An application of fractional derivatives to a thermo-convective viscous fluid with Dufour and Schmidt effects over a rotating disk

Article type: Research Article

Authors: Shuaib, Muhammad | Bilal, Muhammad | Khan, Muhammad Altaf^*

Affiliations: Department of Mathematics, City University of Science and Information Technology, Peshawar, Pakistan

Correspondence: [*] Corresponding author: Muhammad Altaf Khan, Department of Mathematics, City University of Science and Information Technology, Peshawar, K.P.K, Pakistan. E-mail: altafdir@gmail.com.

Abstract: The unsteady, free convective and incompressible fluid flow over a rotating porous disk with mass and heat transfer under the radiation effect has been studied. The governing equations are transformed into a set of first-order differential equations by using suitable transformation. The first-order differential equations are then transform into a system of fractional order differential equations through Caputo derivatives. The numerical solution of the system of fractional order differential-equations are obtained by using the predictor-corrector method. The Runge Kutta method order 4 method has been used to obtained the classical solution. The effect of all physical parameter involved in the problem are presented graphically. It shows that both the concentration and temperature get decreased with Dufour effect. The radial, axial and azimuthal velocities decreases with suction effect in the boundary layer. These observation are obtained by using Predictor-corrector method and to point out the validity of the result, the well known numerical technique Runge Kutta order 4 method is used.

Keywords: Fractional derivatives, predictor-corrector method, similarity transformation, RK4, schmidt effect

DOI: 10.3233/JCM-190029

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 20, no. 2, pp. 645-664, 2020