Characterizing Natural Convection and Thermal Behavior in a Square Cavity with Curvilinear Corners and Central Circular Obstacles

Thermal analysis through natural convection and heated obstacles in a different shape of cavity become an emerging concept among the scientific community. In this framewaork, this study investigates the natural convection phenomena occurring within a square cavity featuring a non-standard curvilinear shape and internally placed circular obstacles. The analysis focuses on the heat and fluid flow behavior in this unique geometrical configuration, exploring the influence of the curvilinear boundaries and obstacles on convective heat transfer. The flow is assumed steady, laminar and incompressible whereas a magnetic field with a strength B0 is applied perpendicular to the fluid flow. No slip conditions are applied on each surface. The curvilinear corners and the inner circular obstacle are kept hot and the others including bottom, left, right and top walls are considered at cold temperature. Numerical simulations are conducted to elucidate the complex interactions between the thermal gradients and fluid motion induced by the presence of circular obstacles. Galerkin finite element method is applied. The code validation and comparison with the existing data are being made. It is demonstrated that the local Nusselt number depends upon Rayleigh numbers, obstruction size, and Hartmann numbers. As the osbtcales radius increases from 0.1 to 0.3, the temperature distribution in the middle of the cavity increases by almost 400%. This definitely aids engineering in the manipulation of the heat transfer equipment used in this investigation. Around four corners, the local minimum Nusselt number rises by almost 97% as the radius increases from 0.1 to 0.3. These findings offer insightful knowledge about the fluid's dynamic behavior and a nice understanding of the roles played by geometric features, buoyancy-driven convection, and magnetic effects in the overall dynamics of heat transfer in industrial thermal processes. This knowledge aids scientists in designing suitable heat exchangers based on actual conditions.