NATURAL CONVECTION OF WATER NEAR THE DENSITY EXTREMUM FOR A WIDE RANGE OF RAYLEIGH NUMBERS

Abstract

A time-dependent penalty finite element model was used to investigate natural convection of pure water in a rectangular enclosure with vertical end walls differentially heated near the temperature of maximum density. Attention was focused on the main features of the flow at high Rayleigh numbers not considered previously (Ra = 10⁵−10⁸). Water in a rectangular enclosure for the aspect ratio of 1.25 was initially kept at 4^°C. The enclosure was then suddenly heated and cooled on the opposing vertical walls, i.e., 8^°C and 0^°C. The Rayleigh number was varied by the size of the enclosure. In the Rayleigh number range considered here, steady state was reached within a time of the order of 2t_f, where t_f is the time to steady state suggested by Patterson and Imberger [1]. The steady state flow field and temperature structure were symmetric at about the enclosure's midpoint, and a stable sinking jet was formed in the interior of the enclosure as a result of density inversion. The velocity profile near the vertical walls agreed well with Gill's approximation of the laminar boundary layer solution, but the temperature profile disagreed because of the discrepancy in the core temperature.