Analysis on physical properties of micropolar nanofluid past a constantly moving porous plate

The computational analysis is presented for boundary layer heat and mass transfer flow of hydro magnetic micropolar nanofluid flow. In the flow model, viscosity of the fluid is taken as temperature-dependent and varies linearly and the other physical properties such as radiative heat flux, the magnetic field, the viscous dissipation, chemical reaction are additionally assumed in the energy equation and spices concentration equation respectively The PDEs representing the fluid flow have been changed into a framework of dimensionless ODEs and explained mathematically through the 4th order R-K and NS shooting technique. Temperature distribution, velocity distribution, micro rotation, and concentration distribution are explored graphically for a series of solid volume fraction (0<ϕ<2) of nano-solid particles. All the findings for various flow parameters agreed perfectly with physical situation of the flow. It is observed that for increasing value of magnetic parameter, the concentration and temperature of the micropolar nano fluid near the boundary layer declines and increasing value of the volume fraction of nano-solid particle ϕ leads to decrease in velocity and micro rotation of the fluid within the boundary layer decreases.


Introduction
In present technology, there is an important development in the utilization of colloids mass-production by nano-sized particles scattered in a base fluid. Heat controlling has been accepted as important tools in the recent techno-industrial world and it should be used effectively. Prior research shows that thermophysical properties can be enhanced by nanofluids than base fluids such as oil or water. Das Due to the increasing production of metal and polymer sheets in engineering industries, the fluid dynamics of continuously moving plate plays an important role. The theory of continuously moving surfaces was introduced by Sakiadis (1961). Due to their cherished influences in various industrial and engineering processes such as plastic extrusion and polymer, the process of crystal development makes a micropolar fluid flow is a significant space of exploration. The concept of micropolar fluid was initiated by Eringen (1964). Later, many researchers have put forward their work on micropolar fluid past a constantly stretching Fluid viscosity is another important property which quantify the flow but in most of the previous studies on heat transfer in fluid flow it is supposed to be constant, however, if the temperature variation is large this assumption is not valid. So, in the present work viscosity is assumed as variable. Moreover, due to engineering applications, radiation energy plays a significant role in the energy transport flow of moving fluid. The problem of heat and mass transfer flow of micropolar fluid in the presence of radiation is analyzed by . Chemical reaction effects of the above problem were studied by

Problem Formulation
A Problem of two-dimensional, incompressible, steady, micropolar fluid flow on a flat absorbent plate which moves constantly with a continuous velocity in a water-based nanofluid containing different nanoparticles such as CuO, Al2O3, and TiO2, medium at rest is formulated mathematically. The rectangular coordinate system is taken to describe the problem and whose origin is located at the place where the plate is brought into the fluid medium as displayed in Figure 1. The surface is kept along the x-axis and the y-axis is vertical to it. The temperature and concentration on the surface are maintained at uniform value T∞ and C∞ respectively. The fluid is seen to be gray, radiating, and absorbing. Heat fluctuation in the y-direction is significant while comparing with the flux in the xdirection. The fluid viscosity is assumed as variable and it varies with respect to temperature linearly. The governing equations of the above flow model are exposed to the following boundary condition 0 0, , , Where, Where, ( ) and ( ) f g K K are non-dimensional stream functions, with respect to the equation (7), equations The initial and boundary conditions corresponding to dimensionless quantities are given by

3.Numerical Solution
The set of non-linear PDEs (2) -(5) with the equation (6) are converted into ODEs by similarity transformation technic. The system of non-linear ODEs (7) -(10) with the equation (11) are solved by using the 4th order R-K method along with NS procedure (Adams and Rogers (1973)) for the proposed parameter ɸ, Fw, N, Pr, K, N, M and Sc. The system of ODE (7) -(10) which is subjected to the condition (11) solved by implementing a computer program. A step size of 0.01

K '
was designated to fulfill the convergence criterion of 10-4 in all cases.

Results and Discussion
The mathematical solution of the above system is given in terms of graphs. Figure 2 expresses the influence of hydro magnetic parameter on fluid velocity near the plate. Figure 2 displays that the velocity of the fluid decrease as the hydro magnetic parameter increases.    Figure 4 exhibits the concentration distribution of the micropolar nanofluid and it is observed that fluid concentration close to the plate decrease as the hydro magnetic parameter increases. Figure 5 exhibits the temperature distribution of the micropolar nanofluid and it states a slight variation in the temperature of the fluid when hydro magnetic parameter changes.   Figure 6 exhibits the influence of coupling constant on Velocity of the fluid with in the boundary layer and it is found that for increasing K velocity of the fluid with in the boundary layer increases. Figure 7 exhibits the Influence of coupling constant on angular Velocity of the fluid with in the boundary layer and it reveals that for increasing K angular velocity of the fluid with in the boundary layer decreases. Effect of coupling constant on concentration of the fluid with in the boundary layer of the flow is shown in figure 8 and it reveals that for increasing K concentration of the fluid increases with in the boundary layer.    Figure 9 shows that the velocity of the fluid decrease as the volume fraction of nano-solid particles increases. Figure 10 shows the micro rotation of the micropolar nanofluid near the boundary layer for different values of volume fraction of nano-solid particles. It observes that the angular velocity of the micropolar nanofluid decreases as ɸ rises.  Figure 11 exhibits the temperature distribution of the micropolar nanofluid and it states a slight variation in the temperature of the fluid when the volume fraction of nano-solid particle changes. Figure 12 exhibits the concentration distribution of the micropolar nanofluid and it shows that the concentration of the fluid falls when the volume fraction of nano-solid particle increases changes.

Conclusion
The mathematical exploration has been performed on the influence of microrotation, velocity, concentration and temperature of the fluid flow inside the boundary layer. Execution is done for the parameters such as hydro magnetic parameter M, volume fraction of nano-solid particle ɸ, coupling constant K, and Prandtl number. Moreover, the effect of the above-mentioned parameters on the fluid properties in the boundary layer are presented graphically.
Final conclusion are as follows; ¾ The concentration and temperature of the fluid in the boundary layer declines when magnetic parameter increase. ¾ The velocity and microrotation of the fluid close to the boundary layer drops when magnetic parameter increases. ¾ For increasing K, the fluid velocity close to the boundary layer increases, but angular velocity of the fluid decreases near the boundary layer. ¾ For increasing value of the volume fraction of nano-solid particle ɸ, the velocity and micro rotation of the fluid within the boundary layer decreases. ¾ An upsurge in ɸ reduces the concentration and temperature of the fluid flow significantly while it raises the velocity of the fluid flow. ¾ The temperature and velocity declines due to an rise in Prandtl number and concentration declines as the Prandtl number decreases.