Effect of Hall current generated by a radial magnetic field on transient natural convection between vertical annuli

The Hall effect phenomena has a long standing history, yet its relevance and application continue to grow across numerous industries. Spanning from technological advancements to innovations in medical equipment, the influence of Hall current effects remains critical for enhancing efficiency and driving innovation. Despite its origins over a century ago, the phenomena remains highly relevant and is constantly being integrated into modern systems, reflecting its enduring significance and versatility across both scientific and industrial domains. Building on these historical context, the present study examines the effects of Hall current on transient natural convective flow within cylindrical annuli subjected to a radial magnetic field. The system of partial differential equations derived from the mathematical model is first transformed into a nondimensional form by applying the relevant nondimensional parameters. Subsequently, these nondimensional PDEs are addressed using the implicit Crank–Nicolson finite difference method. Furthermore, the results section offers detailed graphical representations of both primary and secondary velocity profiles, as well as quantities data on temperature and velocities, along with the Nusselt number and skin friction at the cylinder boundaries. These results are systematically presented across a range of flow parameters, providing in-depth analysis of the system’s response to varying conditions. The key outcomes of this study indicate that both the Hall parameter and the radii ratio play a significant role in augmenting the primary and secondary velocities, as well as increasing skin friction values. On the other hand, the Prandtl number and Hartmann number exhibit opposing influences on the primary velocity, each influencing it in a contrasting manner.