Relative analysis between step and sinusoidal temperature distribution during natural convection inside a square porous enclosure actuated from below

The main objective of this study is to predict the energy transfer characteristics in an air-saturated porous square enclosure. The energy transfer is driven by buoyancy force resulting from sinusoidal or step heating source at the bottom. The study is particularly relevant to industries such as food and material processing, as well as thermal insulation systems, where accurate predictions of performance are important. The study includes an analysis of vortex patterns, Nusselt numbers, entropy generation, and isotherm patterns, and investigates the effects of relevant input parameters such as Ra and Da. The governing equations are solved using Ansys Fluent, with the SIMPLE algorithm used to link the velocity and pressure terms in the governing relations. A notable observation from the study is that total \({S}_{\uptheta }\) $S_{\mathrm{\theta }}$ increases 2.48 times and total \({S}_{\mathrm{\varphi }}\) $S_{\phi }$ increases 1.3 times for step heating compared to sinusoidal heating at Ra = 10⁶ and Da = 10^–2. The thermal behaviors and irreversibility of the system are found to vary significantly with Ra, Da, and the heating strategy used.