Eur. Phys. J. Plus (2018) 133: 224
https://doi.org/10.1140/epjp/i2018-11857-7

Regular Article

Soret effects on simultaneous heat and mass transfer in MHD viscous fluid through a porous medium with uniform heat flux and Atangana-Baleanu fractional derivative approach

¹ Department of Mathematics, University of Management and Technology Lahore, C-II Johar Town, 54700, Lahore, Pakistan
² Basic Sciences Department, College of Engineering Majmaah University, P.O. Box 66, 11952, Majmaah, Saudi Arabia

^* e-mail: imran.asjad@umt.edu.pk

Received: 29 November 2017
Accepted: 5 January 2018
Published online: 14 June 2018

Abstract

The present paper is about the application of a non-local and non-singular fractional derivative to the unsteady flow of incompressible MHD viscous fluid with uniform heat flux through a porous medium. In addition the Soret, radiation, heat sink and chemical reaction effects were also applied to this physical model. The transport model of an ordinary derivative can be extended to the fractional model of a non-integer order derivative with non-local and non-singular kernel. The Laplace transform was used to obtain the expressions for temperature, concentration and velocity fields in non-dimensional form and numerical techniques were used to obtain the inverse Laplace transform for these expressions. At the end, influence of flow parameters on temperature, concentration and velocity fields have been discussed and explained graphically. As a result, the flow behavior can be enhanced with the non-integer order fractional parameter of non-local and non-singular kernel.