing length of both isothermal and isoflux heaters for a constant \(Ra\).