{"title":"MATHEMATICAL MODELLING ELECTRICALLY DRIVEN FREE SHEAR FLOWS IN A DUCT UNDER UNIFORM MAGNETIC FIELD","authors":"H. Kalis, I. Kangro","doi":"10.3846/mma.2024.19528","DOIUrl":null,"url":null,"abstract":"We consider a mathematical model of two-dimensional electrically driven laminar free shear flows in a straight duct under action of an applied uniform homogeneous magnetic field. The mathematical approach is based on studies by J.C.R. Hunt and W.E. Williams [10], Yu. Kolesnikov and H. Kalis [22,23]. We solve the system of stationary partial differential equations (PDEs) with two unknown functions of velocity U and induced magnetic field H. The flows are generated as a result of the interaction of injected electric current in liquid and the applied field using one or two couples of linear electrodes located on duct walls: three cases are considered. In dependence on direction of current injection and uniform magnetic field, the flows between the end walls are realized. Distributions of velocities and induced magnetic fields, electric current density in dependence on the Hartmann number Ha are studied. The solution of this problem is obtained analytically and numerically, using the Fourier series method and Matlab.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3846/mma.2024.19528","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a mathematical model of two-dimensional electrically driven laminar free shear flows in a straight duct under action of an applied uniform homogeneous magnetic field. The mathematical approach is based on studies by J.C.R. Hunt and W.E. Williams [10], Yu. Kolesnikov and H. Kalis [22,23]. We solve the system of stationary partial differential equations (PDEs) with two unknown functions of velocity U and induced magnetic field H. The flows are generated as a result of the interaction of injected electric current in liquid and the applied field using one or two couples of linear electrodes located on duct walls: three cases are considered. In dependence on direction of current injection and uniform magnetic field, the flows between the end walls are realized. Distributions of velocities and induced magnetic fields, electric current density in dependence on the Hartmann number Ha are studied. The solution of this problem is obtained analytically and numerically, using the Fourier series method and Matlab.
我们考虑的是在外加均匀均质磁场作用下，直管中二维电驱动层流自由剪切流的数学模型。数学方法基于 J.C.R. Hunt 和 W.E. Williams [10]、Yu.Kolesnikov 和 H. Kalis [22,23]的研究为基础。我们求解的是速度 U 和诱导磁场 H 两个未知函数的静态偏微分方程 (PDE)系统。液体中的注入电流与位于管道壁上的一个或两个线性电极耦合的外加磁场相互作用产生流动：我们考虑了三种情况。根据电流注入方向和均匀磁场，实现了端壁之间的流动。研究了速度和感应磁场的分布，以及取决于哈特曼数 Ha 的电流密度。利用傅立叶级数法和 Matlab，对该问题进行了分析和数值求解。
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