Optimization of MHD natural convection heat and mass transfer of non-Newtonian power-law ferrofluids in complex enclosures using response surface methodology

This work presents a comprehensive numerical investigation into magnetohydrodynamic (MHD) influence in natural convection of non-Newtonian ferrofluids in complex cavity geometries, aiming to quantify and optimize thermal transport. The ferrofluid's behavior is modeled by the power-law equation, with buoyancy-driven flow governed by the Boussinesq approximation. A systematic parametric study involving the Rayleigh ( Ra ) and Hartmann ( Ha ) numbers, power-law index ( n ), and nanoparticle volume fraction ( ϕ ) was conducted, and the results were used to develop a statistically robust predictive model for the average Nusselt number ( Nu ) using Response Surface Methodology (RSM) with Central Composite Design (CCD) and ANOVA. The model exhibits excellent accuracy ( R 2 (adj) = 90.82%; R 2 (pred) = 85.51%) and confirms that shear-thinning characteristics ( n < 1) can increase Nusselt number by up to 31%, while shear-thickening ( n > 1) and higher nanoparticle concentration ( ϕ ) reduce Nusselt number by up to 6.7%, with magnetic effects ( Ha ) having a moderate impact. Crucially, sensitivity analysis identified the power-law index ( n ) as the dominant factor, whereas the volume fraction ( ϕ ) imposes the main performance constraint on Nu . Furthermore, the coupled effects of cavity irregularities and concentration differences act synergistically to improve heat transfer. The outcomes provide quantified physical insights and establish an optimized parametric foundation for designing compact, energy-efficient thermal systems with enhanced control and performance.