Vol.123, No.1, 2020, pp.377-400, doi:10.32604/cmes.2020.08076
OPEN ACCESS
ARTICLE
Fractional Analysis of Viscous Fluid Flow with Heat and Mass Transfer Over a Flexible Rotating Disk
• Muhammad Shuaib1, Muhammad Bilal1, Muhammad Altaf Khan2, *, Sharaf J. Malebary3
1 Department of Mathematics, City University of Science and Information Technology, Peshawar, Pakistan.
2 Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa.
3 Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Rabigh, Saudia Arabia.
∗ Corresponding Author: Muhammad Altaf Khan. Email: altafdir@gmail.com.
(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)
Received 25 July 2019; Accepted 14 November 2019; Issue published 01 April 2020
Abstract
An unsteady viscous fluid flow with Dufour and Soret effect, which results in heat and mass transfer due to upward and downward motion of flexible rotating disk, has been studied. The upward or downward motion of non rotating disk results in two dimensional flow, while the vertical action and rotation of the disk results in three dimensional flow. By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations. The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables. Then, we generalize the model by using the Caputo derivative. The numerical result for the fractional model is presented and validated with Runge Kutta order 4 method for classical case. The compared results are presented in Table and Figures. It is concluded that the fractional model is more realistic than that of classical one, because it simulates the fluid behavior at each fractional value rather than the integral values.
Keywords
Caputo derivatives, similarity transformation, RK4, soret effect, Dufour effect.