Mathematical Modeling of Emission in Small-Size Cathode

Vladimir Danilov, Roman Gaydukov, Vadim Kretov, et al.

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Springer Singapore img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Theoretische Physik

Beschreibung

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.​

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Schlagwörter

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