LARGE-EDDY SIMULATION OF AIR FLOW WITHIN A SQUARE ENCLOSURE WITH A PARTIALLY HEATED BOTTOM SURFACE AND COOLED VERTICAL WALLS

Turbulent natural convection of air that happens into inner square cavity with localized heating from horizontal bottom surface has been numerically investigated. Localized heating is simulated by a centrally located heat source on the bottom wall, and two values of the dimensionless heat source length are considered in this present work. Solutions are obtained for several Rayleigh numbers with Prandtl number 0.7. The horizontal top surface is thermally insulated and the vertical surfaces are assumed to be the cold isothermal surfaces whereas the heat source on the bottom wall is isothermally heated. In this study, the Navier-Stokes equations are used considering a two-dimensional and turbulent flow in the unsteady state. The Finite Element Method (FEM) with a Galerkin scheme is considered for solving the conservation equations. The formulation of the conservation equations is carried out for turbulent flow and the turbulence is modeled using Large-Eddy Simulation (LES). The stream function and temperature distributions are determined as functions of thermal and geometrical parameters. The average Nusselt number is shown to increase with an increase in the Rayleigh number as well as in the dimensionless heat source length. The results of this work can be applied to the design of electronic components. Natural convection in enclosures is an area of interest due to its wide application and great importance in engineering. Transient natural convection flows occur in many technological and industrial applications. Therefore, it is important to understand the heat transfer characteristics of natural convection in an enclosure. Along the years, researchers have looked for more flows with the objective to approximate the real case found in geophysical or industrial means. Then, we can define four basic types of boundary conditions. They are: the natural convection due to a uniformly heated wall (with a temperature or a constant heat flux); the natural convection induced by a local heat source; the natural convection under multiple heat sources with the same strength and type; and the natural convection conjugated with inner heat-generating conductive body or conductive walls. The boundary conditions mentioned previously are based on a single temperature difference between the differentially heated walls. Most of the previous studies have addressed natural convection in enclosures due to either a horizontally or vertically imposed temperature difference. However, departures from this basic situation are often encountered in fields such as electronics cooling. The cooling of electronic components is essential for their reliable performance. The characteristics of fluid flow and heat transfer under the multiple temperature differences are more complicated and have a practical importance in thermal management and design. In the present work, a two-dimensional numerical simulation in a cavity is carried out for a turbulent flow. The turbulence study is a complex and challenging assumption. There are few works in literature that deal with natural convection in closed cavities using the turbulence model LES. The motivation to accomplish this work relies on the fact that there are a great number of problems in engineering that can use this geometry. One turbulence model is implemented here together with the finite element method. A large eddy simulation (LES) seems a promising approach for the analysis of the high Grashof number turbulence that contains three-dimensional and unsteady characteristics. A direct simulation of turbulence gives us more accurate and precise data than experiments; it is essentially unsuitable for high Grashof number flows because of computational