A study of transient flows of Newtonian fluids through micro-annuals with a slip boundary

Abstract

In this paper, we study the pressure gradient driven transient flow of an incompressible Newtonian liquid in micro-annuals under a Navier slip boundary condition. By using the Fourier series expansion in time and Bessel functions in space, an exact solution is derived and is shown to include some existing known results as special cases. By analysing the exact solution, it is found that the influences of boundary slip on the flow behaviour are qualitatively different for different types of pressure fields driving the flow. For pressure fields with a constant pressure gradient, the flow rate increases with the increase in the slip parameter l almost linearly when l is large; while, for pressure fields with a wave form pressure gradient within a certain frequency range, as the slip parameter l increases, the amplitude of the flow rate increases first and then approaches a constant value when l becomes sufficiently large. It is also found that to achieve a given flow rate, one could have different designs and the graphs for the design are presented and discussed in this paper.