Simulation of partial magnetic field effects on Cu-TiO₂-water hybrid nanofluid natural convection flow in a Darcy–Brinkman–Forchheimer porous media enclosure with a MAC-FVM combined scheme

This study introduces an innovative numerical analysis of natural convection heat transfer within a differentially heated square enclosure containing a porous medium, permeated by an electrically conductive hybrid nanofluid (Cu [Formula: see text] TiO 2 /water), under the effect of a localized magnetic field. Unlike conventional studies that apply uniform magnetic fields, this work introduces a partial magnetic field, allowing localized control of heat transfer and flow dynamics. The analysis is conducted using the Brinkman–Forchheimer-extended Darcy model, which accounts for both viscous and inertial effects in the porous medium, while the partial differential equations are solved using the Finite Volume Method (FVM) combined with a Marker-and-Cell (MAC) scheme for enhanced accuracy. The effects of key dimensionless parameters — thermal buoyancy parameter, i.e., Rayleigh number (Ra), porosity ([Formula: see text], Hartmann magnetic number (Ha), permeability parameter, i.e., Darcy number (Da), and heat source/sink parameter ([Formula: see text] — on the natural convection of thermal transport of hybrid nanofluids (Cu [Formula: see text] TiO 2 /water) in a porous enclosure. Validation with previous computational studies is included for some special cases of the present model. An increase in Ra from [Formula: see text] enhances buoyancy-driven convection, resulting in a significant rise in the average Nusselt number ([Formula: see text]) by approximately 10 times, indicating more efficient heat transfer. The partial magnetic field introduces a unique damping effect, where higher Ha values reduce convective flow and decrease heat transfer efficiency by up to 50%, highlighting its potential as a precise thermal control mechanism. With increasing porosity, the singular vortex cell morphs from a circular structure to an elliptic structure and eventually a peanut-shaped topology stretched laterally across the enclosure. These findings underscore the importance of parameter optimization for improving heat transfer efficiency in hybrid nanofluid systems, with potential applications in chamber, materials processing, cooling technologies, magnetic fuel cells and other energy storage devices.