Investigation of a Fully Developed Oscillatory MHD Convective Viscoelastic Flow

1. INTRODUCTION

Over the most recent couple of decades, the magnetohydrodynamic (MHD) warmth and mass exchange flow drives a wide significant importance in fluid flow engineering innovation industries. The laminar fluid flow which results from the stretching of a level surface in a nanofluid has been investigated numerically by Khan et al. (2010) and Noghrehabadi et al. (2012), which was to dissect the development of the consistent limit layer flow, warm exchange and nano-particle fraction over a stretching surface in a nanofluid. The viscoelastic nanofluid flow and warmth exchange over a linearly stretching sheet within the sight of remotely applied magnetic field. The impacts of Brownian motion and thermophoretic volume fraction of nano-particles have been investigated by Shit et al. (2016). The issue is explained numerically by using finite difference plot alongside the Newton's linearization technique. A wide scope of applications can be found in a few fields, for example, aerodynamic extrusion of plastic sheets, vitality stockpiling units, biological transportation, liquid metal fluids oil reservoirs, high-temperature plasmas, geothermal frameworks, warm insulation and metal and polymer extrusion, warm vitality stockpiling devices, electronic cooling, boilers, atomic process, micro MHD siphons, ground water frameworks and so on. Investigations of MHD flows are generally in vertical moving permeable plate Mohamed et al. (2009), vertical permeable plate Nandy et al. (2013) and Murthy et al. (2015), vertical insulated permeable plate, infinite inclined permeable plate Ramachandra et al. (2011), semi-infinite vertical permeable plate Das et al. (2015). As of late, nanotechnology has received a great deal of attention where the further development of higher execution is still going because of effective applications in the field of cooling (transformer cooling, electronics device cooling, silicon mirror cooling, vehicles cooling, controlling fusion), biomedical (magnetic cell separation, tranquilize delivery, malignancy therapeutics, cryopreservation, nano cryosurgery) and so on. The expression "nano fluid" can be alludes to a class of fluids by suspending nanometre sized (1-100 nm diameters) particles in like manner base fluids of highly upgraded warm properties (Ferdows et al., 2013; Dogonchi et al., 2016). This sort of fluids has highly industrial importance due to its unique chemical and physical properties. It has a higher warm conductivity which controlled significant upgrade because of the rate of warmth exchange. Viscoelastic fluid model is one of the subclass of rate type fluids which has gained wide attractions among the scientists in most recent 10 years. The fluid of both viscosity and elasticity properties is purported viscoelastic fluid. The main favorable position of using this kind of fluids is it can predict the pressure relaxation whilst other

insignificant be that as it may, it's beneficial for significant relaxation time in concentrated polymeric fluids of low sub-atomic weight Ibáñez et al. (2016) and Fetecau et al. (2003). Khan et al. investigated MHD warmth and mass exchange axisymmetric chemically reactive Maxwell fluid flow of driven by exothermal and isothermal stretching disks. Within the sight of nano particles, Ramesh et al. (2016) studied Maxwell fluid stagnation point flow of almost a penetrable surface. As of late, the radiation and viscous dissipation consequences for Maxwell fluid flow in a combined MHD warm exchange warm extrusion framework was studied by Hsiao (2017). Flow and warmth exchange of MHD nanofluid between parallel plates within the sight of warm radiation display has been dissected analytically with Duan– Rach Approach (DRA) by Dogonchi et al. (2016). Biswas et al. (2017) investigated the impact of quality of magnetic field, warm radiation, warm source, viscous dissipation on limit layer shaky mixed convective Jeffrey nanofluid flow over a vertical stretching sheet has remained unexplored. Subsequently, it is thought desirable to investigate this issue in the present examination. An outstanding explicit finite difference strategy (EFDM) (Khan et al., 2012; Bég et al., 2014) utilized as a numerical instrument to tackle the flow governing model. Dogonchi et al. (2017) investigated MHD Go-water nanofluid flow and warmth move in a permeable divert within the sight of warm radiation impact with DRA strategy. This strategy modifies the standard A domian Decomposition Method by evaluating the inverse administrators at the limit conditions directly . To the best of the writer's information, the investigation of normal convective and chemically reactive viscoelastic fluid flow with nanoparticle through a vertical permeable stretching sheet in nearness of warm radiation, warm generation and radiation absorption has remained unexplored. Subsequently, this wonder is tended to in this examination. The specific objectives of this numerical investigation are listed underneath: a) To investigate temperamental chemically reactive viscoelastic fluid flow with nano particle through a vertical permeable stretching sheet with the influence of warm radiation, mass diffusion with warmth source, mass exchange and radiation absorption. b) Mathematical solution of the flow governing model which includes transient force, vitality and diffusion balance equations numerically using surely understood explicit finite difference strategy (EFDM). c) Optimizing the numerical flow parameters and predicting high exactness of EFDM solutions by analyzing stability and union analysis (SCA). Nusselt number and Sherwood number with different physical parameters. e) Evaluation of the warm and force limit layer thickness with isotherms and streamlines analysis.

