A Numerical Investigation of the Free Flow in a Square Porous Cavity with Non-Uniform Heating on the Lower Wall

Natural convection in a steady state of incompressible air inside a cavity’s porous with a heated low wall of a sinusoidal profile is investigated numerically in this paper. The upper horizontal wall is kept cold while the two sides are thermally insulated. The proposed physical model was developed and studied with two-dimensional conditions, using the finite element method and adapting the Darcy-Brinkman model. This paper examines the laminar natural convection in a square porous cavity for different Rayleigh numbers (10 ≤ Ra ≤ 104), aspect ratios (0.25 ≤ AR ≤ 1.0), and sinusoidal temperature amplitude (0.25 ≤ λ ≤ 1.0). Moreover, the variation effect of Ra, AR, and λ on isotherms, streamlines, and the mean and local Nusselt numbers has been presented and analyzed. The results showed that an increase in the sinusoidal thermal amplitude, mean Nusselt number, and AR reduced somewhat the Rayleigh number. This provided a solution in which the mean Nusselt number increased by increasing the sinusoidal thermal amplitude and the Rayleigh number. On the other hand, it decreases slightly by increasing the AR. In addition, the convection transfer mechanism is the main mode when the Rayleigh number is high. Thus, it was found that the Darcy number also has an effect on heat transmission. The obtained results were compared with those found in the literature and were found to be in good accordance.