Numerical study of Hall currents induced by radial magnetic fields on free convective flow through asymmetrically heated/cooled vertical annuli

The Hall effect, discovered over a century ago, continues to be significant and increasingly relevant across various sectors. Its applications range from technological advancements to medical technology, where Hall current phenomena are essential for optimizing performance and driving innovation. The ongoing integration of Hall effects into contemporary systems highlights its enduring value in both research and industry. In continuation of this enduring relevance, we studied the influence of Hall currents in vertical concentric cylinders subjected to a radial magnetic field, with the outer cylinder asymmetrically heated or cooled. The governing system of partial differential equations was solved using the Crank–Nicolson method to analyze fluid temperature, velocity, and skin friction under the influence of various dimensionless parameters, with results presented through both graphical and tabular perspectives. The outputs are verified with different numerical methods and validated against existing literature to ensure the accuracy and reliability of the results. The study reveals that the Hall current induced by the radial magnetic field is approximately 15% stronger than that generated by a conventional magnetic field at $r=1.5$. However, the radial magnetic field has a lesser impact in reducing fluid flow compared to the conventional magnetic field, due to its directional dependence on the radial axis. Furthermore, when the buoyancy force parameter is in the range $0\le R<1$, the maximum velocity is concentrated near the inner cylinder and decreases towards the outer cylinder, whereas at $R=1$, the maximum velocity shifts towards the central region and takes a parabolic shape.