Transient Electro-osmotic Slip Flow of an Oldroyd-B Fluid with Time-fractional Caputo-Fabrizio Derivative

Abstract

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally, Stehfest’s algorithm is used for inverse Laplace transform. The solutions for fractional Maxwell, ordinary Maxwell and ordinary Newtonian fluids are obtained as limiting cases of the obtained solution. Finally, the influence of fractional and some important physical parameters on the fluid flow are spotlighted graphically.

Keywords

• Electro-osmotic flow
• Slip boundary condition
• Oldroyd-B fluid
• Time-fractional Caputo-Fabrizio derivative
• Stehfest’s algorithm