A general methodology for treating mixed convection problems using asymptotic computational fluid dynamics (ACFD) ☆ C. Balaji ⁎ , M. Hölling, H. Herwig Institute of Thermo-Fluid Dynamics, Hamburg University of Technology, Denickestrasse 17, D- 21073, Hamburg, Germany Available online 19 April 2007 Abstract 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. © 2007 Elsevier Ltd. All rights reserved. Keywords: Mixed convection; Asymptotics; ACFD; Perturbation, Blending 1. Introduction Mixed convection heat transfer takes place in a variety of situations, as for example in the thermal control of electronic equipment, cooling of nuclear reactors, lubrication, and heat transfer in the atmosphere. In view of this, mixed convection has attracted the attention of many researchers in the recent past. The frequently studied geometries include the classical vertical flat plate, the parallel plate channel and enclosures. The problem of mixed convection from a vertical flat plate has been studied by several researchers (see for example Chen et al. [1] and Gururaja Rao et al. [2]). In the above mentioned studies, correlations have been developed for the dependent variable, which happens to be the Nusselt number in most of the cases (sometimes this could be the maximum temperature in the geometry), based on detailed parametric studies, with a large number of data, obtained using either numerical solutions or experiments. As far as channel flows are concerned, several studies are available [3–6]. In the case of enclosure flows, one of the walls has to move in order that one obtains mixed convection. Strangely enough, mixed convection from enclosures seems to be the least studied, though a lid driven, differentially heated International Communications in Heat and Mass Transfer 34 (2007) 682 – 691 www.elsevier.com/locate/ichmt ☆ Communicated by E. Hahne and K. Spindler. ⁎ Corresponding author. E-mail address: balaji@iitm.ac.in (C. Balaji). 0735-1933/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2007.03.006