{"title":"The Structure of a Two-Layer Flow in a Channel\nwith Radial Heating of the Lower Substrate\nfor Small Marangoni Numbers","authors":"V. K. Andreev, M. V. Efimova","doi":"10.1134/S1990478924020017","DOIUrl":null,"url":null,"abstract":"<p> The three-dimensional flow of a system of a viscous heat-conducting fluid and a binary\nmixture with a common interface in a layer bounded by solid walls is studied. A radial\ntime-varying temperature distribution is specified on the lower substrate; the upper wall is\nassumed to be thermally insulated. Assuming a small Marangoni number, the structure of\na steady-state flow is described depending on the layer thickness ratio and taking into account the\ninfluence of mass forces. The solution of the nonstationary problem is determined in Laplace\ntransforms by quadratures. It is shown that if the given temperature on the lower substrate\nstabilizes over time, then with increasing time the solution reaches the resulting steady-state mode\nonly under certain conditions on the initial distribution of concentrations in the mixture.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 2","pages":"179 - 191"},"PeriodicalIF":0.5800,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924020017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The three-dimensional flow of a system of a viscous heat-conducting fluid and a binary
mixture with a common interface in a layer bounded by solid walls is studied. A radial
time-varying temperature distribution is specified on the lower substrate; the upper wall is
assumed to be thermally insulated. Assuming a small Marangoni number, the structure of
a steady-state flow is described depending on the layer thickness ratio and taking into account the
influence of mass forces. The solution of the nonstationary problem is determined in Laplace
transforms by quadratures. It is shown that if the given temperature on the lower substrate
stabilizes over time, then with increasing time the solution reaches the resulting steady-state mode
only under certain conditions on the initial distribution of concentrations in the mixture.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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