{"title":"铝电解槽的磁流体动力学平衡","authors":"M.V. Romerio, M.-A. Secrétan","doi":"10.1016/0167-7977(86)90002-X","DOIUrl":null,"url":null,"abstract":"<div><p>The stationary states of an electrolytic cell for aluminium production are studied for a special case in which one of the dimensions (<em>x</em><sub>3</sub> direction) is infinite.</p><p>The system is assumed to be invariant for the translations in the <em>x</em><sub>3</sub> direction; its finiteness is simulated through additional conditions on flow rates and external forces.</p><p>The problem is considered in the frame of magnetohydrodynamic theory.</p><p>With the above assumption the set of equations, satisfied by the velocity, electric potential, magnetic and pressure fields, yields a unique solution, characterized by an absence of motion in the sections orthogonal to <em>x</em><sub>3</sub>.</p><p>A weak formulation of the equations for the different fields is derived. It constitutes the basis for a discrete approximation by a finite element method.</p><p>Computations on a realistic cell are discussed.</p></div>","PeriodicalId":100318,"journal":{"name":"Computer Physics Reports","volume":"3 6","pages":"Pages 327-359"},"PeriodicalIF":0.0000,"publicationDate":"1986-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0167-7977(86)90002-X","citationCount":"6","resultStr":"{\"title\":\"Magnetohydrodynamics equilibrium in aluminium electrolytic cells\",\"authors\":\"M.V. Romerio, M.-A. Secrétan\",\"doi\":\"10.1016/0167-7977(86)90002-X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The stationary states of an electrolytic cell for aluminium production are studied for a special case in which one of the dimensions (<em>x</em><sub>3</sub> direction) is infinite.</p><p>The system is assumed to be invariant for the translations in the <em>x</em><sub>3</sub> direction; its finiteness is simulated through additional conditions on flow rates and external forces.</p><p>The problem is considered in the frame of magnetohydrodynamic theory.</p><p>With the above assumption the set of equations, satisfied by the velocity, electric potential, magnetic and pressure fields, yields a unique solution, characterized by an absence of motion in the sections orthogonal to <em>x</em><sub>3</sub>.</p><p>A weak formulation of the equations for the different fields is derived. It constitutes the basis for a discrete approximation by a finite element method.</p><p>Computations on a realistic cell are discussed.</p></div>\",\"PeriodicalId\":100318,\"journal\":{\"name\":\"Computer Physics Reports\",\"volume\":\"3 6\",\"pages\":\"Pages 327-359\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0167-7977(86)90002-X\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Physics Reports\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/016779778690002X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Reports","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/016779778690002X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Magnetohydrodynamics equilibrium in aluminium electrolytic cells
The stationary states of an electrolytic cell for aluminium production are studied for a special case in which one of the dimensions (x3 direction) is infinite.
The system is assumed to be invariant for the translations in the x3 direction; its finiteness is simulated through additional conditions on flow rates and external forces.
The problem is considered in the frame of magnetohydrodynamic theory.
With the above assumption the set of equations, satisfied by the velocity, electric potential, magnetic and pressure fields, yields a unique solution, characterized by an absence of motion in the sections orthogonal to x3.
A weak formulation of the equations for the different fields is derived. It constitutes the basis for a discrete approximation by a finite element method.
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