Investigation of free convection in a wavy trapezoidal porous cavity with MWCNT- Fe ₃ O₄ /Water hybrid nanofluid under MHD effects: Galerkin finite element analysis

Abstract

Our study focuses on numerically investigating natural convection within a three-dimensional trapezoidal cavity featuring a corrugated hot bottom wall, with a particular emphasis on enhancing heat exchange using a water -based hybrid nanofluid. Employing a steady-state regime assumption, the study considers laminar and incompressible three-dimensional flow. The DarcyForchheimer model is incorporated to account for inertial advection effects within the porous layer. Predictions of the thermal and hydrodynamic behaviors of the system are achieved by solving dimensionless equations utilizing the Galerkin Finite Element Method (GFEM). Notably, a range of influential parameters, including the volume fraction of nanoparticles ( phi ), Darcy number (Da) spanning from 10 - 5 to 10 -2 , Hartman number ( Ha ) across the range of 0-100, phi within the range of 0-0.08, porosity (epsilon) ranging from 0.2 to 0.9, and Rayleigh numbers (Ra) varying from 10 3 to 10 6 was explored. The investigation also evaluates the geometrical impact of the enclosure by considering undulation numbers (N) of the warm bottom ranging from 1 to 4. Our results provide novel quantitative insights. Specifically, we observe an inverse relationship between undulation number (N), Hartman number ( Ha ), and porosity (epsilon) with large Rayleigh (Ra) flows, significantly influencing effective heat transfer. Notably, this influence diminishes at lower Ra flows. At the highest Ra, we find that increasing Da, epsilon, and phi enhances the Nusselt number (Nu avg ) by 26 %, 17 %, and 23.5 %, respectively. Conversely, increasing Ha and N reduces Nu avg by 13 % and 40 %, respectively. These findings highlight the nuanced interplay of parameters and offer valuable quantitative data for optimizing heat transfer processes in similar systems.