Computer Science
Scientific paper
Aug 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975jfm....70..689g&link_type=abstract
Journal of Fluid Mechanics, vol. 70, Aug. 26, 1975, p. 689-703.
Computer Science
75
Compressible Flow, Convective Flow, Digital Simulation, Free Convection, Two Dimensional Flow, Boundary Value Problems, Boussinesq Approximation, Equations Of Motion, Finite Difference Theory, Flow Stability, Ideal Gas, Rayleigh Number, Thermal Conductivity, Viscous Fluids
Scientific paper
A procedure for obtaining numerical solutions to the equations describing thermal convection in a compressible fluid is outlined. The fluid is considered to be confined in a rectangular region by fixed slippery boundaries and motions are restricted to two dimensions. The upper and lower boundaries are maintained at fixed temperatures and the side boundaries are thermally insulating. The onset of convection has been studied both by obtaining solutions to the nonlinear equations in the neighbourhood of the critical Rayleigh number and by solving the linear stability problem. Solutions have been obtained for values of the Rayleigh number up to 100 times the critical Rayleigh number and for pressure variations of a factor of 300 within the fluid. The Nusselt number increases with decreasing Prandtl number for moderate values of the depth parameter. Steady finite amplitude solutions have been found in all the cases considered. As the horizontal dimension of the rectangle is increased, the length of time needed to reach a steady state also increases.
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