https://doi.org/10.1140/epjp/i2017-11456-2
Regular Article
Heat transfer analysis in a Maxwell fluid over an oscillating vertical plate using fractional Caputo-Fabrizio derivatives
1
Basic Engineering Sciences Department, College of Engineering Majmaah University, P.O. Box 66, 11952, Majmaah, Saudi Arabia
2
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3
Department of Theoretical Mechanics, Technical University of Iasi, Iaşi, Romania
* e-mail: i.said@mu.edu.sa
Received:
3
February
2017
Accepted:
15
March
2017
Published online:
27
April
2017
This article is focused on heat transfer analysis in the unsteady flow of a generalized Maxwell fluid over an oscillating vertical flat plate with constant temperature. The well-known equation of the Maxwell fluid with classical derivatives, describing the unidirectional and one-dimensional flow, has been generalized to a non-integer-order derivative, known as fractional derivative, with free convection term of buoyancy. A new definition of the fractional derivative introduced by Caputo and Fabrizio has been used in the mathematical formulation of the problem. Exact solution of the dimensionless problem has been obtained by using the Laplace transform. These solutions are expressed with complementary error and modified Bessel functions. Similar solutions for classical Maxwell and Newtonian fluids and generalized Newtonian fluid performing the same motion are obtained as limiting cases of our general results. Graphical illustrations show that the velocity profiles corresponding to a generalized Maxwell fluid are similar to those for an ordinary Maxwell fluid when the fraction order approaches 1. A comparison amongst four different types of fluids is also shown graphically.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017