International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Andreev V.K.   Бекежанова В.Б.  

The convective two-layer stationary flows and their stability

Reporter: Andreev V.K.

     A study is made of the motion of two incompressible fluids separated by a interface where the surface tension linearly depending on the temperature is taken into account. The Oberbeck-Boussinesq equations which assume that the density variations are neglected everywhere except the body force terms are used. For this system the exact solutions describing unidirectional steady flows with a plane interface are found. There are four physical mechanisms due to flows in layers occur, more exactly, the buoyancy resulting from the expansion of a heated fluids, the pressure gradient, the thermocapillarity producing by tractions arising from the variation with temperature of surface tension, the movement of the upper solid wall. Linear stability analysis of the steady flows mentioned above in layers of fluids is considered.
     Special feature of the task is its non-self-adjointness, which leads to appearance of oscillatory instability. For zero volume rate in the second layer the flow crisis is generated by hydrodynamic or thermal mode. If the temperature gradient is chosen so that pressure gradient is equal to zero, then the flow crisis is induced by thermal waves. For flow formed by thermocapillary forces and solid wall motion the instability is connected with development of the monotonic thermal or oscillatory hydrothermal waves.

This work was supported by the RFBR (Grant 11-01-00283).

Abstracts file: eng_tez-1.doc

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