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On one mathematical model of the flow in a thin plastic layerстатья
- Автор: Kadymov V.
- Журнал: Mathematical Methods in the Applied Sciences, (Special Issure: Nonlinear Phenomena in Biology, Physics and Mechanics)
- Том: 38
- Номер: 16
- Год издания: 2015
- Первая страница: 1421
- Последняя страница: 1431
- Аннотация: The problem of plastic layer spreading between two converging surfaces of external bodies has been considering. To describe the mentioned processes A.Ilyushin proposed the two-dimensional, averaged over a layer thickness, mathematical model. On the basis of this model he formulated the boundary-value problem for general case (so called model for “viscous liquid”) which is described by nonlinear differential equations in partial derivatives of the second order .Then he proposed its simplified formulation on the case of “ideal liquid”, which is described by nonlinear differential equations in partial derivatives of the first order. The main results of conducted researches: 1. The new forms of evolution equation for determining the contour of freely spreading plastic layer on a plane have been obtained. It is shown that the evolution equation passes to the particular case of nonlinear heat equation. The new exact private solutions, which were obtained with the help of variables separation method and the method of using the self-similar variables, are presented.These methods allow us to transform the evolution equation in partial derivatives to the simpler form of ordinary differential equation. 2. The problem of plastic layer spreading in the domain of wedge form which is composed of two contacting media with different properties on the basis of simplified model is solved. The obtained solution for simplified model does not correctly describe the physical process because one of the conditions on the contact boundary between two plastic layers is not satisfied. For correct description you should use the general model of “viscous liquid”. 3. The experimental researches of spreading of the plastic layer in domain with fixed boundaries have been carried out. It is shown that the conducted experimental researches are impossible to describe with the help of exact solutions for the simplified model of ideal liquid. On the other hand, the indicated experimental results can be described on the basis of general model for “viscous liquid” and method of boundary layer, which have been presented in detail in author’s recently published research.
- Добавил в систему: Кадымов Вагид Ахмедович