Effect of Magnetic Field with Parabolic Motion on Fractional Second Grade Fluid

Fractal and Fractional

Jan Awrejcewicz¹  Ali Akgül²  Muhammad Bilal Riaz³  Nazish Iftikhar⁴ 

[1] Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland;Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey;Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan;Department of Science & Humanities, Lahore Campus, National University of Computer and Emerging Sciences, Lahore 54000, Pakistan;

关键词: second grade fluid;    memory effect;    magnetic field;    inversion algorithm;   

DOI  :  10.3390/fractalfract5040163

来源: DOAJ

【 摘 要 】

This paper is an analysis of the flow of magnetohydrodynamics (MHD) second grade fluid (SGF) under the influence of chemical reaction, heat generation/absorption, ramped temperature and concentration and thermodiffusion. The fluid was made to flow through a porous medium. It has been proven in many already-published articles that heat and mass transfer do not always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such a dynamical process very accurately; thus, a different concept of differentiation is needed to capture such a process. Very recently, new classes of differential operators were introduced and have been recognized to be efficient in capturing processes following the power law, the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. The Laplace transform, inversion algorithm and convolution theorem were used to derive the exact and semi-analytical solutions for all cases. The obtained analytical solutions were plotted for different values of existing parameters. It is concluded that the fluid velocity shows increasing behavior for $\kappa$, $G_r$ and $G_m$, while velocity decreases for $P_r$ and M. For $K_r$, both velocity and concentration curves show decreasing behavior. Fluid flow accelerates under the influence of $S_r$ and R. Temperature and concentration profiles increase for $S_r$ and R. Moreover, the ABC fractional operator presents a larger memory effect than C and CF fractional operators.

【 授权许可】

Unknown