Theoretical research on high-efficiency region in cryogenic micro flow heat transfer based on thermal and viscous Knudsen numbers

Abstract

Cryogenic micro flow heat transfer (CMFHT) has been increasingly interest nowadays due to the urgent needs of superconductive technology, quantum engineering, space cryocooler and other frontier fields. Chasing its high-efficiency region is a key challenge as thermal penetration depth is limited in cryogenic microscale. Therefore, this paper focuses on high-efficiency region in CMFHT, and newly proposes two parameters: thermal and viscous Knudsen numbers (KnT and Knv) based on traditional Knudsen number Kn, which can improve the errors on micro measurement and the inconveniences on high-efficiency region analysis induced by Kn. High-efficiency region is modeled by the three Knudsen numbers and is separated into slip or continuum type bounded by Kn = 0.001. The effects of gas species, temperature and pressure on KnT and Knv are studied and it is found that the reductions of both thermal penetration depth and the range between thermal and viscous penetration depths with temperature dropping deteriorate heat transfer at low temperature. After applicability validations based on opened literatures, it is suggested that in cryogenics ensuring Kn>KnT (L<δT) is put in the first for good heat transfer, and the next is trying the best to ensure Kn<Knv (L>δv) or making Kn and Knv as close as possible.