Simulation of mixed convection in a nanofluid-filled cavity with inner hot permeable block: A two-phase MRT-LBM approach

Abstract

This study explores the intricate dynamics of a mixed convection phenomenon in a cavity filled with nanofluid while employing a novel approach based on the two-phase lattice Boltzmann method (LBM) with multiple-relaxation-time (MRT). The introduction of a permeable hot square block with blockage ratios (BR) of 0.25 and 0.5 further augmenting the complexity of the phenomena. The current research aims to evaluate the effectiveness of the two-phase MRT-LBM approach in analyzing the slip mechanisms of nanofluids and drag forces within porous media, while making rigorous validation against established experimental and numerical benchmarks. A comprehensive parametric study is conducted by varying the nanoparticle concentration of Al₂O₃/water nanofluid ($\phi \le 0.03)$, Richardson numbers (0.1$\le \mathrm{Ri}\le 10$), and permeability of the inner block (10⁻² $\le$ Da $\le$ 10⁻⁶) to assess their impact on flow structure, thermal field, and entropy distribution. The results demonstrate that increasing $\phi$ enhances thermal conductivity and improves heat transfer, while simultaneously increasing viscous dissipation and entropy generation. Permeability plays a crucial role in governing flow penetration and heat transfer performance, transitioning the system from conduction- to convection-dominated regimes. The blockage ratio critically impacts performance: at low Ri, BR = 0.5 boosts heat transfer through enhanced shear and localized thermal gradients, whereas at high Ri, BR = 0.25 improves efficiency by minimising flow resistance and promoting smoother circulation. The outcome of this research sheds light on the interactions between the permeable block, nanofluid, and mixed convection effects and reveals that nanofluid usage can be thermodynamically advantageous under optimised flow conditions.