Existence and structure of steady solutions of the Bénard problem in a two dimensional quadrangular cavity. (August 2015)

• Record Type: Journal Article
• Authors: Neustupa, Jiří; Siginer, Dennis
• Is Part Of: Nonlinear analysis. Volume 123/124(2015)
• Page Start: 68
• Page End: 88
• Publication Date: 2015-08
• Subjects: 35 Q 35 -- 35 Q 79 -- 76 D 03 -- 80 A 20; Bénard problem -- Navier–Stokes equations -- Boussinesq approximation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.03.024
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the existence of a strong–weak solution ( u, p, T ) ( = velocity, pressure, temperature) of the steady Bénard 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.