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.
General
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