Problem of Critical Convective Flows in Horizontal-Cylindrical Cavities
The results of an analysis of the linear perturbations of equilibrium of a viscous heat-conducting fluid or gas in cavities with simple geometric cross-sections are given. Both plane motions and motions periodic in the direction of the horizontal generator of the boundary surface are considered. Variants in which the acceleration of the mass force field can be both constant and periodically modulated are calculated. The solutions of the problem for the stream function (or the vertical velocity component) and the temperature are represented in the form of double or triple Fourier series. For the coefficients in the expansions an infinite system of equations which admits reduction is obtained. The results are found to be in good agreement with the known data.
KeywordsBoussinesq approximation modulations plane and three-dimensional perturbations infinite systems isolines
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