USE OF THE FINITE-ELEMENT METHOD FOR NATURAL CONVECTION IN A HORIZONTALLY CONFINED INFINITE LAYER OF FLUID

Abstract

Natural convection in a horizontally confined, infinite layer of fluid, heated from below and cooled from above, was computed by a finite-element method. The behavior was modeled in terms of a two-dimensional roll cell with a square cross section. Triangular elements of three different sizes were tested for Pr = 10 and a range of Rayleigh numbers from the critical value up to 3000. The Nusselt numbers obtained by extrapolation to zero element size agree well with the experimental values of Silveston. The critical Rayleigh numbers computed for the three element sizes extrapolated similarly to close agreement with the theoretical value of 1708. Contrary to some prior claims, these extrapolations indicate that the truncation error for finite-element computations is significant. Hence computations for two or more element sizes, followed by extrapolation to zero element size, are essential.