Analysis of enhanced magnetohydrodynamic natural convection in a non-Darcy porous cavity with alumina-water fluid and conductive baffles

Abstract

Purpose The purpose of this study is to explore numerically the conjugate natural convection of a nanofluid (Al 2 O 3 /water) within a non-Darcy’s porous square cavity containing two opposing solid blocks influenced by a horizontal external magnetic field. Design/methodology/approach The configuration studied involves a square cavity filled with a porous medium saturated by Al 2 O 3 /water nanofluid. The vertical walls are isothermal with hot and cold wall temperatures, while the horizontal walls are adiabatic. Two baffles, with high thermal conductivity relative to the fluid, are positioned midway on the vertical hot and cold walls. A constant horizontal magnetic field is applied, influencing natural convection, heat transfer and fluid motion within the cavity. The Koo–Kleinstreuer–Li (KKL) model, which provides a more accurate representation of the viscosity and thermal conductivity at the nanoscale, was used to include the effect of Brownian motion on the nanofluid’s properties. Conservation equations are modelled via the Darcy–Brinkman–Forchheimer formulation and solved numerically with the finite volume method implemented in a FORTRAN program. Velocity-pressure coupling is achieved using the SIMPLER algorithm. The study investigates the influence of various parameters such as Rayleigh and Darcy numbers, nanoparticle volume fraction and magnetic field strength. Findings The results indicate that increasing Rayleigh number (Ra), Darcy number (Da) and nanofluid volume fraction (f) enhances flow dynamics, promoting convection and significantly improving heat transfer, particularly nanoparticle-facilitated. Conversely, Hartman number Ha diminishes heat transfer by restraining fluid motion through the Lorentz force. Later, a novel correlation of the average Nusselt number (Nu) ¯ versus Ra, Da, f and Ha has been established to simplify future predictions of the heat transfer rate for similar configurations. Research limitations/implications This study has several limitations. It relies on steady-state conditions, potentially overlooking transient behaviours that could arise in real applications. The assumption of a uniform magnetic field and homogeneity in nanofluid properties may not accurately represent actual conditions. Additionally, while the Darcy–Brinkman–Forchheimer model is effective, it may not fully capture scenarios where inertial effects are significant. The investigation covers a range of Rayleigh and Darcy numbers as well as nanoparticle volume fractions but does not consider factors such as temperature-dependent fluid properties and non-Newtonian behaviour, which could further influence heat transfer and fluid dynamics. Practical implications The implications of this research are considerable for the design of thermal systems using nanofluids in porous media, especially in applications involving magnetic fields. The derived correlation for the average Nusselt number serves as a valuable predictive tool for engineering applications. Future work should address these limitations by incorporating transient analyses and exploring a wider array of operational parameters to deepen the understanding of nanofluid behaviour in magnetically influenced settings. Social implications The findings of this study have significant social implications, particularly in enhancing energy efficiency in thermal management systems. Improved heat transfer in applications such as HVAC, refrigeration and renewable energy systems can lead to reduced energy consumption and lower utility costs for consumers. Furthermore, the application of nanofluids in environmentally friendly technologies aligns with global sustainability goals, potentially reducing carbon footprints and promoting cleaner energy solutions. By advancing the understanding of nanofluid behaviour in porous media, this research contributes to the development of innovative, sustainable technologies that can improve energy accessibility and environmental quality for communities. Originality/value This study presents a novel numerical analysis of the natural convection of Al 2 O 3 /water nanofluid in a non-Darcy porous cavity influenced by a horizontal magnetic field, with the consideration of conjugated opposing baffles on hot and cold walls. It investigates the effects of Ra, Da and Ha numbers and nanoparticle volume fraction on flow and heat transfer using the Darcy–Brinkman–Forchheimer model. A new correlation between the average Nusselt number and key parameters is introduced, providing an advanced predictive tool for engineering applications. The findings have direct relevance to advanced thermal management systems, including electronic cooling, energy storage and industrial heat exchangers, where optimizing heat transfer efficiency is critical.

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