Magnetohydrodynamic Natural Convection in a Circular Dome-Shaped Enclosure

Abstract

The design of flow structures plays a crucial role in enhancing natural convective heat transfer within enclosures. By optimizing the geometry of enclosures to influence flow structures, we can significantly improve their natural convective heat transfer performance. Specifically, the dome-shaped wall can alter flow direction, improving flow circulation and natural convection. The current study conducts a numerical investigation of the laminar flow and natural convective heat transfer of air within a dome-shaped enclosure, while also considering the impact of a magnetic field. The analysis encompasses the interaction between magnetic field and buoyancy-driven flow. Governing equations for momentum, energy, and angular momentum are formulated, integrating the influence of the Lorentz force. The working fluid Pr = 0.71 is considered in this study. The equations are transformed into dimensionless form using key parameters, such as the buoyancy number (Ra) and Hartmann number (Ha). The modeled partial differential equations were carried out with a vorticity-stream function algorithm to explore the influence of magnetic field strength on the flow and thermal characteristics. Results indicate significant alterations in flow patterns and temperature distribution behavior under varying magnetic field and Rayleigh number. The interaction between buoyancy and magnetic fields plays a critical role in determining the heat transfer characteristics of an incompressible fluid, with Ra enhancing, and Ha suppressing, convective efficiency. Heat transfer enhancement of 82.84% is noticed for a Rayleigh number ranging from 10³ to 10⁴, while a 48.316% decrement is found for a Hartmann number ranging from 0 to 10 with Ra = 10⁵. The transition from a magnetically dominated regime (high Ha) to a thermally driven regime (low Ha) leads to a shift from a uniform temperature field to one with more complex thermal layering and mixing, which is reflected in the varying shapes and amplitudes of the Nusselt number distributions. At higher Ha values, magnetic forces dominate, significantly suppressing buoyancy-driven convection, and reducing the intensity of thermal mixing.