EFFECT OF VERTICAL POSITION OF HEATED SQUARE OBSTACLE ON NATURAL CONVECTION IN POROUS CAVITIES SATURATED BY A NANOFLUID USING BUONGIORNO’S TWO PHASE MODEL

Abstract

Laminar flow, heat transfer and mass transfer of nanofluid in a porous medium have been studied using Buongiorno’s two phase model. The porous medium in place is a non-uniform octagonal shape. In order to increase the rate of heat transfer within the porous cavity, it has been equipped with a heated square at different vertical positions from position 1 (P1) to position 5 (P5). The left wall of this cavity is maintained at a high temperature and a unit volume fraction; whereas the right wall is exposed to a low temperature and a canceled volume fraction, and the other walls have been assumed to be adiabatic. The purpose of this paper is to highlight the effect of the heated square at different vertical positions on the evolution of the hydrodynamic, thermal and mass profiles taking into account the influence of certain parameters, such as: Rayleigh number (102≤Ra≤104), Darcy number (10-6≤Da≤10-2), thermophoresis ratio (0.1 ≤ Nt ≤ 1), buoyancy ratio (0.1 ≤ Nr ≤ 1), Brownian motion ratio (0.1 ≤ Nb ≤ 1) and Lewis number (0.1 ≤ Le ≤ 1). The physical phenomenon studied is governed by the Navier-Stokes equations coupled with the energy equation and the mass conservation equation (continuity of nanoparticles). These differential equations of boundary conditions are solved using the finite element method. The results show that an increase in the Rayleigh number and the Darcy number improves natural convection, leading to an increase in the Nusselt number at the square. It is also found that the lowest values of the Nusselt number are located at the extremities of the cavity while the highest are located at the intermediate position between the positions P3 and P4 regardless of the values of the different parameters. On the other hand, an increase in the Darcy number leads to an increase in the vertical and horizontal velocity where the highest values are located at position P4.