The fluid with the both viscosity and elasticity properties is known as viscoelastic fluid. Flimsy warmth and mass exchange flow of viscoelastic fluid along a semi-considered within the sight of a uniform warm radiation and magnetic field. The flow is considered to be in the x - direction which is brought the plate in the upward x-direction and y - axis is typical to it. At the point when, the plate velocity U ( t ) is given plate just as the fluid particle is very still at the equivalent at alland a similar concentration level C C ( )  temperature T T ( ) points. Where, and C fluid concentration and temperature species T B0 of uniform quality is applied typical to the flow region. The of uniform flow respectively. It is additionally accepted that a magnetic field By physical configuration and co-ordinate arrangement of the issue is displayed in the following Fig. 1 . To the best of the writer's learning, the investigation of common convective and chemically reactive viscoelastic fluid flow with nano particle through a vertical permeable plate in nearness of warm radiation, warmth and radiation absorption has remained unexplored. Hence, this marvel is tended to in this examination. Under the above assumptions, the equations that described the physical circumstances are given beneath (Shit et al., 2016)

To understand the governing coupled non-dimensional partial differential equations with the associated initial and limit conditions. The strategy for explicit finite difference has been utilized to settle (6) - (9) subject to the initial and limit conditions. Thus, the territory within the limit layer is divided by some perpendicular lines of Y - axis, where the typical of the medium is Y - axis as appeared in Fig-2. It is expected that the maximum length of limit layer max Y 20 as corresponds to . i.e. Y Y vary from 0 to 20 and the number of grid spacing in Y directions are andm( 100) , with then( 200) smaller time step   0.005 . Using the explicit finite difference approximation, we have,

To investigate the physical wonders of the fluid flow issue from numerical solution, a finite difference solution is obtained by the utilization of an explicit technique. The numerical estimations of non-dimensional velocity, temperature and concentration within the limit layer for different estimations of non-dimensional parameter have been figured by a FORTRAN program. For the consistent state solutions, the computations have The interaction of electrically conducting fluids with magnetic fields, through electromagnetic powers called Lorentz powers. Solid magnetic parameter ( compel and the power impact the fluid velocity to diminish and temperature profiles increase. Which are showing in Fig. 3 and Fig. 2.

The Numerical solutions for viscoelastic fluid with nano - particle towards a moving semi-infinite permeable stretching sheet with warm radiation, warm source, chemical reaction, and mass diffusion is broke down. The outcomes are given graphically various parameters. Shape the graphical representation, we have the following observations: • Temperature and concentration profiles increase yet velocity profiles decline with the increase of magnetic parameter. • Profiles decline with the increase of magnetic parameter. For the increase of viscoelastic parameter, the velocity profile diminishes and temperature profiles increase. • Velocity profiles increase with the increase of Grash of number and concentration profiles decline for modified Grash of number. • Due to increase of Brownian parameter temperature profiles increase and concentration profiles decline. • For the increase of thermophoresis parameter temperature profiles decline and concentration profiles increase. • For the increase of thermophoresis parameter temperature profiles decline and concentration profiles increase. • Temperature, skin friction and Nusselt number profiles decline for increase of Prandtl number and concentration bends decline for Lewis number. Sherwood number profiles increase with the increase of Lewis number. • For the increase of viscoelastic parameter, the warm and concentric limit layer increases. • Increase of magnetic parameter the warm and concentric limit layer diminishes.

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Assistant Professor, Mathematics