Eur. Phys. J. Plus (2016) 131: 310
https://doi.org/10.1140/epjp/i2016-16310-5

Regular Article

Solutions with special functions for time fractional free convection flow of Brinkman-type fluid

¹ Department of Mathematics, City University of Science and Information Technology, 25000, Peshawar, Pakistan
² Basic Engineering Sciences Department, College of Engineering Majmaah University, 11952, Majmaah, Saudi Arabia

^* e-mail: farhadaliecomaths@yahoo.com

Received: 20 June 2016
Revised: 27 July 2016
Accepted: 9 August 2016
Published online: 9 September 2016

Abstract

The objective of this paper is to report the combined effect of heat and mass diffusion on time fractional free convectional incompressible flow of Brinkman-type fluid over an oscillating plate in the presence of first-order chemical reaction. The Laplace transform has been used to obtain the exact solutions for the fractional-order distributions. Exact expressions for temperature, concentration and velocity have been presented in terms of special functions. For instance, we presented temperature in terms of Wright function, concentration in the form of Fox-H function and velocity in terms of Mittag-Leffler and general Wright functions. The effects of various physical parameters on the fluid motion are sketched and discussed graphically. The present solutions have been reduced by taking one or more parameters approaching to zero and an excellent agreement is observed with the published work. The numerical results for skin-friction, Nusselt and Sherwood numbers have been shown in tabular form.