A numerical study of natural convective heat transfer from a horizontal isothermal square element imbedded in an adiabatic surface with a parallel adiabatic covering surface

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.Natural convective heat transfer from a square horizontal flat isothermal heated element imbedded in a larger flat square adiabatic surface with a square flat horizontal adiabatic surface mounted parallel to the heated surface at a relatively short distance from it has been numerically studied. The surface of the heated element is in the same plane as the surface of the surrounding adiabatic material. The square heated element considered in this study is at a higher temperature than that of the surrounding fluid. Both the case where the square heated element is facing upwards and the surrounding adiabatic covering surface is above the heated element (upward facing case) and the case where the square heated element is facing downwards and the surrounding adiabatic covering surface is below the heated element (downward facing case) have been considered. The situation considered is a simplified model of some situations that arise in engineering practice examples occurring in some electrical and electronic component cooling problems. In this study, the range of conditions considered is such that laminar, transitional, and turbulent flows occur. The purpose of this study was to numerically determine how the heat transfer rate from the square heated element varies with the distance of the adiabatic covering surface from the heated element. The solution was obtained by numerically solving the governing equations subject to the boundary conditions using the commercial CFD solver ANSYS FLUENT© using the kepsilon turbulence model with full account being taken of buoyancy force effects. Because of the applications that motivated this study, results have been obtained for a Prandtl number of 0.74, i.e., effectively the value for air. The effect of the dimensionless distance between the heated element and the cover on the variation of the Nusselt number with Rayleigh number has been studied in detail for both the upward and the downward facing cases.