Thermo-hydrodynamic behavior of hybrid nanofluids in a wavy-cooled Gamma-shaped porous cavity under magnetic field

Purpose This study aims to investigate the coupled effects of magnetic-field orientation, magnetic-field strength, thermal radiation, porous-medium permeability and wavy-wall characteristics on natural convection heat transfer in a porous enclosure saturated with a Cu–Al₂O₃/water hybrid nanofluid (HNF). The objective is to clarify the dominant mechanisms governing thermal transport and identify favourable operating conditions for enhanced heat-transfer performance. Design/methodology/approach A two-dimensional wavy porous enclosure is considered, with sinusoidal cold vertical and horizontal top boundaries and G-shaped internal partitions maintained at a uniform hot temperature, while the remaining walls are adiabatic. Fluid flow through the porous medium is modeled using the Darcy–Brinkman formulation. The effects of the magnetic field are incorporated through the Lorentz-force term, whereas thermal radiation is modeled using the Rosseland diffusion approximation. The resulting dimensionless governing equations are formulated in vorticity–stream function form and solved using a second-order finite difference scheme on a Cartesian cut-cell finite difference method. Parametric simulations are performed for Rayleigh number 103 < Ra < 106, Darcy number 10−3 < Da < 10−1, magnetic field inclination angle 0° < γ < 90°, Hartmann number 0 < Ha < 50 and radiation parameter 0 < Rd < 5. Findings Increasing the Rayleigh number from 103 to 106 enhances the mean Nusselt number by approximately 324%, confirming the dominant contribution of buoyancy-driven convection to heat transfer. By contrast, increasing the Hartmann number from 0 to 50 decreases the average Nusselt number from 14.4904 to 6.9145, corresponding to a reduction of 52.2822%. This reduction is attributed to the Lorentz force, which suppresses buoyancy-driven fluid motion and consequently weakens convective heat transfer. Reducing the Darcy number from 0.1 to 0.0001 decreases the average Nusselt number from 13.8058 to 6.5834, corresponding to a reduction of 52.3142%. The reduction is associated with the increased hydraulic resistance of the porous medium, which restricts fluid motion and weakens convective heat transfer. The combined effects of wall undulation and amplitude enhance thermal performance by up to 6%, while favorable magnetic-field inclination angles increase the average Nusselt number by approximately 3.8%. Overall, buoyancy and porous-medium permeability are identified as the primary mechanisms promoting heat transfer, whereas magnetic damping represents the dominant suppressing mechanism. Originality/value The study provides a comprehensive assessment of the combined effects of magnetic-field orientation, Lorentz-force damping, thermal radiation, porous-medium permeability and wavy-wall geometry on HNF natural convection. The findings provide useful guidelines for controlling and optimising heat transfer in magnetically influenced porous thermal systems with complex enclosure geometries.