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`Advances in Mathematical PhysicsVolume 2017, Article ID 9724381, 10 pageshttps://doi.org/10.1155/2017/9724381`
Research Article

## Unsteady Helical Flows of a Size-Dependent Couple-Stress Fluid

1Department of Computer Sciences, Air University Multan Campus, Multan, Pakistan
2Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3Department of Mathematics, University of Management and Technology, Sialkot Campus, Pakistan
4Department of Management Sciences, Air University Multan Campus, Multan, Pakistan

Correspondence should be addressed to Qammar Rubbab; moc.liamg@rammaqbabur

Received 1 December 2016; Accepted 15 January 2017; Published 8 February 2017

Academic Editor: John D. Clayton

Copyright © 2017 Qammar Rubbab 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 helical flows of couple-stress fluids in a straight circular cylinder are studied in the framework of the newly developed, fully determinate linear couple-stress theory. The fluid flow is generated by the helical motion of the cylinder with time-dependent velocity. Also, the couple-stress vector is given on the cylindrical surface and the nonslip condition is considered. Using the integral transform method, analytical solutions to the axial velocity, azimuthal velocity, nonsymmetric force-stress tensor, and couple-stress vector are obtained. The obtained solutions incorporate the characteristic material length scale, which is essential to understand the fluid behavior at microscales. If characteristic length of the couple-stress fluid is zero, the results to the classical fluid are recovered. The influence of the scale parameter on the fluid velocity, axial flow rate, force-stress tensor, and couple-stress vector is analyzed by numerical calculus and graphical illustrations. It is found that the small values of the scale parameter have a significant influence on the flow parameters.