Thermal and roto-hydrodynamics behaviors of Fe3O4-based ferrofluid under magnetohydrodynamic flow and Joule heating in a sliding fillet chamber

This research presents a novel numerical study that introduces Joule heating into magnetohydrodynamic flow to investigate the combined free-forced convective flow of Fe 3 O 4 -water ferrofluid in a corner-heated, lid-driven, square-shaped fillet chamber containing a rotating isothermal cylinder. Numerical solutions for the two-dimensional Navier-Stokes and thermal energy equations are obtained employing the Galerkin finite element weighted residual technique. The study varies key parameters, including Richardson (0.1 ≤ Ri ≤ 10), Grashof (10 3 ≤ Gr ≤ 10 6 ), Reynolds (31.62 ≤ Re ≤ 10 3 ), Stuart (0 ≤ N ≤ 3.16), and Hartmann (0 ≤ Ha ≤ 31.62) numbers, as well as the non-dimensional heater size (1/3 ≤ L s / L ≤ 2/3). This study aims to optimize thermal performance and minimize system irreversibility by evaluating heater performance and entropy generation while several governing and geometric parameters are varied. The novelty of this study lies in the integrated modeling of Joule heating, magnetohydrodynamic effects, and a rotating cylinder within a filleted square enclosure for free-forced convective flow of Fe 3 O 4 -water ferrofluid, accounting for the impact of Ri, Gr, Re, N , and Ha , as well as variable heater size. The results show the variations in the Nusselt number near the heated wall, the average ferrofluid temperature, the total entropy generation, and the system’s thermal performance criterion ( TPC ). They reveal that the shortest heater improves heat transmission by up to 25% and reduces TPC by approximately 53% relative to the longest heater, indicating optimal heater configuration. Furthermore, the total entropy generation decreases by a factor of 6.7 under pure mixed convection at a low Gr (= 2 × 10 3 ) with an optimal heater size.