Effects of the Form Factor and the Force of the Gravity on the Thermal Exchanges by Natural Convection in a Rectangular Cavity Filled with Nanofluid

Abstract

Effects of the form factor on natural convection heat transfer and fluid flow in a two-dimensional cavity filled with Al 2 O 3 -nanofluid has been analyzed numerically. A model was developed to explain the behavior of nanofluids taking account of the volume fraction φ . The Navier-Stokes equations are solved numerically by alternating an implicit method (Method ADI) for various Rayleigh numbers varies as 10 3 , 10 4 and 10 5 . The nanofluid used is aluminum oxide with water Pr = 6.2; solid volume fraction φ is varied as 0%, 5% and 10%. Inclination angle Φ varies from 0 ° to 90 ° with a step the 15 ° and the form report varies as R = 0.25, 0.5, 1 and 4. The problem considered is a two-dimensional heat transfer enclosure. The vertical walls are differentially heated; the right is cold when the left is hot. The horizontal walls are assumed to be insulated. The nanofluid in the cavity is considered as incompressible, Newtonian and laminar flow. The nanoparticles are assumed to have a shape and a uniform size. However, it is supposed that the two fluid phases and nanoparticles are in a state of thermal equilibrium and they sink at the same speed. The thermophysical properties of nanofluids are assumed to be constant at the exception of the variation of density in the force of buoyancy, which is based on the approximation of Boussinesq values.