Existence and structure of steady solutions of the Benard problem in a two dimensional quadrangular cavity

Journal article

Authors/Editors

Siginer, Dennis

Research Areas

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Publication Details

Author list: Neustupa J, Siginer D

Publisher: Elsevier

Place: OXFORD

Publication year: 2015

Journal: Nonlinear Analysis (0362-546X)

Journal acronym: NONLINEAR ANAL-THEOR

Volume number: 123-124

Start page: 68

End page: 88

Number of pages: 21

ISSN: 0362-546X

Languages: English-Great Britain (EN-GB)

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Abstract

We prove the existence of a strong-weak solution (u, p, T) (= velocity, pressure, temperature) of the steady Benard problem in a 2D quadrangular cavity, heated/cooled on two opposite sides and thermally insulated on the other sides. Applying the tools of nonlinear analysis, we study the structure of the set of solutions in dependence on the acting volume force and on the given temperature profiles on the heated/cooled sides. Particularly, in the case when the cavity has the form of a trapezoid, we also study the structure of the solution set in dependence on the angle of inclination from the horizontal-vertical position. (C) 2015 Elsevier Ltd. All rights reserved.

Keywords

Benard problem, Boussinesq approximation, Navier-Stokes equations

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