Natural convective heat transfer from a cylinder in an enclosure partly filled with a porous medium

Heat transfer from a cylinder placed on the vertical centre-line of a square enclosure partly filled with a porous medium that is saturated with a fluid has been numerically studied. The cylinder is buried in the porous medium. The horizontal upper surface of the porous medium is separated from the rest of the enclosure by a horizontal impermeable barrier that is assumed to offer negligible resistance to heat transfer. The gap between the barrier and the top of the enclosure is filled with the same fluid as that with which the porous medium is saturated. The surface of the cylinder is at a uniform high temperature. The bottom and sides of the enclosure are assumed to be adiabatic while the horizontal upper surface of the enclosure is assumed to be kept at a uniform low temperature. The natural convective flows that occur in the porous medium and in the fluid layer above the barrier have been assumed to be steady, laminar, two-dimensional and symmetrical about the vertical centre-line of the enclosure. Fluid properties have been assumed constant except for the density change with temperature which gives rise to the buoyancy forces. The governing equations have been expressed in dimensionless form and solved using a finite element procedure. Results have been obtained for a Prandtl number of 0.7 for a wide range of the governing parameters. The main aim of the study was to determine how the mean heat transfer rate from the cylinder is affected by the size of the fluid gap at the top of the enclosure. The effect of this gap size has been related to changes in the flow pattern in the porous and fluid regions.