Pattern formations in heat convection problems

Autor:	Takaaki Nishida, Yoshiaki Teramoto
Rok vydání:	2009
Předmět:	Convection Natural convection Applied Mathematics General Mathematics Mathematical analysis Boundary (topology) Physics::Fluid Dynamics Nonlinear system Bifurcation theory Free surface Boundary value problem Nonlinear Sciences::Pattern Formation and Solitons Bifurcation Mathematics
Zdroj:	Chinese Annals of Mathematics, Series B. 30:769-784
ISSN:	1860-6261 0252-9599
DOI:	10.1007/s11401-009-0101-x
Popis:	After Benard’s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by the bifurcation theory, weakly nonlinear theories and computational approaches. The boundary conditions for the velocity on the upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part of this paper, some bifurcation pictures for the case of the stress-free on the upper boundary and the no-slip on the lower boundary are obtained. In the second part of this paper, the bifurcation pictures for the case of the stress-free on both boundaries by a computer assisted proof are verified. At last, Benard-Marangoni heat convections for the case of the free surface of the upper boundary are considered.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::be50c47dc81545f03c4732105d674fe9 https://doi.org/10.1007/s11401-009-0101-x Zobrazit plný text záznamu Plný text ve formátu PDF