Eur. Phys. J. Plus (2018) 133: 127
https://doi.org/10.1140/epjp/i2018-11981-4

Regular Article

Influence of non-integer-order derivatives on unsteady unidirectional motions of an Oldroyd-B fluid with generalized boundary conditions

¹ Department of Mathematics, GC University, Lahore, Pakistan
² Department of Mathematics, University of Management and Technology, Lahore, Pakistan
³ Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

^* e-mail: Bilalsehole@gmail.com

Received: 13 January 2018
Accepted: 23 February 2018
Published online: 27 March 2018

Abstract

The objective of this article is to study some unsteady Couette flows of an Oldroyd-B fluid with non-integer derivatives. The fluid fills an annular region of two infinite co-axial circular cylinders. Flows are due to the motion of the outer cylinder, that rotates about its axis with an arbitrary time-dependent velocity while the inner cylinder is held fixed. Closed form solutions of dimensionless velocity field and tangential tension are obtained by means of the finite Hankel transform and the theory of Laplace transform for fractional calculus. Several results in the literature including the rotational flows through an infinite cylinder can be obtained as limiting cases of our general solutions. Finally, the control of the fractional framework on the dynamics of fluid is analyzed by numerical simulations and graphical illustrations.