TY - JOUR
T1 - Existence and structure of steady solutions of the Bénard problem in a two dimensional quadrangular cavity
AU - Neustupa, Jiří
AU - Siginer, Dennis
N1 - Publisher Copyright:
© 2015 Elsevier Ltd.
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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U2 - 10.1016/j.na.2015.03.024
DO - 10.1016/j.na.2015.03.024
M3 - Article
AN - SCOPUS:84929379089
SN - 0362-546X
VL - 123-124
SP - 68
EP - 88
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -