Three-Dimensional Rotating Flow of MHD Jeffrey Fluid Flow between Two Parallel Plates with Impact of Hall Current

This article deals with three-dimensional non-Newtonian Jeﬀrey ﬂuid in rotating frame in the presence of magnetic ﬁeld. The ﬂow is studied in the application of Hall current, where the ﬂow is assumed in steady states. The upper plate is considered ﬁxed, and the lower is kept stretched. The fundamental equations are transformed into a set of ordinary diﬀerential equations (ODEs). A homotopy technique is practiced for a solution. The variation in the skin friction and its eﬀects on the velocity ﬁelds have been examined numerically. The eﬀects of physical parameters are discussed in various plots.


Introduction
e rotation of fluid exists in nature due to the fact that the fluid particles rotate internally and rises with fluid movement. Due to engineering and industrial applications, the scientist considers the rotational fluid coupled with various features. Rotational fluids have many applications in engineering. Taylor and Geoffrey introduced the motion of viscous fluid in the rotating system [1]. e detailed study of fluid in rotating system is done by Greenspan [2] and Goodman [3]. e effects of MHD in a rotating system and stretched and porous mediums have been studied by Attia and Kotb [4], Borkakoti and Bharali [5], and Vajravelu and Kumar [6]. is work has been magnified along with the temperature effects by Mehmood and Ali [7], Das et al. [8], and Tauseef et al. [9]. e non-Newtonian fluid is used in many industry and technology appliances. Hayat et al. studied the non-Newtonian fluid in a rotating frame, considering the effects of MHD for micropolar nanofluids [11,12]. Jeffrey's model was presented by Jeffrey as a subclass of non-Newtonian fluid and studied with convection term [13,14].
Most of the physical problems are nonlinear and have rare exact solutions. e numerical methods (NMs) and analytical methods (AMs) are used to get the results. e NMs required discretization techniques which can affect the results. Among the AMs, HAM proposed by Liao is the most powerful and fast convergent [15][16][17][18][19]. Hall introduced Hall current and proves that, in case of strong magnetic field, the Hall current effects cannot be ignored [20]. Similar other interesting studies are provided in [21][22][23][24][25][26][27][28][29][30][31][32] for different fluid models. is article aims to elaborate the non-Newtonian nanofluid in the rotating frame with Hall effect. Hall effect is produced due to the potential difference across an electrical conductor when a magnetic field is acting in a direction vertical to that of the flow of current. So, for this aim, Jeffrey fluid flow is considered. For the proposed model, HAM is used.

Problem Formulation
Assume the Jeffrey fluid between two parallel plates having d separation. e plate and fluid rotate about y axis with Ω. e lower plate is stretched by two opposite and equal forces.
A uniform magnetic field B 0 is applied perpendicularly with a steady-state condition ( Figure 1). e fundamental identities are e similarity transformation used is Using equation (6) in (1)- (4), we get Substituting equation (8) in (7), we get 2 Mathematical Problems in Engineering where C f is given as

Solution Procedure
HAM was introduced by Liao. Let Ψ 1 , Ψ 2 are two continuous functions defined on topological spaces Χ, Y, then such that x ∈ Χ: e initial guesses are e linear terms are with differential operator where D n represents arbitrary constants, where n � 1, 2, 3, . . . ,6.

Zeroth-Order Problem.
Express q ∈ 0 1 as an embedding parameter with h f and h g , where h ≠ 0. en, e BCs are where -15 -10

lth-Order Deformation Problem
. where

Convergence of HAM
With the help of assisting constraints h f and h g , the convergence region is achieved. e possible region of convergence for the proposed model is given in Figure 2 and Table 1.

Results and Discussion
e effect of R on f(η) and g(η) is given in Figures 3 and 4. An increase in R decreases f(η) and g(η). e large amounts of viscous energy reduction produce large inertial forces, which decreases f(η) and g(η). e effect of kr on the f(η) and g(η) is shown in Figures 5 and 6. It is evident that an increase in kr increases fluid flow due to increase in Cariolis force. is fluid rotation increases kinetic energy which also increases the flow rate. e influence of m and c 1 on f(η) and g(η) is given in Figures 7-10, respectively. Both reduce velocity profile. e effect β is given in Figures 11 and  12, showing that the velocity profile increases by increasing β. e relaxation time gets smaller by enhancing c 1 . e effects of Μ on f(η) and g(η) are presented in Figures 13  and 14, respectively. β and Μ oppose the flow due to large relaxation time and magnetic effects. e magnetic field opposes the flow in the y direction and enhance in the z direction.
e numerical values of R, c 1 , β, and kr on C f are presented in Table 2. We see that C f has inverse relations with R, c 1 , β and decreases C f while on direct relation with kr.

Data Availability
e data used to support the findings of this study are available in the manuscript.

Conflicts of Interest
e authors declare that they have no conflicts of interest.