Numerical computation of natural convection for a low-Prandtl-number fluidin a shallow rectangular region heated from below

Transient natural convection in a low-Prandtl-number fluid was computed for a shallow rectangular enclosure of 5 x 5 x 1 heated from below and cooled from above with four dragless, adiabatic, vertical walls. The model consist s of three-directional mass, momentum and energy balances. These equations were approximated by a HSMAC finite-difference method with a hybrid scheme for the inertial terms. Computations for Ra = 2000 and Pr = 0.01 required a n accumulative time of two months. The transient response after a step incr ease of the lower-wall temperature was at first a regular oscillation, whic h then evolved to a series of long rolls with their axes in one direction. These transient characteristics of the velocity and temperature fields are presented graphically. (C) 1998 Elsevier Science S.A. All rights reserved.