Magneto-Thermo-Hydraulic Analysis of Ostwald-de Waele Ferrofluid Flow in a Partially Corrugated Domain with a Heated Obstacle

The current research presents a comprehensive mathematical approach to investigate the magnetohydrodynamic free convective circulation of an Ostwald-de Waele ferrofluid, with a focus on the thermo-hydraulic characteristics and the effectiveness of magnetically controlled heat exchange. It specifically identifies the impact of wall corrugation, obstacle geometry, and magnetic field strength to address the design challenges in compact thermal management and energy conversion systems. It involves a non-Newtonian Fe3O4-water ferrofluid with a ferro particle volume fraction of 2% within a partly corrugated square compartment featuring a heated obstacle. The Galerkin finite element weighted residual method is applied to obtain numerical findings for the power-law ferrofluid-related Navier-Stokes model and the corresponding energy equation. An in-depth analysis of the mean fluid temperature and Nusselt number is performed to optimize heat transfer by adjusting various geometrical parameters. Qualitative findings from streamlines and isotherms further support these results. One circular and two types of elliptical obstacles are examined by maintaining the equivalent volume of all solid obstacles to ascertain the impact of the internal obstacle’s geometry. Additionally, the amplitude and frequency of the corrugated top wall are varied to conduct numerical simulations and evaluate the effectiveness of heat transfer. Parametric simulations are performed across different nondimensional constraints, including the Rayleigh number ranging from 103 ≤ Ra ≤ 105, the Hartmann number within 0 ≤ Ha ≤ 10, and the power-law index within 0.6 ≤ n ≤ 1.4. The outcomes show that maximum heat transport in terms of the maximum Nusselt number (Nu ≈ 16), is achieved when the obstacle is circular, along with the lowest corrugation amplitude (A = 0.04) and frequency (f = 4.5). Moreover, convection heat transfer is maximized in shear-thinning ferrofluids (n < 1) with no magnetic impact (Ha = 0). The result indicates that the magnetic effect (Ha = 10) reduces Nu by about 7%, while non-Newtonian shear-thinning behavior (n = 0.6) boosts Nu by nearly 66% relative to shear-thickening (n = 1.4). Moreover, the circular obstacle configuration improves heat transfer efficiency by almost 11% compared with the elliptical case. Finally, the lowest corrugation amplitude (A = 0.04) reveals about 1.3% improvement of thermal transport compared to the highly corrugated profile (A = 0.06), whereas the wavy-walled corrugation frequency has a negligible impact (0.07%). The design guidelines for magnetically tunable ferrofluid enclosures are established by these quantitative results, which show novel ways to combine wall topology, non-Newtonian behavior, and magnetic control to improve overall thermal effectiveness. This work combines corrugated geometry, obstacle shape variation, and magnetic impacts in a novel manner, with applications in electric cooling, heat exchangers, microfluidic devices, and energy systems. In contrast to earlier studies, which primarily considered smooth-walled or purely Newtonian fluids, this approach offers a distinct perspective.