Author(s)

R. L. Frederick & S. Courtin

Abstract

Flow patterns and heat transfer in square cavities with perfectly conducting horizontal walls: the case of high Rayleigh numbers (106–109) R. L. Frederick & S. Courtin Universidad de Chile, Departamento de Ingeniería Mecánica, Santiago, Chile Abstract Flow patterns and heat transfer in a square cavity with perfectly conducting horizontal walls are described by direct simulation for Rayleigh numbers of 106– 109. The code uses second order time and space discretisations and non-uniform grids. For Ra = 106 or less a steady final state is found. Periodic characteristics are obtained at Ra = 107, and non periodic behaviour is found at higher Ra. Time averaged wall and mid plane Nusselt numbers (not previously known for this case) are reported and correlated. Their oscillation frequencies are determined to characterize the regime. The mid plane Nusselt number, mid Nu , always exceeds wall Nusselt numbers. mid Nu represents the total heat moved by the cavity under the perfectly conducting condition. At Rayleigh numbers from 108 onwards, mid Nu exceeds the corresponding value for the adiabatic problem. Keywords: natural convection, enclosures, perfectly conducting walls. 1 Introduction Natural convection in differentially heated square enclosures has received considerable attention in the CFD and Heat Transfer literature. Although the condition of perfectly conducting horizontal walls is more realistic when air is the test fluid, most studies use the adiabatic condition. In the present study, numerical simulations of the natural convection in a square cavity with perfectly conducting horizontal walls at high Rayleigh numbers are reported. Nusselt number values for some cases not previously treated in the literature are given.

Keywords

natural convection, enclosures, perfectly conducting walls.