Vol.65, No.3, 2020, pp.2033-2047, doi:10.32604/cmc.2020.011817
OPEN ACCESS
ARTICLE
Exact Analysis of Non-Linear Fractionalized Jeffrey Fluid. A Novel Approach of Atangana-Baleanu Fractional Model
1 Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtnkhwa, Pakistan.
2 Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
3 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
4 Department of Mathematics, College of Science Al-Zulfi, Majmah University, Al-Majmah, 11952, Saudi Arabia.
5 Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser, Saudi Arabia.
* Corresponding Author: Aamina. Email: aamina@tdtu.edu.vn.
Received 30 May 2020; Accepted 02 August 2020; Issue published 16 September 2020
Abstract
It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation. Therefore, this article aims to investigate the viscous dissipation (VD) effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane. Based on the Atangana-Baleanu operator, the fractional model is developed from the fractional constitutive equations. VD is responsible for the non-linear behavior in the problem. Upon taking the Laplace and Fourier sine transforms, exact expressions have been obtained for momentum and energy equations. The influence of relative parameters on fluid flow and temperature distribution is shown graphically. As special cases, and for the sake of correctness, the corresponding results for second-grade fluid and Newtonian viscous fluid are also obtained. It is interesting to note that fractional parameter α provides more than one line as compared to the classical model. This effect represents the memory effect in the fluid which is not possible to elaborate by the classical model. It is also worth noting that the temperature profile of the generalized Jeffrey fluid rises for higher values of Eckert number which is due to the enthalpy difference of the boundary layer.
Keywords
Viscous dissipation, atangana-baleanu fractional derivative, laplace transform, fourier sine transform.