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ISSN Online: 2377-424X

International Heat Transfer Conference 12
August, 18-23, 2002, Grenoble, France

Linear stability analysis for three dimensional Rayleigh-Bénard convection with radiatively participating medium

Get access (open in a dialog) DOI: 10.1615/IHTC12.20
6 pages

要約

A fluid subject to combined natural convection and radiation is studied by employing the Boussinesq approximation of the Navier-Stokes equations and solution using the spectral method. The equation of radiation transfer for the participating medium is analyzed by the exact integral formulation. Black boundaries and a gray medium are prescribed. In this work, two approaches are presented − by linear stability analysis and weakly nonlinear analysis. From these approaches, insight into the effect of radiation on this classical problem can be accomplished. Linear stability analysis and weakly nonlinear analysis are used to determine the critical Rayleigh number for the onset of convection in the combined mode. The results show that the presence of a radiative source changes the static temperature gradient of the fluid, and generally results in increasing the flow critical values. The characteristic conduction-radiation parameter ranges from 0.01 to 1, and optical thickness ranges from 0.01 to 10. Comparisons are made with some existing results. The influence of the conduction-radiation parameter, Rayleigh number and optical thickness on flow instabilities and bifurcations is discussed. It is shown that the effect of radiation on critical Rayleigh number in large optical thickness media can be predicted by use of a modified thermal diffusivity.