Eur. Phys. J. Plus (2018) 133: 500
https://doi.org/10.1140/epjp/i2018-12315-4

Regular Article

Fractional-order three-dimensional thin-film nanofluid flow on an inclined rotating disk

Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, Pakistan

^* e-mail: altafdir@gmail.com

Received: 26 June 2018
Accepted: 11 October 2018
Published online: 10 December 2018

Abstract

The aim of the present study is to examine the fractional-order three-dimensional thin-film nanofluid flow over an inclined rotating plane. The basic governing equations are transformed through similarity variables into a set of first-order differential equations. The Caputo derivatives have been used to transform the first-order differential equations into a system of fractional differential equations. The Adams-type predictor-corrector method for the numerical solution of the fractional-differential-equations method has been used for the solution of the fractional-order differential. The classical solution of the problem has been obtained through the RK4 method. The comparison of the classical- and fractional-order results has been made for the various embedded parameters like variable thickness, unsteadiness parameter, Prandtl number, Schmidt number, Brownian-motion parameter and thermophoretic parameter. The important terms of the Nusselt number and Sherwood number have also been analysed physically and numerically for both classical and fractional order.