NUMERICAL STUDY OF MHD FLOW AND HEAT TRANSFER OF SUTTERBY NANO FLUID OVER A STRETCHING SURFACE WITH ACTIVATION ENERGY AND NIELD’S CONDITION

The present study examines the numerical study regarding MHD Sutterby nano fluid flow over a stretching surface in the existence of activation energy. This investigation has been performed by using convective Nield boundary conditions. Effects of variable thermal conductivity, activation energy; nonlinear thermal radiation are considered. The governing nonlinear partial differential equations (PDEs) with convective boundary conditions are converted into the nonlinear ordinary differential equations (ODEs) with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with MATLAB built inbvp4c solver. The computed results of velocity, temperature and concentration profiles are displayed by means of graphs. Skin-friction coefficient, Nusselt number and Sherwood number are computed and analyzed.


INTRODUCTION
The combined mass and heat transportation phenomenon driven by buoyancy force, due to variation of mass species and temperature is encountered in various chemical and process engineering applications, and therefore attention has been devoted by engineers in last decade.

NUMERICAL STUDY OF MHD FLOW AND HEAT TRANSFER
The impact of buoyancy-driven force on mass and heat transportation phenomenon is also momentous in the chemical processes where mass species differences of dis-similar species exist.
Most interesting applications of this phenomenon include food processing, absorption, thermal wadding, diffusion of nutrition in tissues heat oil, heterogeneous catalysis in suspension cooling of nuclear reactors, and geothermal reservoir.
Nanofluids have gained immense importance in the present era in reference to its utility in controlling heat transfer within the system. In the present era, the cooling process is a much needed phenomenon in terms of applications to mitigate heating effects in computer chips, car engines etc. In past, the conventional liquids like water, oil, ethylene glycol were used for controlling the heat effects. Later on, a new technique containing solid-liquid mixture of nanoparticles and base liquid, named as nanofluid, was introduced by Choi [1]with lot of applications in biomedical, optical, electronics and ceramic industry. The heat absorption tendency of nanofluids is much higher than that of the traditional liquids. Research on nanoparticles by Das et al., [2]Wang and Mujumdar [3],Usria et al., [4]and Murshed et al. [5] has concluded that mixing of nanoparticles with liquids enhances the thermal conductivity.
Buongiorno [6] developed a model with Brownian motion and thermophoresis aspects.
Magnetohydrodynamics (MHD) is a study of magnetic effects in electrically conducting fluids.MHD has immense involvement in processes like earth magnetic field, solar wind, fusion, cooling of fission reactors, star formation, tumor therapy, X-ray radiation, plasmas, electrolytes etc. Dogonchi et al. [7] discussed the dissipative and MHD impacts in radiative convective nanofluid flow under diffusion theory. Dogonchi et al. [8] depicted the Darcian flow of radiative CuO-water nanofluid.
Recently, the activation energy has attained the interests of engineers, which was originally proposed by Arrhenius in 1889. This is known as base energy supplied to reactants in chemical processing for the conversion of products. The potential and kinetic energies are employed in molecules to stretch, twist, and break bonds. The idea of energy activation is more prominent in oil suspensions, industries of oil storage, hydrodynamics, and geothermal systems.
Activation energy is defined as the minimum amount of energy owned by reacting specie to undergo an indicated reaction. The Arrhenius equation is usually of the form (Tencer et al. [9]): Where K represents reaction rate constant, Ea is the activation energy, T the fluid temperature and B the pre-exceptional factor depicting an increase in the temperature with respect to increase in there action rate. Tointerpolate such energy activation effects, Maleque [10] studied the role of endothermic exothermic chemical reactions under energy activation. He noticed that the velocity profile increases by increasing the value of the Grashof number. Khan et al., [11] discussed the radiative nanofluid with energy activation. Rotating aspects in the flow of rate type material under energy activation were explored by Shafique et al., [12].

