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Unsteady axisymmetric boundary-layer equations: Transformations, properties, exact solutions, order reduction and solution methodстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 4 января 2018 г.
- Авторы: Polyanin Andrei D., Zhurov Alexei I.
- Журнал: International Journal of Non-Linear Mechanics
- Том: 74
- Год издания: 2015
- Издательство: Pergamon Press Ltd.
- Местоположение издательства: United Kingdom
- Первая страница: 40
- Последняя страница: 50
- DOI: 10.1016/j.ijnonlinmec.2015.03.007
- Аннотация: The paper deals with equations describing the unsteady axisymmetric boundary layer on a body of revolution. The shape of the body is assumed to be arbitrary. The axisymmetric boundary-layer equation for the stream function is shown to reduce to a plane boundary-layer equation with a streamwise-coordinate-dependent viscosity of the form w(tz)+w(z)w(xz)-w(x)w(zz)=nu r(2)(x)w(zzz)+F(t,x). We describe a number of new generalized and functional separable solutions to this non-linear equation, which depend on two to five arbitrary functions. The solutions are obtained with a new method (direct method of functional separation of variables) based on using particular solutions to an auxiliary ODE. Many of the solutions are expressed in terms of elementary functions, provided that the arbitrary functions are also elementary. Two theorems are stated that enable one to generalize exact solutions of unsteady axisymmetric boundary-layer equations by including additional arbitrary functions. Furthermore, we specify a von Mises-type transformation that reduces the unsteady axisymmetric boundary-layer equation to a non-linear second-order PDE. We also present several new exact solutions to the plane boundary-layer equation and solve a boundary layer problem for a non-uniformly heated flat plate in a unidirectional fluid flow with temperature dependent viscosity. The method proposed in this paper can also be effective for constructing exact solutions to many other non-linear PDEs.
- Добавил в систему: Левитин Александр Леонидович
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | Unsteady_axisymmetric_boundary-layer_equations.pdf | 404,4 КБ | 14 декабря 2018 [Andrey_Bryzgalov] |