Journal of Fluid Mechanics

Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory

D. E.  Cormack a1, L. G.  Leal a1 and J.  Imberger a2
a1 Chemical Engineering, California Institute of Technology, Pasadena
a2 Department of Mathematics and Mechanical Engineering, University of Western Australia, Nedlands

Article author query
cormack de   [Google Scholar] 
leal lg   [Google Scholar] 
imberger j   [Google Scholar] 


The problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A [rightward arrow] 0, are derived.

(Published Online March 29 2006)
(Received March 23 1973)
(Revised February 15 1974)