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ORIGINAL PAPER
Exact Solutions for Fractionalized Second Grade Fluid Flows with Boundary Slip Effects
1
Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, 67480, Nawabshah, Pakistan
2
Department of Electrical Engineering, Quaid-e-Awam University of Engineering, Science and Technology, 67480, Nawabshah, Pakistan
3
Department of Business Administration, Shaheed Benazir Bhutto University, 67480, Nawabshah, Pakistan
Online publication date: 2021-01-29
Publication date: 2021-03-01
International Journal of Applied Mechanics and Engineering 2021;26(1):88-103
KEYWORDS
ABSTRACT
In this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under the influence of slip has been obtained. A coupled system of partial differential equations representing the equation of motion has been re-written in terms of fractional derivatives form by using the Caputo fractional operator. The Discrete Laplace transform method has been employed for computing the expressions for the velocity field u(y, t) and the corresponding shear stress τ (y, t). The obtained solutions for the velocity field and the shear stress have been written in terms of Wright generalized hypergeometric function pψq and are expressed as a sum of the slip contribution and the corresponding no-slip contribution. In addition, the solutions for a fractionalized, ordinary second grade fluid and Newtonian fluid in the absence of slip effect have also been obtained as special case. Finally, the effect of different physical parameters has been demonstrated through graphical illustrations.
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