Eur. Phys. J. Plus (2017) 132: 380
https://doi.org/10.1140/epjp/i2017-11651-1

Regular Article

Analysis of unsteady natural convective radiating gas flow in a vertical channel by employing the Caputo time-fractional derivative

¹ Department of Mathematics, Islamia College University Peshawar Khyber Pakhtunkhwa, 25000, Peshawar, Pakistan
² Abdus Salam School of Mathematical Sciences, GC University, 54600, Lahore, Pakistan

^* e-mail: bakhtiarahmad881@gmail.com

Received: 2 June 2017
Accepted: 17 July 2017
Published online: 6 September 2017

Abstract

In this paper the exact solution of the unsteady natural convection radiating flow in an open ended vertical channel is studied. The channel is stationary with non-uniform temperature. The governing equations are fractional differential equations with the Caputo time-fractional derivative. Closed form analytical solutions for the temperature and velocity fields are obtained by using the Laplace transform technique. These solutions are expressed with the Wright function, the Robotnov and Hartley function. The effects of the fractional order and physical parameters on temperature and fluid velocity are presented graphically.