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Example of an exact solution of the stationary problem of two-layer flows with evaporation at the interface

O. N. Goncharova^ab, E. V. Rezanova<sup>a

a</sup> Altai State University, Barnaul, 656049, Russia
^b S.S. Kutateladze Institute of Thermophysics, Siberian Division of the Russian Academy of Sciences, Novosibirsk, 630090, Russia

Abstract: Stationary two-layer liquid and gas flows with fluid evaporation at the interface are studied. On the solid impermeable boundaries of the channel, no-slip conditions are satisfied and a linear temperature distribution along the longitudinal coordinate and a condition for the vapor concentration at the upper boundary are specified. On the thermocapillary interface, remaining undeformed, the following conditions are specified: kinematic and dynamic conditions, a condition for thermal flows with mass transfer, continuity conditions for the velocity, temperature, and mass balance, and a relation for the saturated vapor concentration. An exact solution of the stationary problem for a given gas flow rate is obtained. Examples of velocity profiles are given for stationary flows of the ethanol-nitrogen system under normal and reduced gravity are given. The effect of longitudinal temperature gradients specified at the boundaries of the channel on the flow pattern is investigated.

Keywords: convection, thermocapillary interface, two-layer flow, evaporation, exact solution.

UDC: 536.25

Received: 17.06.2013
Revised: 11.09.2013

 English version: Journal of Applied Mechanics and Technical Physics, 2014, 55:2, 247–257

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