FINITE-ELEMENT ANALYSIS OF LAMINAR NATURAL CONVECTION IN CONFINED RECTANGULAR REGIMES—EXTRAPOLATION TO ZERO ELEMENT SIZE

Abstract

Natural convection between horizontal plates heated from below was computed by using a finite-element method based on a second-order approximation, and the average Nusselt number was extrapolated to zero element size. This process of extrapolation was required to obtain good agreement with the experimental data. Even when a second-order approximation was used for all of the variables, such an extrapolation was found to be necessary. This behaviour was further confirmed for natural convection in a square channel heated on one sidewall and cooled on the opposing one. Sample calculations for these two cases suggest, contrary to prior assertions and implications, that extrapolation or the equivalent is essential to eliminate numerical error and thereby obtain reliable results even with higher-order finite-element formulations.