Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation

Abstract

Thermal convection in a fluid contained between two rigid walls with different mean temperatures is considered when either spatially periodic temperatures are prescribed at the walls or surface corrugations exist. The amplitudes of the spatial non-uniformities are assumed to be small, and the wavelength is set equal to the critical wavelength for the onset of Rayleigh-Bénard convection. For values of the mean Rayleigh number below the classical critical value, the mean Nusselt number and the mean flow are found as functions of Rayleigh number, Prandtl number, and modulation amplitude. For values of the Rayleigh number close to the classical critical value, the effects of the non-uniformities are greatly amplified, and the amplitude of convection is then governed by a cubic equation. This equation yields three supercritical states, but only the state linked to a subcritical state is found to be stable.

The regular and chaotic dynamics of structures in fluid flows

“…Наконец, третье -хао-тическое -когда период решетки изменяется в пространстве нерегуляр-ным образом. Такие состояния могут наблюдаться как в статических твердотельных решетках (в частности, в криптоне, обсорбированном на графите [199]; в магнитоупорядоченных системах [200]), так и в об-суждаемых здесь ансамблях гидродинамических структур, образующих-ся, например, при термоконвекции Рэлея -Бенара [201][202] или при электрогидродинамической неустойчивости в тонких слоях жидких кри-сталлов [92,203,204]. При малых надкритичностях последние два слу-чая не имеют принципиальных различий, однако из-за чисто техниче-ских трудностей экспериментальные исследования проведены лишь для жидких кристаллов.…”

Competition of intrinsic and topographically imposed patterns in Bénard–Marangoni convection

“…Raised features modulate both the temperature gradient in the system and the shearing interaction of the fluid with the solid surface. 15 In 1:1 commensurate structures, the convection cells tend to form with the center of each cell-where fluid is ascending-above the raised surface features, because the fluid layer directly over a post is thinner than over the flat points of the surface, and the surface of the fluid film is correspondingly hotter; these hot spots become upwellings in the pattern of convection cells. We tiled the surface with convection cells of all three possible perfect polygonal shapes: Triangles ͑which have not previously been observed in Bénard-Marangoni convection͒, squares ͑previously observed only at higher Marangoni numbers 16 ͒, and hexagons.…”

Numerical Analysis for Prandtl Number Dependency on Natural Convection in an Enclosure Having a Vertical Thermal Gradient With a Square Insulator Inside

“…The isotherm is not exactly orthogonal to the gravitational direction in the whole domain because of the inner body, and a negligibly small convection stream is detected. Kelly and Pal [26] and Lee et al [27] noted this kind of appearance which is detected only below the critical Rayleigh number as a quasi-steady conduction state. Despite this nearly non convective heat transfer mode, the surface-averaged Nusselt number is estimated to be 0.77 in this calculation, as depicted in Fig.…”