Natural convection and multidirectional magnetic field inside a square shaped cavity with sinusoidal temperature and heated/cold blocks

This study explores several pivotal facets of physical phenomena that emerge in mechanics and model formulation, driven by the intricate realm of partial differential equations. Our focus converges on a specific problem encompassing an incompressible electrically conductive fluid confined within a square -shaped enclosure. This enclosure consists of two insulated horizontal walls, while the right vertical wall maintains a constant temperature. Notably, the left wall is governed by a variable sinusoidal temperature profile, introducing complexity to the scenario. Our study embarks on a comprehensive examination of natural convection, further compounded by the presence of multidirectional magnetic fields within this square cavity. A distinctive feature of this study is the introduction of obstacles strategically placed to influence the temperature distribution. The right -side obstacles are deliberately heated, serving as sources of elevated temperature, whereas the left -side obstacles adopt a contrasting role by promoting lower temperatures. The results of this study promise to enhance our understanding of natural convection phenomena in electrically conductive fluids subjected to multidirectional magnetic fields and gave the way for further advancements in fluid mechanics. It is demonstrated that except for the Hartmann number, higher values of all parameters provide enhanced heat transfer in the enclosure.