Abstract
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 κ, Gr and Gm, while velocity decreases for Pr and M. For Kr, both velocity and concentration curves show decreasing behavior. Fluid flow accelerates under the influence of Sr and R. Temperature and concentration profiles increase for Sr and R. Moreover, the ABC fractional operator presents a larger memory effect than C and CF fractional operators.
Highlights
Introduction iationsOver the past thirty years, fractional derivatives have fascinated multiple investigators as compared to classical derivatives
The circumstances are complicated in fractional order derivatives (FODs) because several different competing definitions exist in the literature
We propose the mathematical modeling of fractional second grade fluid (SGF) with the help of Laplace transform and fractional operators
Summary
We begin with SGF on an upright and unbounded plate, with the impact of a magnetic field having strength B0. At the time τ > 0, the temperature of the plate is either raised or lowered to T∞ + ( Tw − T∞ ) ττ0 , when τ ≤ τ0 , and thereafter, for τ > t0 , a constant temperature τw is maintained and the level of mass transfer at the surface of the wall is either raised or lowered to C∞ + (Cw − C∞ ) τt0 , when τ ≤ τ0 , and thereafter, for τ > τ0 is maintained at the constant surface concentration Cw , respectively. The physical model of the problem can be given as follows in Figure 1 [75]. Governing equations for momentum, heat and mass are presented by [75]:. For the simplification of Equations (1)–(7), we introduce the dimensionless variables given below: ζ=.
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