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Continuum-based slip model and its validity for micro-channel flows. (English) Zbl 1159.74391

Summary: The low Mach number helium and nitrogen flows in micro-channels are investigated numerically with variations of inlet-to-outlet pressure ratios and aspect ratios by using different continuum-based slip models. Theoretical solutions based on perturbation expansions of the Navier-Stokes equations have been developed under different order slip conditions. The validity of slip models has been examined by the corresponding experiments and the DSMC method at different Knudsen numbers. Simulations have shown good predictions of the compressibility, rarefaction and thermal creep effects on micro-channel flows. The higher-order slip models relatively decrease the rarefaction effects comparing with a first-order slip model. Both the Knudsen number and the Reynolds numbers have been identified as key parameters which govern the rarefaction effects and thermal creep effects, respectively. The present slip models have been also demonstrated to be appropriate for micro-channel nitrogen flows with the Knudsen number less than 0.15, and the higher-order slip conditions improve the Navier-Stokes predictions in the slip flow regime with Knudsen number 0.08. However, the continuum-based slip models significantly under-predict the rarefaction effects in the transitional flow regime as the Knudsen number exceeds 0.2.

MSC:

74P05 Compliance or weight optimization in solid mechanics
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76M35 Stochastic analysis applied to problems in fluid mechanics
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