The Two-Component Bénard Problem with Flow. II. Further Numerical Results

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Abstract
A numerical solution for the two-component Benard problem with flow is presented, taking into account the contribution of thermal diffusion to the total density gradi-ent. The results are compared with the approximate solution obtained by the variational technique of the local potential introduced some years ago by Glansdorff and Prigogine. With a transverse rolls pattern, the destabilizing effect of a flow in a fluid mixture stabilized by the thermal diffusion effect is confirmed. A further checking of these results is presented. Using again the local potential technique, calculations are conducted with a Chebyshev polynomial expansion as trial functions. The two methods produce critical Rayleigh numbers which are in agreement with each other. Thus it is conjectured that a decrease of the critical Rayleigh number with the Reynolds number, is a real phenomenon. © 1978, Walter de Gruyter. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe