Abstract-The heat transfer processis simulated in a nano-sized cone-shaped cathode. A model of heat transfer is constructed using the phase field system and theNottingham effect. We considerinfluence of the free boundary curvature and the Nottingham effect on the heat balance in the cathode.

This paper presents the results of mathematical modeling of heat transfer in the field emission process in a conic cathode of small dimensions with its possible melting considered. It is shown that the possibility of melting is determined by the cathode vertex angle. The melting is modeled in the framework of the phase field system using the proposed methods for the formation of the liquid phase zone.

This book series publishes monographs and professional books in all fields of heat and mass transfer, presenting the interrelationships between scientific foundations, experimental techniques, model-based analysis of results and their transfer to technological applications. The authors are all leading experts in their fields.Heat and Mass Transfer addresses professionals and researchers, students and teachers alike. It aims to provide both basic knowledge and practical solutions, while also fostering discussion and drawing attention to the synergies that are essential to start new research projects.

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