Journal of Fluid Mechanics

Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

D. E.  Cormack a1, L. G.  Leal a1 and J. H.  Seinfeld a1
a1 Chemical Engineering, California Institute of Technology, Pasadena

Article author query
cormack de   [Google Scholar] 
leal lg   [Google Scholar] 
seinfeld jh   [Google Scholar] 


Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6·983, 10 [less-than-or-equal] Gr 2 × 104 and 0·05 [less-than-or-eq, slant] A [less-than-or-eq, slant] 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A [less, similar] 0·1 and Gr2A3Pr2 [less, similar] 105. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr [rightward arrow] [infty infinity].

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