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In this study, we investigated buoyancy-induced convection in a permeable square hollow containing four embedded cylinders and subjected to a magnetic field using numerical methods. The finite element approach was used to solve the governing equations of the system as well as the initial and boundary conditions. We analyzed the effects of the emerging non-dimensional quantities on the flow pattern and thermal field, as well as entropy production, in relation to the thermophysical properties of the obstacles. In the limiting case, we compared our results with already published work and found outstanding concurrence. Our simulations revealed that increasing cylinder spacing leads to higher thermal entropy generation, while fluid friction irreversibility has the opposite effect. Additionally, the imposed magnetic field significantly suppressed temperature distribution and flow field, resulting in low thermal transmission within the cavity.
Charreh et al. (Mon,) studied this question.