A general methodology for treating mixed convection problems using asymptotic computational fluid dynamics (ACFD)

In this paper, the technique of combining asymptotics with computational fluid dynamics (CFD), called the asymptotic computational fluid dynamics (ACFD), has been used to first perturb the limiting solutions of natural and forced convection, in order to obtain correlations for the average Nusselt number, that work very well in the extreme limits of a mixed convection problem. These are then blended suitably, such that a unified, composite correlation for the average Nusselt number can be obtained for the entire range of Richardson numbers. To illustrate the technique, the problem of two dimensional, laminar, mixed convection from air in a differentially heated, lid driven cavity with the top wall moving and the bottom wall stationary has been used. FLUENT 6.2 has been used to generate the “few” solutions required for developing the correlation using ACFD. The study reveals that for a given fluid with as few as 5 solutions, one can get a composite correlation for the average Nusselt number that is also asymptotically correct.