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Published August 28, 1974 | Published
Journal Article Open

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


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 ≤ Gr ≤ 2 x 10⁴ and 0.05 ≤ A ≤ 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A ≾ 0.1 and Gr²A³Pr² ≾ l0⁵. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

Additional Information

© 1974 Cambridge University Press. Received 23 March 1973; in revised form 15 February 1974; published Online March 29 2006. This work was supported, in part, by National Science Foundation Grant GK-35476.

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