Turbulent natural convection in enclosures using large-eddy simulation with localized heating from horizontal bottom surface and cooling from vertical surfaces

Abstract

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 the present work. Solutions are obtained for several Rayleigh numbers with Prandtl number Pr = 0.70. 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 unsteady state. The Finite Element Method (FEM) with a Galerkin scheme is utilized for solving the conservation equations. The formulation of conservation equations is carried out for turbulent flow and the implementation of turbulent model is made by Large-Eddy Simulation (LES). The distributions of the stream function and of the temperature are determined as functions of thermal and geometrical parameters. The average Nusselt number Num is shown to increase with an increase in the Rayleigh number Ra as well as in the dimensionless heat source length ∈. The results of this work can be applied to the design of electronic components.