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標題: Effect of a non-uniform temperature gradient on the onset of oscillatory Benard-Marangoni convection of an electrically conducting liquid in a magnetic field
作者: Char, M.I.
Chen, C.C.
關鍵字: cellular convection;stability theory;surface tension;layer;fluid;buoyancy;instability;boundary
Project: International Journal of Engineering Science
期刊/報告no:: International Journal of Engineering Science, Volume 41, Issue 15, Page(s) 1711-1727.
This study deals theoretically with the effect of a non-uniform. basic temperature gradient on the linear stability of the oscillatory Benard-Marangoni convection in a horizontal layer of a viscous quiescent, electrically conducting fluid in the presence of a uniform vertical magnetic field. The upper surface of a fluid layer is deformably free and the lower surface is rigid. The eigenvalue equations of the perturbed state obtained from the normal mode analysis are solved by using the fourth order Runge-Kutta-Gill's method with the shooting technique. The results show that the critical Rayleigh number Ra-c and the critical Marangoni number -Ma(c) become larger as the Chandrasekhar number Q or the Biot number Bi of the upper free surface increases, and the Crispation number Cr decreases. When compared with the linear temperature profile, the inverted parabolic temperature profile indicates a reinforcement of stability, while the parabolic temperature profile indicates a diminution of stability in both Rayleigh-Benard and Benard-Marangoni convections. In addition, for the piecewise linear temperature profiles, the influences of thermal depth on the critical conditions are also obtained. Comparisons are also made of the critical conditions [-Ma(c), a(c), q(ic)] between the present results and published data sets for the linear basic temperature profile case, and the agreement is found out to be generally good. (C) 2003 Elsevier Science Ltd. All rights reserved.
ISSN: 0020-7225
DOI: 10.1016/s0020-7225(03)00068-5
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