Numerical Simulation of Natural Convection in a Square Cavity with Two Partitions and Two Fluids

Abstract

This work's objective deals with the mathematical modeling and numerical simulation of stationary laminar natural convection, where we promote the conjugated heat transfer in a confined square cavity H=L filled with two fluids: a mixture of nanoparticles of Aluminum oxide and water (water + Al2O3) in one partition and a pure water in the other partition. A solid conductive wall with different thickness e (e=H/e) and thermal conductivities ks, constitutes the exchange surface between these two partitions. The mathematical model equations, of momentum and heat transfers in this mixture and in the solid wall are solved by a finite volume method and SIMPLE algorithm for pressure-velocity coupling. The Brinkman model was used to approximate the nano-fluid dynamic viscosity, while the effective thermal conductivity is approximated by a semi-empirical correlation based on experimental results. The results are discussed with particular attention to the average and local Nusselt number, streamlines and isotherms. A parametric study for the Rayleigh number Ra (10^2 to 10^6), the thermal conductivity ratio Kr (ks/knf) and the volume fraction φ in nanoparticles (0 % to 15 %) was conducted.