Effect of Discrete Heating on Natural Convection in a Rectangular Porous Enclosure

The main objective of this article is to study the effect of discrete heating on free convection heat transfer in a rectangular porous enclosure containing a heat-generating substance. The left wall of the enclosure has two discrete heat sources and the right wall is isothermally cooled at a lower temperature. The top and bottom walls, and the unheated portions of the left wall are adiabatic. The vorticity-stream function formulation of the governing equations is numerically solved using an implicit finite difference method. The effects of aspect ratio, Darcy number, heat source length, and modified Rayleigh number on the flow and heat transfer are analyzed. The numerical results reveal that the rate of heat transfer increases as the modified Rayleigh number and the Darcy number increases, but decreases on increasing the aspect ratio. The average heat transfer rate is found to be higher at the bottom heater than at the top heater in almost all considered parameter cases except for ε = 0.5. Also, the maximum temperature takes place generally at the top heater except for the case ε = 0.5, where the maximum temperature is found at the bottom heater. Further, the numerical results reveal that the maximum temperature decreases with the modified Rayleigh number and increases with the aspect ratio.