Response surface optimization of heat transfer in magnetic nanofluid flow within a permeable square enclosure: Corrugated wall and Joule heating effects

Abstract This paper presents a comprehensive numerical computation of the natural convection of magnetized permeable nanoliquids contained within a composite wavy cabinet. The domain of interest includes two parts. One portion is filled with a nanofluid fluid saturated with a porous matrix, whereas the other region is filled solely with the nanofluid. The finite element approach is utilized to solve the coupled highly nonlinear partial differential equations numerically. A selected set of graphical results illustrating the effects of frequency, amplitude, Rayleigh number, Hartmann number, Darcy number, and different porous materials on the streamlines and isotherms are presented. The variations in these parameters enable us to examine the impact on Nusselt number, flow patterns, and thermal performance. The addition of a response surface technique based on sensitivity analysis is a major innovation in this study, and the findings reveal intricate interactions between magnetohydrodynamics (MHDs), Joule heating, and porous medium effects, providing valuable insights into optimizing thermal management and energy efficiency in advanced MHD systems.