Numerical analysis of laminar flow in micro-tubes with a slip boundary

Abstract

Investigated numerically are the effects of slip and viscous heat dissipation on the friction number of thermally developing laminar water flow in micro-tubes. Also investigated are the effects of the micro-tube diameter, D, aspect ratio, L/ D, and Reynolds number on the friction number. The decrease in the dynamic viscosity slightly decreases the friction number below that of the Hagen–Poiseuille, determined from the solution of the Navier–Stokes equations assuming thermally and hydro-dynamically fully developed flow and constant fluid properties. A slip at the wall decreases the friction number with increased L/ D and decreased D. Results confirmed that the flow in micro-tubes is never thermally developed, significantly increasing the friction number with increased Reynolds number beyond critical values. Below the critical Reynolds numbers, the effect of the thermally developing flow is negligible and the friction numbers in micro-tubes is almost identical to those of the Hagen–Poiseuille, with and without slip at the wall. The comparison with reported experimental data confirmed the results of the present analysis.