Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 416837, 17 pages
doi:10.1155/2010/416837
Research Article

Unsteady Unidirectional Flow of Second-Grade Fluid through a Microtube with Wall Slip and Different Given Volume Flow Rate

Cha'o-Kuang Chen, Hsin-Yi Lai, and Wei-Fan Chen

Department of Mechanical Engineering, National Cheng Kung University, No.1, University Road, Tainan 70101, Taiwan

Received 9 March 2010; Accepted 3 August 2010

Academic Editor: Saad A. Ragab

Copyright © 2010 Cha'o-Kuang Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The second-grade flows through a microtube with wall slip are solved by Laplace transform technique. The effects of rarefaction and elastic coefficient are considered with an unsteady flow through a microtube for a given but arbitrary inlet volume flow rate with time. Five cases of inlet volume flow rate are as follows: (1) trapezoidal piston motion, (2) constant acceleration, (3) impulsively started flow, (4) impulsively blocked fully developed flow, and (5) oscillatory flow. The results obtained are compared to those solutions under no-slip and slip condition.