Eur. Phys. J. Plus (2018) 133: 272
https://doi.org/10.1140/epjp/i2018-12098-6

Regular Article

Analytical solution of a Maxwell fluid with slip effects in view of the Caputo-Fabrizio derivative^⋆

¹ School of Science, University of Management and Technology, Lahore, Pakistan
² E3MI, Département de Mathématiques, FST Errachidia Université Moulay Ismail, BP.509, Boutalamine 52000, Errachidia, Morocco
³ Department of Mathematics, Firat University, Elazığ, Turkey

^* e-mail: hammouch.zakia@gmail.com

Received: 18 November 2017
Accepted: 30 April 2018
Published online: 24 July 2018

Abstract

Couette flows of an incompressible Maxwell fluid with non-integer order derivative without singular kernel due to the motion of a bottom flat plate are analyzed under the slip boundary condition. An analytical transform approach is used to obtain the exact expressions for both velocity field and shear stress. Three particular cases from the general results with slip at the wall are obtained. These solutions, which are organized in simple forms in terms of exponential and trigonometric functions, can be conveniently engaged to obtain known solutions from the literature. The control of the new non-integer order derivative on the velocity and shear stress of the fluid is analyzed for some flows with practical applications. The non-integer order derivative with non-singular kernel is more appropriate for handling mathematical calculations of the obtained solutions.