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

Jiří Neustupa, Dennis Siginer

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)68-88
Number of pages21
JournalNonlinear Analysis, Theory, Methods and Applications
Volume123-124
DOIs
Publication statusPublished - May 19 2015

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Cavity
Trapezium or trapezoid
Temperature Profile
Inclination
Nonlinear analysis
Solution Set
Nonlinear Analysis
Weak Solution
Horizontal
Vertical
Angle
Temperature
Form

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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T1 - Existence and structure of steady solutions of the Bénard problem in a two dimensional quadrangular cavity

AU - Neustupa, Jiří

AU - Siginer, Dennis

PY - 2015/5/19

Y1 - 2015/5/19

N2 - 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.

AB - 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.

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DO - 10.1016/j.na.2015.03.024

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VL - 123-124

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

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