N. V. Burmasheva, E. Yu. Prosviryakov
EXACT SOLUTIONS FOR NATURAL CONVECTION OF LAYERED FLOWS OF A VISCOUS INCOMPRESSIBLE FLUID WITH SPECIFIED TANGENTIAL FORCES AND THE LINEAR DISTRIBUTION OF TEMPERATURE ON THE LAYER BOUNDARIES
DOI: 10.17804/2410-9908.2017.4.016-031 A new exact solution of the Oberbeck-Boussinesq equations for the convective flow of a viscous incompressible fluid is considered. Layered flows of a viscous incompressible fluid are investigated within the class of the Sidorov-Lin exact solutions, which generalizes the family of the Ostroumov-Birikh solutions. The use of an exact solution allows an overdetermined system of fluid motion equations to be solved. The fluid is heated by setting a heat source at both boundaries. The dimension of the studied boundary value problem cannot be lowered by the transformation of the rotation. The obtained exact solution describes the counterflow in the fluid. Thermocline and a boundary layer occur near one of the boundary layers in the fluid flow.
Acknowledgement: This work was supported by the Foundation for Assistance to Small Innovative Enterprises in Science and Technology (the UMNIK program); the agreement no. 12281 GU/2017. Keywords: layered flow, exact solution, counterflows References:
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Н. В. Бурмашева, Е. Ю. Просвиряков
ТОЧНЫЕ РЕШЕНИЯ ДЛЯ ЕСТЕСТВЕННОЙ КОНВЕКЦИИ СЛОИСТЫХ ТЕЧЕНИЙ ВЯЗКОЙ НЕСЖИМАЕМОЙ ЖИДКОСТИ ПРИ ЗАДАНИИ ТАНГЕНЦИАЛЬНЫХ СИЛ И ЛИНЕЙНОГО РАСПРЕДЕЛЕНИЯ ТЕМПЕРАТУРЫ НА ГРАНИЦАХ СЛОЯ
В статье рассмотрено новое точное решение уравнений Обербека-Буссинеска для конвективного течения вязкой несжимаемой жидкости. Слоистые течения вязкой несжимаемой жидкости исследуются в рамках класса точных решений Сидорова-Линя, обобщающего семейство решений Остроумова-Бириха. Использование точного решения позволяет разрешить переопределенную систему уравнений движения жидкости. Нагрев жидкости осуществляется посредством задания источника тепла на обеих границах. Размерность изучаемой краевой задачи не может быть понижена преобразованием поворота. Полученное точное решение описывает противотечения в жидкости. При течении жидкости возникает термоклин и пограничный слой вблизи одной из границ слоя.
Благодарность: Работа выполнена при поддержке фонда содействия развитию малых форм предприятий в научно-технической сфере (программа УМНИК), договор № 12281ГУ/2017. Ключевые слова: слоистое течение, точное решение, противотечения Библиография:
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Библиографическая ссылка на статью
Burmasheva N. V., Prosviryakov E. Yu. Exact Solutions for Natural Convection of Layered Flows of a Viscous Incompressible Fluid with Specified Tangential Forces and the Linear Distribution of Temperature on the Layer Boundaries // Diagnostics, Resource and Mechanics of materials and structures. -
2017. - Iss. 4. - P. 16-31. - DOI: 10.17804/2410-9908.2017.4.016-031. -
URL: http://dream-journal.org/issues/content/article_145.html (accessed: 21.12.2024).
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