ABSTRACT Buoyancy‐driven viscous fluid flow across a curved surface is investigated numerically in this work using the coupled Maxwell and Navier–Stokes equations, with variable fluid characteristics represented as nonlinear functions of temperature. Realistic magneto‐hydrodynamic effects are captured by including the Lorentz force and the influence of a fluctuating magnetic field in curvilinear coordinates. The governing partial differential equations are solved using the parametric continuation method (PCM) after being converted into a system of ordinary differential equations by similarity transformations. Results demonstrate excellent agreement when compared to previously published data using MATLAB's PCM solver to confirm correctness. According to the parametric study, buoyancy () improves fluid motion by around 15%, whereas greater curvature factors , Stuart numbers , and Prandtl numbers result in a 12%–16% drop in radial and arc‐length velocities. The temperature profile falls by more than 23% as and increase, indicating the significance of thermal diffusivity in preventing heat buildup. It increases by 25% with higher magnetic interaction (, ). The induced magnetic field is strengthened by 6%–7% with a little increase in the magnetic interaction parameter , whereas the magnetic field intensity is reduced by about 25% with a larger . Skin friction falls by almost 10% with greater at moderate , but increases by 4% under larger Lorentz forces (, ). Overall, the results show that velocity, temperature, magnetic field distribution and surface forces are strongly influenced by buoyancy, curvature and electromagnetic parameters. The findings shed light on efficient energy optimisation, thermal control, and electromagnetic regulation of MHD flows over curved geometries.
Khan et al. (2026) studied this question.