Analysis of Unsteady Flow Through a Microtube With Wall Slip and Given Inlet Volume Flow Rate Variations

This study examines the effects of rarefaction of an unsteady flow through a microtube for a given but arbitrary inlet volume flow rate. Four cases of inlet volume flow rate proposed by Das and Arakeri (2000, ASME J. Appl. Mech., 67, pp. 274–281) are as follows: (1) trapezoidal piston motion, (2) constant acceleration, (3) impulsively started flow, and (4) impulsively blocked fully developed flow. During the analysis process, the Knudsen number (Kn) is used to represent the degree of rarefaction. The analytical results are presented graphically and compared to the results for a continuum under a no-slip condition. The effect of wall-slip became significant with the increasing degrees of rarefaction. The velocity in the boundary layer increased, whereas the velocity in the potential core of the microtube decreased, under the same condition. The influence of the rarefaction for the pressure gradient varied for the four cases.