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

Abstract

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 ≤ 2x10^4 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 Gr^2A^3Pr^2 ≾ l0^5. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.