Eur. Phys. J. Special Topics 226, 3791–3802 (2017)
https://doi.org/10.1140/epjst/e2018-00097-5

Regular Article

Application of time-fractional derivatives with non-singular kernel to the generalized convective flow of Casson fluid in a microchannel with constant walls temperature

¹ Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
² Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan

^a e-mail: ilyaskhan@tdt.edu.vn

Received: 18 October 2017
Received in final form: 8 November 2017
Published online: 25 July 2018

Abstract

In this article, time-fractional derivatives with non-singular kernel have been applied to study the generalized convective flow of Casson fluid passing through a vertical microchannel with constant walls temperature. A newly introduced fractional derivative namely Caputo–Fabrizio fractional derivative is adopted for the generalization of classical partial differential equations that govern the flow. The fluid flow is subjected to physical initial and boundary conditions. The problem is solved using Laplace transform procedure and semi-analytical solutions for velocity and temperature are determined. Zakian method was used to obtain the inverse Laplace transform for both velocity and temperature distributions. The influence of specifics parameters such as Casson fluid parameter, Gashof number, Prandtl number and radiation parameter on velocity and temperature profiles are presented in plots and tables.