Two-Layer Fluid Flows with Evaporation at an Interface in the Presence of an Anomalous Thermocapillary Effect
Abstract
Mathematical modeling of stationary convective flows with evaporation at an interface is carried out with the help of the exact solutions of the Boussinesq approximation of the Navier- Stokes equations for the two-dimensional case. The effects of thermodiffusion and diffusive heat conductivity in the gas-vapor layer are taken into consideration. The gas flow rate in the upper layer of the system is considered as a given. At the fixed impermeable walls of the channel the no-slip conditions for the velocity vector are fulfilled. The lower rigid boundary is assumed to be a heat insulated boundary. The constant heat flux is defined at the upper boundary of the channel. On the straight interface, being a thermocapillary boundary, the kinematic and dynamic conditions, the condition of heat transfer and the mass balance equations are satisfied. The vapor concentration saturation is defined as a sequence of the Clapeyron- Clausius equation, and a condition of zero vapor flux is assumed to be fulfilled at the upper rigid boundary. The constructed exact solutions can be applied for modeling of flows in two-layer gasliquid system for the case when a liquid has a property of the anomalous thermocapillary effect.
DOI 10.14258/izvasu(2015)1.2-18
Downloads
Metrics
References
Goncharova O.N., Hennenberg M., Rezanova E.V., Kabov O.A. Modeling of the convective fuid fows with evaporation in the two-layer systems // Interfacial Phenomena and Heat Transfer (IHMT). - 2013. - Vol. 1.
Гончарова О.Н., Резанова Е.В. Пример точного решения стационарной задачи о двухслойных течениях с испарением на границе раздела // Прикладная механика и техническая физика. - 2014. - №2.
Шлиомис М.И., Якушин В.И. Конвекция в двухслойной бинарной системе с испарением // Гидродинамика. - 1972. - №4.
Бирих Р.В О термокапиллярной конвекции в горизонтальном слое жидкости // Прикладная механика и техническая физика. - 1966. - №3.
Саночкин Ю.В. Некоторые задачи о термокапиллярном движении жидкости // ПМТФ. - 1989. - №5.
Попов В.В. Смешанная конвекция в двухслойной жидкости // Теоретические основы химической технологии. - 1981. - №XV (3).
Андреев В.К., Бекежанова В.Б. Устойчивость неизотермических жидкостей. - Красноярск, 2010.
Остроумов Г.А. Свободная конвекция в условиях внутренней задачи. - М. ; Л., 1952.
Андреев В.К., Гапоненко Ю.А., Гончарова О.Н., Пухначев В.В. Современные математические модели конвекции. - М., 2008.
Гебхарт Б., Джалурия Й., Махаджан Р., Саммакия Б. Свободноконвективные течения, тепло- и массообмен. - Кн. 1. - М., 1991.
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
