This paper gives a review of studies of flow stability for viscous heat-conducting fluids.

Stability of non-isothermal fluids (Review)

Mathematical and numerical modeling of convection in a horizontal layer under co-current gas flow

Stability of exact solutions describing two-layer flows with evaporation at the interface

The study of convective processes caused by impact of various forces on the fluid and gas media is actual nowadays. The increased interest to these problems is determined by preparation of the new experiments on the International Space Station in the frame of the scientific project CIMEX of the European Space Agency. They are the experiments to investigate the convective flows of the fluids with a thermocapillary interface between liquid and gas phases. In the case, when a co-current gas flux generates the tangential stresses on a free boundary the additional characteristics of the convective flows should be detected. In this paper the exact solutions of a stationary problems of convection and of gas flow in the horizontal layers with a free thermocapillary interface are constructed. An evaporation through the fluid-gas flow interface is modeled qualitatively with the help of a heat exchange condition. It is determined that the velocity on the fluid-gas interface can be positive and negative. The equal-zero condition for the interface velocity is found, as well. In the experiments an open horizontal fluid layer is studied so that the closed flux condition is not needed. Although the closed flux requirement is not set explicitly a parameters relation is found, when this condition is fulfilled. The paper presents the velocity and temperature profiles in the conditions, which correspond qualitatively to the CIMEX experiment.

Gas Flow and Thermocapillary Effects on Fluid Flow Dynamics in a Horizontal Layer

An exact solution describing the convective flow of a vortical viscous incompressible fluid is derived. The solution of the Oberbeck–Boussinesq equation possesses a characteristic feature in describing a fluid in motion, namely, it holds true when not only viscous but also inertia forces are taken into account. Taking the inertia forces into account leads to the appearance of stagnation points in a fluid layer and counterflows, as well as the existence of layer thicknesses at which the tangent stresses vanish on the lower boundary. It is shown that the vortices in the fluid are generated due to the nonlinear effects leading to the occurrence of counterflows and flow velocity amplification, compared with those given by the boundary conditions. The solution of the spectral problem for the polynomials describing the tangent stress distribution makes it possible to explain the absence of the skin friction on the solid surface and in an arbitrary section of an infinite layer.

Nonuniform convective Couette flow

Abstract Plane Poiseuille flow of two immiscible fluids in a non-isothermal “capillary” channel under the combined action of pressure gradients, gravitational fields and surface tension gradients is studied. Conditions for attaining a Poiseuille-type regime are derived. Closed form solutions are obtained and discussed.

L. G. Napolitano

Papers

Plane Marangoni-Poiseille flow of two immiscible fluids