Nonviscous Oblique Stagnation Point Flow towards Riga Plate

Purpose. .e flow of nonviscous Casson fluid is examined in this study over an oscillating surface. .e model of the fluid flow has been inspected in the presence of oblique stagnation point flow..e scrutiny is subsumed for the Riga plate by considering the effects of magnetohydrodynamics. .e Riga plate is considered as an electromagnetic lever which carries eternal magnets and a stretching line up of alternating electrodes coupled on a plane surface.We have considered nonboundary layer two-dimensional incompressible flow of the fluid. .e fluid flow model is analyzed in the fixed frame of reference. Motivation. .e motivation of achieving more suitable results has always been a quest of life for scientists; the capability of determining the boundary layer of flow on aircraft which either stays laminar or turns turbulent has encouraged the researcher to study compressible flow in depth. .e compressible fluid with boundary layer flow has been utilized by numerous researchers to reduce skin friction and enhance thermal and convectional heat exchange. Design/Approach/Methodology. .e attained partial differential equations will be critically inspected by using suitable similarity transformation to transform these flows thrived equations into higher nonlinear ordinary differential equations (ODE). .en, these equations of motion are intercepted by mathematical techniques such as the bvp4c method in Maple and Matlab. .e graphical and tabular representation of different parameters is also given. Findings. .e behavior of β and modified Hartmann numberM increases by positively increasing the values of both parameters forF(η), whileω decreases with increasing the values ofω forF(η)..e graph of β shows upward behavior for distinct values for bothG(η) andG′(η) for velocity portray. Prandtl number and β for the temperature profile of θ(η) and θ1(η) goes downward with increasing parameters.


Introduction
e idea of stagnation point flow to find the exact solution of the Navier-Stokes equations was earlier discussed by Hiemenz [1] e applications of heat flow of stagnation point flows are impartially manifested in paper manufacture, melt spinning process, revolving fibers, continuous molding, and crystal puffing, given by Mehmood et al. [2] In the divination of skin friction in addition to mass or heat transfer near to stagnation zone of bodies in transpiration cooling, great speed movements, project of thrust compartment, radial diffusers, thermal oil repossession, and drag decrease along with several substantial control have considerable physical consequences [3]. e flows of magnetohydrodynamic electrical conducting fluids have apprehended the notice of scientists and researchers as they have numeral utilizations in industrial and engineering fields. e skin friction and heat transfer coefficient have higher results for turbulent flow as compared to laminar flow; any numerical technique that can be employed to enhance the stability of laminar flow is worth investigating. However, the properties of high electrical conductivity are not effective in all fluids. Ibrahim [4] analyzed the properties of nonlinear MHD flow with thermal radiations of nanofluid regulated with a stretching sheet in the zone of stagnation point flow with the effects of convective heat transfer. Li et al. [5] studied mannerisms of MHD flow of non-Fourier nanofluid with heat conduction determined by the stretched surface. e radiative flow of MHD nanofluid with the effects of heat transfer regarding a stretching surface was analyzed by Ghasemi et al. [6]. e micropolar boundary layer flow of nanofluid with stretching sheet was described by Turkyilmazoglu [7].
Wall-parallel Lorentz force is processed by using the Riga plate, as Riga plate is a compound of alternating electrodes and persistent magnets connected in a flat surface. In this regulation, first strive was taken into account to produce a wall-parallel Lorentz force which was discussed by Gailitis et al. [8]. In this study, it is initiated that, by suing electromagnetic body forces, the electrically conducting fluid flows can be handled to repay the momentum scarcity in the boundary layer. It can be worn as a sufficient factor for decline of skin friction and pressure drag of submarines circumvents the segregation of the boundary layer.

Problem Statement
Consider the unsteady incompressible flow model for non-Newtonian Casson fluid with the Riga plate. e unsteadiness in the fluid has been induced by the timedependent flow.
e model geometry is shown in Figure 1(a). In the rectangular coordinate system, u and v are velocity components along x-and y-axis. e plate vacillating in its own plan and the flow of the nanofluid distract obliquely on it. e fluid is in the upper half of the plane y ≥ 0. e stress tensor for the given flow field is defined as

Mathematical Analysis
e continuity equation for the given problem is e momentum equations for the given flow field is expressed as Similarly, the energy equation is given as where the current density width of magnet is J 0 , specific heat is C P , and the magnetization of permanent magnets is M 0 . Now, we are going to introduce the occurrence of the stream function as By using stream function in equations (3)-(5), we have z zt

Fixed Frame of Reference for the Fluid Flow Model
Conferring to [9], we consider that where k is a parameter. We examine that the plate is oscillating at the point y � 0, and the fluid engaged at the upper half plane y > 0. e flow function is given by [41] Ψ � (1/2)cy 2 + xy. e above equations can also be written as e boundary conditions are given below: where c is the dimensionless number. We introduce where By using the nondimensional form of equations (10) and (11), we get the following form of equations (9), (11), and (12) as follows: e nondimensional boundary conditions for the above all equations (16)-(20) are given below:

Numerical Solution
e equations which we obtained from the basic governing equations are highly nonlinear which are changed to ODEs numerically. en, we have solved these equations with the help of Maple software (equations (4) and (11)). Now, we are going to introduce new scheme of variables to solve these higher order ODEs into 1 st order equations, i.e., under appropriate boundary conditions:

Graphical Discussion
Newtonian and non-Newtonian fluids are widely used in chemical engineering, bio-chemical engineering, food processing, oil exploration, and medical engineering. In particular, what has been studied most intensely for obvious practical reasons is how heat and momentum are transferred to moving Newtonian and non-Newtonian fluids. e inquisition which we have considered for investigation can be represented graphically by different distinct parameters as stated below. Figure 1 gives the geometry of the given problem for nonviscous behavior of the flow model. Figure 2 represents the Riga plate that persuades Lorentz force opposite to the external free stream. e portray of β for the different values of β, which gives the increasing behavior for F(η) , is shown in Figure 3. e increasing graph of modified Hartmann number M for F(η) is given in Figure 4. Figure 5 illustrates the velocity profile for β with different values for G(η). e graph increases positively by increasing the values of β. Figure 6 shows the decreasing graph of ω for F(η). e upward graph of β for G 1 (η) is demonstrated for distinct values of β in Figure 7. e illustration of β for the temperature profile of θ 1 (η) for positive values of β is given in Figure 8. e Prandtl number for high values of Pr for θ 1 (η) is given in Figure 9, which goes downwards with increasing Pr. Similarly, the decreasing graphs of Pr for θ(η) with positive values of the Prandtl number is shown in Figure 10. e portray for temperature of β decreasing with increasing the values of β for θ(η) represented in Figure 11 e Nusselt number graph of β � 0.1, 0.3, 0.5 is shown in Figure 12, which demonstrates the upward lines in the graph. Figure 13 describes the unsteady flow for the given fluid model. Figures 14-16 Table 2, distinct values of the Nusselt number for θ 1 (η) are given. Table 3 shows the skin friction coefficient.        2 π 3 π 4 π 5 π 6 π 7 π 8 π 9 π 10 π Mathematical Problems in Engineering 7

Concluding Remarks
We have discussed the unsteady the flow of Casson fluid by assuming the Riga plate over the oscillating surface. e obtained results which are given below:       Data Availability e data used to support the findings of the study are available from the corresponding upon request.

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