Heat transport pathways in local thermal non-equilibrium magneto-convection through anisotropic porous medium

The proposed study demonstrates an irreversibility analysis of magneto-convection in a square enclosure filled with an anisotropic porous medium under the local thermal non-equilibrium framework under a uniform inclined magnetic field. Distinct energy equations are solved for the solid and fluid phases, coupled through an interphase heat transfer coefficient. A novel formulation of Bejan's heat function is derived under the non-equilibrium thermal interaction by combining the fluid and solid-phase energy equations, enabling rigorous visualization of total heat energy pathways within the domain. Numerical solutions are obtained using the finite volume method with the semi-implicit method for pressure linked equations algorithm. The coupled effects of anisotropic properties, fluid–solid thermal interaction, magnetic inclination and porosity are systematically examined. The results demonstrate that permeability anisotropy suppresses buoyancy-driven convection and reduces the average fluid Nusselt number Nuf,avg, whereas enhanced fluid–solid thermal coupling progressively drives the system toward local thermal equilibrium and |Δθ|max tending toward zero at high H. The magnetic field orientation produces a non-monotonic heat transfer response with an optimum inclination around 45°–60° enhancing convective transport. The variation in Nuf,avg over the investigated inclination range is ∼5.2%. The fluid–solid conductivity ratio Γ strongly affects the heat transport pathways with the maximum heat function magnitude |H|max decreasing from 5.714 at Γ=0.1 to 0.806 at Γ=100. Increasing porosity from ϵ=0.1 to 0.7 increases |H|max from 0.404 to 1.0269, demonstrating enhanced energy transport through stronger fluid circulation. The combined effects of anisotropy and magnetic field on thermodynamic irreversibility provide actionable insights for optimizing heat transfer in porous media systems such as solar energy collectors, geothermal reservoirs and heat exchangers.