Effect of Second Order Velocity-Slip/Temperature-Jump on Basic Gaseous Fluctuating Micro-Flows

In this work, the effect of the second-order term to the velocity-slip/temperature-jump boundary conditions on the solution of four cases in which the driving force is fluctuating harmonically was studied. The study aims to establish criteria that secure the use of the first order velocity-slip/temperature-jump model boundary conditions instead of the second-order ones. The four cases studied were the transient Couette flow, the pulsating Poiseuille flow, Stoke’s second problem, and the transient natural convection flow. It was found that at any given Kn number, increasing the driving force frequency, increases the difference between the first and second-order models. Assuming that a difference between the two models of over 5% is significant enough to justify the use of the more complex second-order model, the critical frequencies for the four different cases were found. For the cases for which the flow is induced by the fluctuating wall as in cases 1 and 3, we found that critical frequency at $Kn=0.1$ to be $ω=8.$ For the cases of flow driven by a fluctuating pressure gradient as in case 2, this frequency was found to be $ω=1$⁠, at the same Kn number. In case 4, for the temperature-jump model, the critical frequency was found to be $ω=7$ and for the velocity-slip model the critical frequency at the same Kn number was found to be $ω=1.35$⁠.