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Mathematical Modeling of Emission in Small-Size Cathode

  • Vladimir Danilov
  • Roman Gaydukov
  • Vadim Kretov

Part of the Heat and Mass Transfer book series (HMT)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Vladimir Danilov, Roman Gaydukov, Vadim Kretov
    Pages 1-10
  3. Vladimir Danilov, Roman Gaydukov, Vadim Kretov
    Pages 11-58
  4. Vladimir Danilov, Roman Gaydukov, Vadim Kretov
    Pages 59-130
  5. Vladimir Danilov, Roman Gaydukov, Vadim Kretov
    Pages 131-194

About this book

Introduction

This book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account.  This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems. The approach used is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the mathematical model including its parallel implementation. The results of numerical simulation concludes the book. The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.​

Keywords

Thermo-field emission Heat transfer Melting and solidification Phase-field system Numerical simulation Nottingham effect Stefan-Gibbs-Thomson problem Specific conductance Electron heat conductivity Support function in metals Electron tunneling Hugoniot-type conditions Heat conduction equation

Authors and affiliations

  • Vladimir Danilov
    • 1
  • Roman Gaydukov
    • 2
  • Vadim Kretov
    • 3
  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.National Research University Higher School of EconomicsMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-15-0195-1
  • Copyright Information Springer Nature Singapore Pte Ltd. 2020
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering
  • Print ISBN 978-981-15-0194-4
  • Online ISBN 978-981-15-0195-1
  • Series Print ISSN 1860-4846
  • Series Online ISSN 1860-4854
  • Buy this book on publisher's site