Two-Dimensional Flow Of Maxwell, Jeffrey And Oldroyd-B Nanofluid?

Consider a steady two-dimensional flow of Maxwell, Jeffrey and Oldroyd-B nanofluids over a cone having radius and half-angle . x-axis varies along the surface of cone and y-axis is perpendicular to it. The temperature and concentration distributions are vary along the surface of the cone. A variable magnetic field is applied along -direction as shown in Fig.1. A variable temperature along with the thermophoresis and Brownian motion effects are taken into account. and are the ambient temperature and concentration of the fluid. Viscous dissipation and induced magneticfield effects are neglected in this study.
Based on the above assumptions the usual governing boundary layer equations stated as follows: (Sandeep et al. [4] and Hayat et al.
(11) are solved numerically via the Runge-Kutta based shooting method with effective programming language MATLAB. The influence of dimensionless governing parameters namely magneticfield parameter ( ), buoyancy parameter( ), non-uniform heat source/sink parameters ( ), Brownian motion parameter ( ), thermophoresis parameter ( ) on the flow, heat and mass transfer of Maxwell , Jeffrey and Oldroyd-B nanofluids are discussed and presented with the help of graphs and tables. In Addition, the effect of dimensionless governing parameters on the friction factor coefficient, local Nusselt and Sherwood numbers are computed and discussed. For numerical computations we considered . These values are kept as common in entire study except the varied values as shown in the respective figures and
8 and 9. It is clear that the increasing the Brownian motion parameter boost up the temperature profiles and reduces the concentration profiles of the flow. Generally, an improved values of Brownian motion parameter tries to remove the concentration gradients and keeps the more pressure near the boundary layer which heats up the thermal boundary layer, thereby enhancing the temperature profiles. It is also interesting to mention that the temperature profiles of Oldroyd-B fluid is highly influenced by the Brownian motion parameter. However, the concentration profiles are highly influenced by Brownian motion parameter in Maxwell. The effect of thermophoresis parameter on velocity, temperature and concentration profiles is displayed in Figs. 10-12. It is noticed that, rising values of the thermophoresis parameter enhances the velocity, temperature and concentration fields of the flow. This is due to the imbalanced ratio of the heat capacity of nanoparticles and base fluids. In fact, as the thermophoresis increases, nanoparticles eject themselves from the wall, which leads to increase in the nanoparticle volume fraction. It is also noticed that the temperature field of Oldroyd-B fluid is highly influenced due to variation in the thermophoresis