Thermal-hydraulic, irreversibility, and power spectrum analysis in MHD conjugate cooling around a heat-generating oscillating circular rod

This research computationally explores the pure magnetohydrodynamic (MHD) mixed convective flow of a Fe 3 O 4 -water ferrofluid in a square-shaped enclosure holding a centrally positioned, heat-generating, transversely oscillating circular rod. The chamber has cold side walls under the action of a horizontal magnetic field, and the instantaneous and time-averaged characteristics of the anticipated system are compared across various operating conditions. The transient, conjugate thermofluidic problem is solved using a weighted-residual Galerkin finite element formulation of the two-dimensional Navier-Stokes and heat energy equations, with mesh movement handled via an arbitrary Lagrangian-Eulerian (ALE) approach. Parametric studies consider various ranges of controlling variables, including Hartmann (5.62 ≤ Ha ≤ 31.62), Reynolds (31.62 ≤ Re ≤ 10 3 ), and Grashof (10 3 ≤ Gr ≤ 10 6 ) numbers. The system is assessed using instantaneous and time-averaged Nusselt numbers, ferrofluid and solid temperatures, total entropy generation, ecological coefficient of performance, mean drag coefficient, and a performance evaluation criterion. The performance parameters exhibit periodic behavior due to the heat-generating transversely oscillating circular rod. The transverse oscillatory motion significantly enhances heat transfer. The findings indicate that the system reaches a quasi-steady oscillatory state at τ ≥ 600. Furthermore, the transition from a conduction-dominated to a convection-dominated regime is observed when Gr ≥ 10 4 , Re ≥ 100, and Ha ≥ 10. The results show that the maximum convection region at Gr = 10 6 , Re = 10 3 , and Ha = 31.62 produces a 425% enhancement in the average Nusselt number. At the same time, the mean temperatures of the ferrofluid and the solid domains decrease by 71% and 80%, respectively, indicating a noticeably efficient system. As thermal gradients weaken, the total entropy generation declines by 99.9%, while the ecological thermal performance increases by nearly 16 times when Gr increases from 10 5 to 10 6 . Additionally, the mean drag coefficient decreases, resulting in a maximum performance evaluation criterion and indicating a substantial improvement in the system’s hydrothermal efficiency.