Optimization of the heating of a cubic swimming Pool by a spherical heating block under a set of control parameters

The current simulations are for the three-dimensional Fe3O4-water nanofluid flow within a cooled cubical enclosure induced by an isothermally heated solid sphere. It was assumed that the sphere's orientation (horizontal, diagonal, vertical) and placement at ten distinct positions (P1 to P10, with their coordinates highlighted within the manuscript) are systematically analysed to understand their impact on heat transfer and entropy generation. This research is motivated by the need to optimize thermal management systems, which are crucial for applications in electronics cooling, energy storage, and magnetic fluid-based heat exchangers. The vertical walls of the enclosure are subjected to a uniform magnetic field. Simulations have been carried out for Rayleigh number equates 105, Ha = 15 and a volume fraction of ferrofluid 1 %. The conservation equations are solved using an in-house FORTRAN code based on the finite volume method coupled with multigrid acceleration. Results revealed that heat transfer is the primary source of entropy production, while the contributions from fluid friction and magnetic effects are minimal. On the other hand, the optimal positioning of the sphere balances the trade-off between maximizing heat transfer and minimizing entropy generation for heating the cubic swimming pool. This optimal position is identified as P5, corresponding to the sphere's first displacement along the diagonal direction which may be attributed to greater stability in this region, where the flow exhibits more order. Furthermore, heat transfer rates are enhanced by 52.2 % along the top wall of the enclosure and 34.58 % along the inner sphere in comparison with the reference case P1 (0.5, 0.5, 0.5). These results highlight the significant influence of the sphere's orientation and distance from the enclosure center on thermal performance. This study provides insights into improving the design of thermal systems, where magnetic nanofluids are employed for efficient heat dissipation, making it relevant for applications in advanced cooling technologies and compact thermal management systems.