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Exact solutions for layered large-scale convection induced by tangential stresses specified on the free boundary of a fluid layer

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, , Citation N.V. Burmasheva and E.Yu. Prosviryakov 2017 IOP Conf. Ser.: Mater. Sci. Eng. 208 012010 DOI 10.1088/1757-899X/208/1/012010

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nat_burm@mail.ru

evgen_pros@mail.ru

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1 Ural Federal University, 19 Mira Street, Ekaterinburg, 620002, Russia

2 Institute of Engineering Science, 34 Komsomolskya Street, Ekaterinburg, 620049, Russia

3 Kazan National Research Technical University, 10 K.Marx Street, Kazan, 420111, Russia

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1757-899X/208/1/012010

Abstract

A new exact solution for layered convection of a viscous incompressible fluid is found in this paper. A fluid flow in an infinite layer is considered. Convection in the fluid is induced by tangential stresses specified on the upper non-deformable boundary. Temperature corrections are given on the both boundaries of the fluid layer. The analysis of hydrodynamic fields allows us to state the presence of two stagnant points in the flow of a fluid. It is shown that, in the case of thermocapillary convection in a fluid, only one stagnation point can exist.

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10.1088/1757-899X/208/1/012010