Summary
The effect of frequency of fluctuation of the driving force on velocity slip and temperature jump at the wall(s) is theoretically investigated in four cases of basic gas micro-flow problems. The cases considered are the transient Couette flow, the pulsating Poiseuille flow, the Stoke's second problem flow and the transient natural convection flow. The formulation of the problem revealed that the controlling parameter of the problem is a combination of Knudsen number (Kn) and frequency of fluctuation (ω) in the form of an effective Knudsen number, 
that replaced the usual Knudsen number (Kn), and consequently the slip flow regime is found to be valid when 10-3≤ Kneff≤ 10-1. It is found that when the frequency is small the velocity and temperature profiles are similar to the corresponding classical macro-flow profiles at zero frequency. Also, the slip in velocity and the jump in temperature increase as the Knudsen number and/or the frequency of the driving force increases. In addition, the slip in velocity and the jump in temperature are found to be negligible when the frequency and/or Kn are sufficiently small.
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Haddad, O.M., Al-Nimr, M.A. & Abuzaid, M.M. The effect of frequency of fluctuating driving force on basic gaseous micro-flows. Acta Mechanica 179, 249–259 (2005). https://doi.org/10.1007/s00707-005-0237-z
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DOI: https://doi.org/10.1007/s00707-005-0237-z