Об Одном Классе Аналитических Решений Стационарной Осесимметричной Конвекции Бенара - Марангони Вязкой Несжимаемой Жидкости

Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

“…The choice of the two-dimensional layer as the abstract mathematical object is mainly connected with the fact that this geometry can be quite easily realized in an experiment and provides certain conveniences for taking thermal and optical measurements. The two-dimensional horizontal layer is a matter of great importance in connection with the theory of convective stability applications in meteorology, geophysics and astrophysics [1,2].…”

“…A brief survey of the articles and reviews, in which the possibilities of finding exact solutions to free convection equations and the research of stability of these solutions were studied [4][5][6][7][8][9][10], is given in the papers [1,2] and the reference lists.…”

“…This method is offered in the context of the exact solutions class in which velocities linearly depend on horizontal coordinates, and fields of the pressure and temperature are distributed under the square law [2,6,11]. In this case, finding the exact solution is reduced to solving the nonlinear system of one-dimensional evolution heat conduction equations like heat conductivity, and stationary equations of the gradient type.…”

“…In this case, finding the exact solution is reduced to solving the nonlinear system of one-dimensional evolution heat conduction equations like heat conductivity, and stationary equations of the gradient type. When finding the exact solutions, which describe the convective fluid flow [1][2][3][4][5][6][7][8][9][10], an ideal heat transfer on the borders is assumed. The aim of the present work is to investigate the motion of a viscous incompressible fluid with heat exchange on the upper boundary.…”

Complex stationary convection with third-kind boundary conditions at the boundaries of a fluid layer

“…Граничные условия (3) записаны в предположении о неформируемости сво-бодной поверхности при движении жидкости и линейной зависимости поверхностного натя-жения от температуры [6,7]:   На верхней границе h z  и на нижней поверхности 0  z заданы условия теплопере-дачи по закону Ньютона -Рихмана [7,9,29]:…”