Influence of Radially Varying Magnetic Fields and Heat Sources/Sinks on MHD Free-Convection Flow Within a Vertical Concentric Annulus

In this study, an exact solution is developed to elucidate the effects of radially varying temperature-dependent heat sources/sinks (RVTDHS) and magnetic fields on natural convection flow between two vertically oriented concentric cylinders, where heating is administered through both isoflux (constant heat flux) and isothermal (constant wall temperature) conditions. The energy equation incorporates a temperature-dependent heat source/sink term, postulated to vary inversely with the radial coordinate. Through the application of suitable transformations, exact expressions for temperature distributions and fluid velocities as functions of the radial coordinate, the ratio of radii, the heat source/sink parameter, and the Hartmann number (representing magnetic field strength) are derived. Findings indicate that the presence of a radially varying heat source/sink notably influences temperature distribution, velocity profile, skin friction, and mass flux, with the heat source elevating fluid temperature. Consequently, this adjustment shortens the range over which isothermal heating supersedes isoflux heating. Conversely, in the presence of a heat sink, isothermal heating remains predominant over isoflux heating irrespective of the annular gap's size. These results not only provide deeper insights into the dynamics of magnetohydrodynamics (MHD) free-convection flows in engineering and geophysical applications but also enhance the understanding of how magnetic fields and heat sources/sinks can be strategically manipulated to control such flows.