MATHEMATICAL MODELING
We consider the two-dimensional incompressible flow of Sutterby nano fluid past a stretching non porous sheet is analyzed. The Cartesian coordinate system is chosen for the flow analysis as shown in Fig. 1. Let u and v be the components of velocity in x and y directions respectively; the x-axis is taken along the stretching surface inthe direction of motion and the y-axis is perpendicular to it. Magnetic field B0 is applied perpendicular to sheet. Reynolds number is considered very small so that the effect of induced magnetic field current can be neglected. The stretching surface velocity is u(x) = ax along x axis. Temperature is regulated by the convective heating process described by the heat transfer coefficient hf and the temperature of the hot fluid Tf.

Fig 1. Engineering flow diagram
Under boundary layer assumption, the standard equations take the form (Azhar et al [13], Saifur-Rehman et al. [14], Sajid et. Al., [15]): The corresponding boundary conditions are In the concentration equation, the term Here m >0 , the shear thickening or dilatant fluid, m < 0 , the shear thinning or pseudo plastic fluid and form = 0, the fluid is simply a Newtonian fluid.
Let us introduce the following similarity variables: In view of the similarity transformation (8) where, prime represents the differentiation with respect to η, Re is Reynolds number, De is Deborah number, M is magnetic parameter, Nb is Brownian motion parameter, Pr is Prandtl number, Nt is Thermophoresis parameter, Le is Lewis number, σ is reaction rate constant, E is Activation Energy parameter, γ is Biot number, R is Thermal Radiation, n is order of the exponential of chemical reaction, δ is temperature difference.
The physical quantity namely skin friction coefficient for the present flow problem is transmuted below ( ) The local Nusselt number is formulated as Where the heat flux The dimensionless form of Nusselt number is given by 1 2 Re The local Sherwood number is formulated as The dimensionless form of Sherwood t number is given by 12 Re

NUMERICAL SOLUTION
The highly nonlinear transformed system (9 -11) with conditions (12, 13) is evaluated numerically using MATLAB built in bvp4c solver. Here we convert nonlinear equations into the system of first order ordinary differential equations, and then we solved it by using RK method of order 4. The iterative process will be terminated when the error involved is <                  increasing the viscous forces and elastic forces, respectively, which leads to an enhancement in viscous boundary layer, affecting the thermal boundary layer by reducing it. Fig. 6 illustrates that temperature is increasing function of thermal Biot number γ. As expected for γ convective heating at surface increases due to which transfer of heat to fluid increases which results enhancement in fluid temperature and thickness of the thermal boundary layer. Figure 7 indicates the contribution of power-law index m on θ (η). Prominent temperature is observed for shear thinning fluids retards. The behavior of the thermophoresis parameter has been discussed in Fig.   8, where a rise in the thermophoresis parameter Nt seems to rise the fluid temperature. The reason behind the rise in temperature is an increment in the nanoparticles. It is observed that the nanoparticles present close to the hot boundary have been shifted towards the cold fluid in the presence of the thermophoretic force, that's why the thermal boundary layer becomes thicker.

In this portion, influence of the eminent parameters is investigated on the velocity '
The behavior of the Reynolds number has been discussed in Fig. 9, where a rise in the Reynolds number seems to retards the fluid temperature.  Fig. 19. It is seen that, as De increases, concentration retards.

CONCLUSIONS
In this study, the characterization of Sutterby nanoparticles in flow induced by the stretching surface is reported. Results on the behavior of several physical parameters, eminent findings are enlisted as: The presence of nanoparticles improves the thermal conductivity and temperature profile effectively. In general, the radiation phenomenon can play an essential role in the enhancement of heat transfer. Brownian motion and thermophoresis parameters result in increment of fluid temperature. Brownian parameter decreases the fluid concentration whereas concentration grows by the thermophresis parameter. Coefficient of skin friction reinforce for all significant parameters.

CONFLICT OF INTERESTS
The author(s) declare that there is no conflict of interests.