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Fractional Walter’s Liquid Model-B has been used in this work to study the combined analysis of heat and mass transfer together with magnetohydrodynamic (MHD) flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD) has been used in the mathematical formulation of the problem. By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. The problem is solved analytically and solutions of mass concentration, temperature distribution, and velocity field are obtained in the presence and absence of porous and magnetic field impacts. The general solutions are expressed in the format of generalized Mittag-Leffler function

The liquids related to non-Newtonian behavior have diverted the attention of various researchers, due to the involvement of non-Newtonian fluids in industrial processes and engineering. The prominent non-Newtonian liquids are liquid detergents, polymers, shampoos, cosmetic products, printer inks, blood at low shear rate, paints, colloidal fluids, mud, ice cream, suspension fluids, and several others. Due to diverse rheological characteristics in non-Newtonians liquids, no constitutive relation is present in literature. The investigators and scientists have recommended many models of non-Newtonian liquids due to nonlinearity between the shear rate and shear stress, such as Sisko’s model [

Factional calculus is the subject of science of differentiation and it was originated in 1695, while L’Hospital questioned Leibniz what would be the explanation of

In this section, we present some essential information about the Caputo-Fabrizio fractional derivative that will be used in this paper. Firstly, we introduce the definition of the Caputo-Fabrizio fractional derivative of order

The Caputo-Fabrizio fractional derivative of order

The constitutive equations govern the flow of Walters’-B fluid are

In (

Assume an unsteady electrically conducting incompressible free convection porous flow of a Walters’-B fluid over an oscillating plate. As described in the geometry Figure

Geometry of the model.

Meanwhile, we introduce the nondimensional parameters in (

Omitting

Employing Laplace transform on (

Employing Laplace transform on (

Equations (

The purpose of present analysis is to highlight the effects of fractionalized Walter’s Liquid Model-B with heat and mass transfer in a porous medium analytically using newly defined approach of Caputo-Fabrizio fractional derivative. The analytical investigation is performed for the solutions of mass concentration, temperature distribution, and velocity profile in the presence and absence of porous medium and magnetic field effects. The general solutions are expressed in the form of generalized Mittag-Leffler function

Figure

Influence of the Schmidt number on the mass concentration is observed in Figure

Figure

Figure

Figure

The influence of Reynold number is depicted in Figure

The influences of magnetic and porous parameters are demonstrated in Figures

Plot of mass concentration for different values of Caputo-Fabrizio fractional parameter

Plot of mass concentration for different values of Schmidt number

Plot of temperature distribution for different values of Caputo-Fabrizio fractional parameter

Plot of temperature distribution for different values of Prandtl number

Plot of velocity field for different values of Caputo-Fabrizio fractional parameter

Plot of velocity field for different values of Reynold number

Plot of velocity field for different values of magnetic parameter

Plot of velocity field for different values of porous medium

The authors declare that there are no conflicts of interest regarding the publication of this paper.

All authors contributed equally to the writing of this paper. All authors read and approved the final paper.

The authors would like to acknowledge and express their gratitude to the United Arab Emirates University, Al Ain, UAE, for providing the financial support with Grant no. 31S240-UPAR (2) 2016.