Characterizing Natural Convection, Energy, and Thermal Behavior in a Circular Cavity: Finite Element Analysis

Abstract

This study improves understanding of the interaction between magnetic fields and natural convection in complex geometries, addressing a significant challenge in engineering design. By analyzing the effects of multidirectional magnetic fields on fluid flow and heat transfer, this study provides valuable insights into optimizing thermal management in practical applications, such as exhaust manifolds. This work is motivated by the need to enhance thermal efficiency and control in systems with irregular geometries, which are prevalent in advanced technological applications. Employing magnetohydrodynamic (MHD) principles, the flow and heat exchange dynamics are analyzed under real-world conditions, considering a cavity of length $L$ with heated bottom walls and heated/cooled inner obstacles. The circular cavity contains heated rods with different radii. An inclined magnetic field, perpendicular to the fluid flow, is applied, while a no-slip condition is enforced at the walls. Finite Element Method simulations are conducted over a wide range of Rayleigh ($Ra$) and Hartmann ($Ha$) numbers with a fixed Prandtl number ($Pr=6.2$). The streamlines, isotherms, and two-dimensional (2D) plots are produced to show the effects of governing parameters. The present results are compared with the existing data and graphical results. The numerical results reveal that heat transfer is influenced not only by Rayleigh's number and magnetic field strength but also by the magnetic field's inclination.