Eur. Phys. J. Plus (2017) 132: 340
https://doi.org/10.1140/epjp/i2017-11606-6

Regular Article

Heat transfer analysis of fractional second-grade fluid subject to Newtonian heating with Caputo and Caputo-Fabrizio fractional derivatives: A comparison

¹ Department of Mathematics, University of Management and Technology Lahore, Lahore, Pakistan
² Abdus Salam School of Mathematical Sciences, GC University Lahore, Lahore, Pakistan
³ Basic Sciences Department, College of Engineering Majmaah University, P.O. Box 66, 11952, Majmaah, Saudi Arabia

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

Received: 26 April 2017
Accepted: 22 June 2017
Published online: 7 August 2017

Abstract

The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the Caputo fractional derivative (singular kernel) and the Caputo-Fabrizio fractional derivative (non-singular kernel). A physical model for second-grade fluids is developed with fractional derivatives. The expressions for temperature and velocity fields in dimensionless form as well as rates of heat transfer are determined by means of the Laplace transform technique. Solutions for ordinary cases corresponding to integer order derivatives are also obtained. Numerical computations for a comparison between the solutions of the problem with the Caputo time-fractional derivative, problem with Caputo-Fabrizio time-fractional derivative and of the ordinary fluid problem were made. The influence of some flow parameters and fractional parameter on temperature field as well as velocity field was presented graphically and in tabular forms.