Mathematical Modeling of Flows with Evaporation in a Two-layer System with a Thermally Insulated Upper Boundary
Abstract
The problem of two-layer flow in an infinite horizontal channel with solid impermeable walls is studied. The upper boundary of the system is considered to be thermally insulated, and the longitudinal gradient of the temperature on the lower boundary is given. The lower layer is filled with a liquid that evaporates through the thermocapillary interface; the upper layer is a gas–vapor mixture. Stationary flows induced by action of gas flow in the upper layer and longitudinal temperature gradient are studied. The thermodiffusion and diffusive thermal conductivity effects are taken into account in the gas–vapor mixture. The mathematical model is based on the Boussinesq approximation of the Navier–Stokes equations, and the diffusion equation also holds for the upper layer. The exact solutions of a special type are constructed, where only the longitudinal velocity differs from zero and depends on the transverse coordinate, and the temperature and the vapor concentration are linearly dependent on the longitudinal coordinate. Evaporation of the liquid is taken into consideration using the mass balance and heat transfer conditions. Velocity and temperature profiles for liquid-gas systems such as "ethanol-air"and "HFE7100-nitrogen"are presented. The phenomenon of return flows near the interface is investigated.
DOI 10.14258/izvasu(2017)4-16
Downloads
Metrics
References
Бирих Р.В. О термокапиллярной конвекции в горизонтальном слое жидкости // ПМТФ. - 1966. - № 3.
Остроумов Г.А. Свободная конвекция в условиях внутренней задачи. — М. ; Л., 1952.
Пухначев В.В. Нестационарные аналоги решения Бириха // Известия Алтайского гос. унта. — 2011. — № 1/2(69).
Goncharova O.N., Kabov O.A., Pukhnachov V.V. Solutions of special type describing the three dimensional thermocapillary flows with an interface // International Journal of Heat and Mass Transfer. — 2012. — Vol. 55, Issue 4.
Аристов С.Н., Просвиряков Е.Ю. О слоистых течениях плоской свободной конвекции // Нелинейная динамика. — 2013. — № 4.
Шлиомис М.И., Якушин В.И. Конвекция в двухслойной бинарной системе с испарением // Гидродинамика. — 1972. — № 4.
Гончарова О.Н., Резанова Е.В. Пример точного решения станционарной задачи о двухслойных течениях с испарением на границе раздела // ПМТФ. — 2014. — Т. 55, № 2.
Гончарова О.Н., Резанова Е.В., Люлин Ю.В., Кабов О.А. Моделирование двухслойных течений жидкости и газа с учетом испарения // Теплофизика и аэромеханика.— 2015. — Т. 22, № 5.
Резанова Е.В., Шефер И.А. О влиянии тепловой нагрузки на характеристики течения с испарением // СибЖИМ.— 2017. — № 2(70).
Bekezhanova V.B. Three-dimensional disturbances of a plane-parallel two-layer flow of a viscous, heat-conducting fluid //Fluid Dynamics. — 2012. — Vol. 47, №6.
Андреев В.К., Бекежанова В.Б. Устойчивость неизотермических жидкостей. — Красноярск, 2010.
Андреев В.К., Гапоненко Ю.А., Гончарова О.Н., Пухначев В.В. Современные математические модели конвекции. — М., 2008.
Пригожин И. Химическая термодинамика. — Новосибирск, 1966.
Ghezzehei T.A., Trautz R.C., Finsterle S. et al. Modeling coupled evaporation and seepage in ventilated cavities // Vadoze Zone J.— 2004. — Vol. 3, № 3.
Равдель А.А., Пономарева А.М. Краткий справочник физико-химических величин. — СПб., 1998.
Tuma P.E. Using segregated HFEs as heat transfer fluids — avoiding problems in system design // Chemical Processing. — 2001.
Copyright (c) 2017 Д.В. Дягель, Е.В. Резанова
This work is licensed under a Creative Commons Attribution 4.0 International License.
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).
