Effects of rarefaction, viscous dissipation and rotation mode on the first and second law analyses of rarefied gaseous slip flows confined between a rotating shaft and its concentric housing

摘要

A parametric analytical study is carried out to scrutinize the mechanism of fluid flow, heat transfer and entropy generation in a low-speed rarefied gaseous flow confined between a shaft and its concentric housing, i.e., the cylindrical Couette flow. In the first law analysis, closed form solutions for the radial temperature profiles are obtained by incorporating the calculated velocity distribution into the energy equation. The derivations for three thermal cases, which are founded on imposing different thermal conditions, namely, the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT) boundary conditions, are presented. In the second law analysis, the contributions of thermal diffusion and fluid friction irreversibility to the total entropy generation in the micro domain are illustrated, and the relevant expressions for the Bejan number and the entropy generation number as well as the average entropy generation rate are derived. Finally, the variations of major variables with influential parameters such as the Knudsen number, the Brinkman number and rotation mode are investigated to elucidate the associated effects of rarefaction phenomenon, viscous dissipation and geometric condition on the characteristics of the flow.