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This paper deals with a numerical study of mixed convection flow and heat transfer inside lid-driven cavity. The main purpose in this present study is to maximize the heat transfer. For that, a new lid-driven cavity with two wavy walls and non-uniform heating on both sidewalls has been proposed. The two horizontal walls are considered isolated, while two variable sinusoidal temperature distributions are imposed to the left and right vertical side walls with different amplitudes and phases. A finite volume method is used to solve numerically the non-dimensional governing equations. The tests were carried out for Richardson numbers which vary from 0.01 to 100, amplitude ratios from 0 to 1, and phase deviations from 0 to , meanwhile the Prandtl number is fixed to Pr = 0.71. The distributions of streamlines, isotherms, and the variations of local and average Nusselt numbers with the variation of Richardson numbers, amplitude ratios and phase deviations are presented and compared with results given in the literature. The comparisons have showed a satisfactory agreement. Furthermore, the present study showed that the wavy walls with variable temperature have strong influence on enhancing heat transfer.

Laminar natural convection in differentially heated square cavity with right cold wavy wall and horizontal conducting fin attached to its left hot wall has been investigated numerically. The vertical walls are maintained at different isothermal temperatures, while the horizontal walls are insulated. The fluid that filled the cavity is air with Prandtl number of 0.71. The investigation has been performed for Rayleigh number in the range of 103–106, the thermal conductivity ratio was varied from 10 to 105, three fin lengths and positions have been examined (0.25, 0.5, and 0.75), and three numbers of undulation were tested (one, two, and three undulations). The wave amplitude and the fin thickness were kept constant at 0.05 and 0.04, respectively. The results obtained show that increasing the fin thermal conductivity or the Rayleigh number increases the average Nusselt number especially when the fin length increases. It was also found that the fin position enhances the heat transfer when the fin is placed opposite to the crest of the wavy wall. The trend of the local Nusselt number is wavy. The effect of undulations number appears when the fin length is greater than 0.5. The average Nusselt number enhanced when a conducting fin is added to the cavity with wavy wall and without fin by 51.23% and 56.85% for one and three undulations, respectively, when the Rayleigh number is 105 and the fin length is 0.75.

A mathematical study was conducted for the mixed convection inside a cavity for three aspect ratios filled with hybrid nanofluids by moving the vertical walls down, where the upper wall was thermally isolated, and the two vertical walls with a temperature that is less than the lowest wall’s, which was at a sinusoidal temperature. The investigation and discussion focused on the Richardson numbers (0.1–100), hybrid nanoparticle sizes (0.0–0.08), and the impact of size on the thermal and hydrodynamic properties of hybrid nanoparticles. At lower Richardson numbers, hybrid nanoparticle volume fraction impacts the thermal behaviour model. Besides, it was observed that decreasing the effect of average Nusselt number and nanoparticle size was due to the increase in Richardson numbers.The present results also showed the vital role that sinusoidal temperature has on heat transfer.

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.