Study of Laminar Naturel Convection in Partially Porous Cavity in the Presence of Nanofluids

Abstract

The objective of this work is the mathematical modelling and the numerical simulation of the stationary, laminar, and natural convection, in a confined square cavity (H = L) filled with two fluids (a mixture of nanoparticles of aluminum oxide and Al₂O₃ water) in one partition and pure water in the other partition. A porous conductive wall of thickness w (w = L/e) and thermal conductivity K_eff constitutes the exchange surface between these two partitions. The fluid movement is modeled by the Navier-Stokes equations in the two partitions, while the porous medium is modelled by the Darcy–Brinkman equation. Comsol Multiphysics software is used to solve the system of differential equations that is based on the finite element method. The results are discussed with particular attention to the mean and local Nusselt number (Nu), streamlines and isotherms. A parametric study for Rayleigh number Ra (10² to 10⁶), volume fraction j (0% to 10%), and Darcy number Da (10^-7 to 10^-2) is performed. The obtained findings show that the increase in Ra, Da, and j intensifies the flow and improves the thermal exchange on the cold wall. For Da £ 10^-5, Nu remains practically low and the natural convection is being dominated by conduction. For Da > 10^-5, an increase in Nu is observed and the flows tend towards a purely convective situation. Furthermore, an increase in the heat transfer coefficients is observed with the raise of the porous layer permeability, volume fraction and Rayleigh number.