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Fluid flow in the lid driven cavity is a well-known phenomenon in the realm of fluid flow and heat transfer. Different cavity shapes such as square, circular, trapezoidal, and hexagonal have already been studied. However, most of the parametric analyses have previously been done using one specific cavity shape design. The present study intends to generalize the cavity design for a larger range of applications starting from the selection of cavity form due to the enhancement of heat transfer inside that selected cavity for different boundary conditions. Numerical studies using a finite element solver have been carried out to investigate the physics of fluid flow and heat transmission in a cavity where a wall of the enclosure is moving. In this research, the average Nusselt number for six distinct shaped lid-driven cavities is studied (e.g., square, rhombus, circular, rounded rectangular, trapezoidal and hexagonal). The hexagonal-shaped cavity has the largest Nusselt number of all of them. The heat transfer increases by about 90% when the cavity shape changes from square to hexagonal at Ri = 0.1, Pr = 7, Re = 100, Ha = 30, and ? = 60°. To boost the heat transfer rate, magnetohydrodynamics (MHD) mixed convection in a lid-driven cavity with an imposed angled magnetic field was investigated. Richardson number, Reynolds number, Prandtl number, Hartmann number, and magnetic inclination angle within the enclosure are shown in terms of streamline plots, isothermal contour profiles, and Nusselt number. Through parametric investigations of cavity shapes, inclined magnetic fields, and other boundary conditions, the current research intends to improve the Nusselt number within the cavities.

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