Magnetohydrodynamic convection in a heat-generating ferrofluid within a corrugated cavity containing a rotating cylinder

This study introduces a novel approach by combining magnetohydrodynamic flow with Joule heating effects to investigate the conjugate mixed convective flow of ferrofluid in a non-homogenously warmed wavy-walled squared-shaped chamber with a spinning cylindrical object positioned at the center of the chamber. The current study seeks to maximize heat transmission effectiveness by scrutinizing optimum system attributes and conducting entropy production analysis. Numerical solutions are achieved by employing the Galerkin finite element weighted residual approach to solve the two-dimensional Navier–Stokes and heat energy equations representing the mathematical model. The parametric alterations encompass Grashof (103 ≤ Gr ≤ 106), Reynolds (31.62 ≤ Re ≤ 1000), and Hartmann (5.623 ≤ Ha ≤ 31.623) numbers, volumetric heat generation coefficient (0 ≤ Δ ≤ 10), thermal conductivity ratio (K = 20.07, 95.14), corrugation frequency (6.5 ≤ f ≤ 8.5), dimensionless corrugation amplitude (0.02 ≤ A ≤ 0.04), and dimensionless cylinder diameter (0.3 ≤ D ≤ 0.5). The study assesses the thermal characteristics of a heat source and the entropy generated within the computational domain while considering varying corrugation frequency and amplitude, cylinder diameter, thermal conductivity, strength of magnetism, and heat generation. The findings are quantitatively showcased through the Nusselt number of the hot wall, mean fluid temperature, overall entropy production, and thermal performance criterion (TPC) across the domain. After extensive analysis, it is evident that minimum cylinder diameter (= 0.3), corrugation frequency (= 6.5), and amplitude (= 0.02) while the maximum thermal conductivity ratio (= 95.14) ensure optimal system performance. Surprisingly, incorporating interior heat production diminishes thermal performance significantly while increasing TPC. Understanding the impacts of the magnetic field, Joule heating, and interior heat production on convective flow offers key perceptions into temperature variation, heat transport, velocity profile, and irreversible energy loss in numerous engineering applications.