Influence of Transverse Roughness and Porous Medium on Conjugate Heat Transfer in an Inclined Nanofluid-Filled Cavity: A Lattice Boltzmann Study

Abstract

This study numerically investigates the influence of transverse wall roughness and porous medium characteristics on conjugate heat transfer within an inclined cavity filled with Al₂O₃/water nanofluid using the Lattice Boltzmann Method (LBM). The physical model consists of a two-dimensional inclined enclosure with roughened heated walls, where solid–fluid heat conduction coupling is considered to account for conjugate effects. The porous structure is modeled using the Darcy–Forchheimer formulation, while nanofluid thermophysical properties are evaluated based on effective medium theory. The governing equations for momentum and energy transport are solved using a double-distribution LBM scheme. The effects of key dimensionless parameters—including Rayleigh number (10³ ≤ Ra ≤ 10⁶), Darcy number (10⁻⁵ ≤ Da ≤ 10⁻²), porosity (0.4 ≤ ε ≤ 0.9), roughness amplitude and pitch, nanoparticle volume fraction (0 ≤ φ ≤ 0.05), and cavity inclination angle (0° ≤ γ ≤ 90°)—are systematically examined. Results reveal that transverse roughness significantly enhances local mixing and disrupts thermal boundary layers, leading to noticeable augmentation in average Nusselt number, particularly at higher Rayleigh numbers. However, excessive roughness amplitude induces localized recirculation zones that may suppress global heat transfer under low Darcy number conditions. Increasing porosity and Darcy number promotes convective dominance, while higher nanoparticle volume fractions improve effective thermal conductivity but slightly damp fluid motion due to viscosity enhancement. The inclination angle plays a crucial role in reorienting buoyancy-driven circulation, producing optimal thermal performance at intermediate angles. The study demonstrates that an appropriate combination of transverse roughness geometry and porous medium permeability can substantially enhance conjugate heat transfer performance in nanofluid-filled enclosures. These findings provide useful design guidelines for advanced thermal management systems, compact heat exchangers, and energy-efficient engineering applications