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Mathematical Models for Eddy Currents and Magnetostatics

With Selected Applications

  • Book
  • © 2014

Overview

Authors:
  1. Rachid Touzani

    1. Universite Blaise Pascal, Clermont-Ferrand, France

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  2. Jacques Rappaz

    1. Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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    You can also search for this author in PubMed   Google Scholar

  • Thorough description of eddy current processes from an applied mathematics perspective
  • Contains a large list of industrial applications with their mathematical formulations
  • Addresses the mathematical analysis of coupled problems involving eddy currents
  • Includes supplementary material: sn.pub/extras

Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
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  2. Eddy Current Models

    1. Front Matter

      Pages 1-1
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    2. Mathematical Framework

      • Rachid Touzani, Jacques Rappaz
      Pages 3-38

    3. Maxwell and Eddy Current Equations

      • Rachid Touzani, Jacques Rappaz
      Pages 39-54

    4. Two-Dimensional Models

      • Rachid Touzani, Jacques Rappaz
      Pages 55-77

    5. Three-Dimensional Models

      • Rachid Touzani, Jacques Rappaz
      Pages 79-101

    6. Axisymmetric Models

      • Rachid Touzani, Jacques Rappaz
      Pages 103-127

    7. Eddy Current Models with Thin Inductors

      • Rachid Touzani, Jacques Rappaz
      Pages 129-152

    8. Numerical Methods

      • Rachid Touzani, Jacques Rappaz
      Pages 153-194

  3. Selected Applications

    1. Front Matter

      Pages 195-195
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    2. Induction Heating Processes

      • Rachid Touzani, Jacques Rappaz
      Pages 197-219

    3. Magnetohydrodynamics and Magnetic Shaping

      • Rachid Touzani, Jacques Rappaz
      Pages 221-242

    4. Inductively Coupled Plasma Torches

      • Rachid Touzani, Jacques Rappaz
      Pages 243-253

    5. Ferromagnetic Shielding

      • Rachid Touzani, Jacques Rappaz
      Pages 255-269

    6. The Electrolytic Process for Aluminium Production

      • Rachid Touzani, Jacques Rappaz
      Pages 271-290

  4. Back Matter

    Pages 291-305
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Keywords

About this book

This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problems are given. Related issues such as convergence of the approximations and error estimates are discussed. The second part of the monograph presents various coupled problems that involve eddy current or magnetostatic problems, in particular magneto-hydrodynamic problems and magnetic shaping problems concerning the melt flow of electrically conducting metals, induction heating processes, inductively coupled plasmas and ferromagnetic screening modeling. The presentation of each model comes with numerical illustration from industrial applications.

Reviews

From the book reviews:

“This textbook is devoted to the mathematical modeling and the efficient numerical solution of magnetostatic and eddy current problems. … The book is directed to applied mathematicians, and to researchers and developers in electric and electrotechnical engineering as well.” (Johannes Elschner, zbMATH, Vol. 1288, 2014)

Authors and Affiliations

  • Universite Blaise Pascal, Clermont-Ferrand, France

    Rachid Touzani

  • Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jacques Rappaz

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