{"title":"Multiquadric RBF Method and Asymptotic Analysis to Study the Influence of Orientation on the Reaction Fronts Propagation","authors":"Y. Joundy, H. Rouah, A. Taik","doi":"10.1134/S1990478923040208","DOIUrl":null,"url":null,"abstract":"<p> In this work, we study the influence of orientation on the stability conditions of the\nreaction front where the monomer is solid and the polymer is liquid. The mathematical model\nincludes the heat equation, the concentration equation and the Navier–Stokes equation under the\nBoussinesq approximation. We use the method proposed by Zeldovich and Frank-Kamenetskii to\nperform asymptotic analysis. We then perform a stability analysis. The linearized problem is\nsolved numerically using a multiquadric radial basis function method (MQ-RBF) to find the\nstability boundary. This will allow us to deduce the influence of each control parameter of the\nproblem on this stability, in particular the angle of inclination of the experimental tube.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"943 - 955"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","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/S1990478923040208","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
In this work, we study the influence of orientation on the stability conditions of the
reaction front where the monomer is solid and the polymer is liquid. The mathematical model
includes the heat equation, the concentration equation and the Navier–Stokes equation under the
Boussinesq approximation. We use the method proposed by Zeldovich and Frank-Kamenetskii to
perform asymptotic analysis. We then perform a stability analysis. The linearized problem is
solved numerically using a multiquadric radial basis function method (MQ-RBF) to find the
stability boundary. This will allow us to deduce the influence of each control parameter of the
problem on this stability, in particular the angle of inclination of the experimental tube.
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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