Numerical Solutions of the Nonlinear Equations for a Heated Fluid Layer
- 1 October 1965
- journal article
- conference paper
- Published by AIP Publishing in Physics of Fluids
- Vol. 8 (10) , 1757-1769
- https://doi.org/10.1063/1.1761107
Abstract
The equations of the Boussinesq approximation to the Navier—Stokes equations are solved numerically for the problem of a fluid layer heated from below. Solutions are obtained throughout the range of Rayleigh numbers from critical to R = 107. Free boundary solutions are compared with analysis, and rigid boundary solutions are compared with experiment. The dimensionless heat transport varies as R⅓ for free boundaries and for rigid boundaries a variation of about R0.296 is observed. Excellent agreement is obtained with both analysis and experiments and by an examination of various modal behaviors a number of the observed properties of the flow can be explained.Keywords
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