Abstract
The two-dimensional films, flowing down an inclined, non-uniformly heated substrate are studied. The results contain the new mathematical models developed with the help of the long-wave approximation of the Navier-Stokes and heat transfer equations or Oberbeck-Boussinesq equations in the case, when the generalized conditions are formulated at thermocapillary interface. The evolution equations for the film thickness include the effects of gravity, viscosity, capillarity, thermocapillarity, additional stress effects and evaporation.
Highlights
Modelling of the convective processes caused by impact of various forces on the fluid media is important nowadays [1,2,3,4]
The results contain the new mathematical models developed with the help of the long-wave approximation of the Navier-Stokes and heat transfer equations or Oberbeck-Boussinesq equations in the case, when the generalized conditions are formulated at thermocapillary interface
One of the most critical points in the mathematical modelling of the above mentioned processes is the statement of the boundary conditions on the interface
Summary
Modelling of the convective processes caused by impact of various forces on the fluid media is important nowadays [1,2,3,4]. The tangential stresses due to flow in the gas phase on a thermocapillary gas-liquid interface and the evaporation effects should be taken into consideration in the case when the fluid flows are accompanied by the adjacent gas flows. The conditions at the interface are the result of the conservation laws of mass, momentum and energy. The additional relations concerning a continuity of some flow characteristics, laws of the heat and mass fluxes, of the dynamic, energy and phenomenological properties etc. The generalized interface conditions allow to model the evaporative processes in the liquid and gas-vapor phases with interface in the full problem statement and in the long-wave approximation of the governing equations. Numerical results demonstrate the differences in the flow characteristics obtained with the help of alternative mathematical models
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