Hydromagnetic flow over a moving plate of second grade fluids with time fractional derivatives having non-singular kernel

C. Fetecau, A.A. Zafar, D. Vieru and J. Awrejcewicz

Chaos, Solitons & Fractals, 2020, vol. 130, issue C

Abstract: Hydromagnetic flow of second grade fluids with time fractional derivatives without singular kernel over an infinite moving plate is analytically studied. Two equivalent general solutions are established for non-dimensional velocity field using Laplace and Fourier sine transforms. They can be utilized to produce exact solutions of the problems involving any motion of this kind of these fluids. For validation and highlighting the impact of fractional parameter upon the fluid dynamics, the solutions of the Stokes’ problems are brought to light. They are presented as sums of transient and permanent solutions. Moreover, the time consumed in convergence to the equilibrium-state is presented graphically. A comparison between models is also included in the case of the first Stokes’ problem. The flow of fractional order fluids has been found faster as compared to the ordinary fluids at smaller time steps. After a short time the ordinary fluids flow faster and the non-Newtonian effects and the impact of non-integer parameter upon the fluid velocity vanish in time. The present work also witnesses that the time consumed in attaining the equilibrium state for the sine oscillations based plate motions is greater than those of induced by cosine oscillations based plate motions.

Keywords: Hydromagnetic flow; Fractional derivative; Second grade fluid; Moving plate (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:130:y:2020:i:c:s096007791930400x

DOI: 10.1016/j.chaos.2019.109454

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