Mathematical Modeling

An influence of the false bottom on the nonlinear dynamics of the water freezing process

I. G. Nizovtseva^a, D. V. Alexandrov<sup>b

a</sup> Lab. of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, A. M. Gor'ky Urals State University, Ekaterinburg
^b Dept. of Mathematical Physic, A. M. Gor'ky Urals State University, Ekaterinburg

Abstract: The current paper casts the light on the processes of structural-phase transitions during the freezing salt water, including the false bottom effects. A nonlinear mathematical model of heat and mass transfer was obtained. It takes into account the presence of three moving boundaries of phase transition and turbulent fluid flows from the ocean side by the surface of the false bottom. The exact analytical solutions of the nonlinear model were obtained — in their turn, they takes into account the time dependence of temperature and salinity at the depth and fluctuations of friction velocity. The distribution of temperature and salinity, the concentration of solids, the laws of motion of the boundaries of the phase transition, “salt water — the two-phase zone”, “two-phase zone — melted water” and “melt-water — ice” were found. The heat flux at the lower boundary of a false bottom was specified. The latter can change its direction at the time oscillations of the sea water temperature and friction velocity. Also it was shown, that structural transitions in the ice thickness are strictly associated with the processes of evolution of a false bottom.

Keywords: crystallization, heat and mass transfer, Stefan problem, two-phase zone, false bottom.

UDC: 517.958:536.2

MSC: Primary 86A05; Secondary 86A40, 76T99, 35Q79, 35Q35

Original article submitted 12/IX/2010
revision submitted – 12/VII/2011

DOI: 10.14498/vsgtu982

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