NANOFLUID FLOW IN PRESENCE OF GYROTACTIC MICROORGANISMS ON THE STRETCHING SURFACE WITH MAGNETIC FIELD AND ACTIVATION ENERGY

In this paper, reaction of magnetic field and activation energy is applied on nanoparticles and swimming gyrotactic microorganisms under the viscous dissipation is inspecting. The effect of thermophoresis and Brownian motion is also considered. The PDEs are naturalized into ODEs by using similarity transformations. To solving the PDEs by using RK-Fehlberg with shooting approach by MATLAB software. The effect of magnetic parameter, Schmidt number, Prandtl number, Brownian motion, thermophoresis, Peclet number, porosity parameter, on velocity, temperature, concentration, motile microorganism density portrait is in detailed it is discussed and the eventualities are demonstrated in graphs. The effects of these factors on Nusselt number, skin friction coefficient, Sherwood number and density number of motile microorganisms are concluded using tabular form.


INTRODUCTION
Nanofluids has better thermal conductivity as like as normal fluids. So many researchers explained nanofluid flow under the different presumptions. A creature that can only be observed under a microscope. Algae, fungi, bacteria, and protozoa are examples of microorganisms. These types of fluids have a plenty of useful applications in heat transfer, electronic cooling, the transportation industry, bio-medical devices, and spacecraft equipment. This investigation looked at the appearance of partial slides on the disc surface. Salahuddin et al. (2022) examined under the influence of varying thickness and slip circumstances, the hybrid nanofluid's flow moved through a stretchy hot cylindrical wave at a 3D stagnation point. Bilal et al. (2021), investigated Carbon nanotubes (CNTs) and ferric oxide water-based hybrid nanofluid flow created by a wavy fluctuating spinning disc with energy propagation is numerically simulated. The nanofluid is created in the power of carbon nanotubes and magnetic nanoparticles Nano particles of iron with carbon nanotubes have been intensively studied for their extraordinary Electrical and thermal conductivity, flexibility, and tensile strength. The goal of the suggested analysis is to improve the efficiency of transport of heat energy for many industrial and medicinal purposes. The incidents are explained by a number of partial differential equations (PDEs) that include equations for momentum, energy, concentration, and motile microorganisms. Muthuku et al. (2014) introduce the sake of introducing motile microorganisms into the nanoparticle suspension was present improved nanofluid consistency, microscale fraternization, greater mass transmission, and application in micro volumes. Khan W. A (2014) Many bio microsystems, such as nanochips, can use nanofluids with bacteria to test toxicity and cellulose optimization. Nanofluids with microorganisms * Corresponding author. Email : mrmadhavi5@gmail.com are also useful micro volumes are used in enzyme biosensors and microfluidics and micro mixers mechanized. Our discoveries could help improve the performance of microbial fuel cells. Gyrotactic microorganisms can additionally increase the flow's nanofluids stability. The effects of gyrotactic organisms on nanofluid flows have been extensively researched. Heat and mass transmission gyrotactic creatures and nanoparticles in the flow were investigated by Ramzan et al. (2017). The flow of nanofluids containing gyrotactic microorganism was studied in an experiment., Chakraborty et al. (2018) noticed by raising the magnetic field factor, temperature transit area, reduced flow of motile bacteria through the fluid media and lowered boundary layer thickness, while nanoparticle absorption enhanced. Tausif et al. (2016) described the movement of nanofluid with motile microorganisms and nanoparticles and several slipstream effects. To achieve critical outcomes in the polymer sector, the values of a number of slip parameters were increased, allowing fluid qualities such as microbe, rate of mass and flux or rate of heat transfer to be reduced or improved. Iqbal et al. (2017) nanofluid flowing steadily in two dimensions. with nanoparticles and gyrotactic bacteria was examined. This study includes the flow of a discursively striking nanofluid at its stagnation point. Atif et al. (2019) the density of motile microorganisms was raised by buoyancy ratio parameters but declined by micro polar parameters, according to the research. Atashafrooz, M., et al (2021) discussed Three-dimensional analysis of entropy generation for forced convection over an inclined step with presence of solid nanoparticles and magnetic force. Atashafrooz, M. et al investigate (2020) "Interacting influences of Lorentz force and bleeding on the hydrothermal behaviours of nanofluid flow in a trapezoidal recess with the second law of thermodynamics analysis. Atashafrooz, M., (2020) studied Influence of radiative heat transfer on the thermal characteristics of nanofluid flow over an inclined step in the presence of an axial magnetic field. Atashafrooz, M., (2019) invented the

Frontiers in Heat and Mass Transfer
Available at www.ThermalFluidsCentral.org effects of buoyancy force on mixed convection heat transfer of MHD nanofluid flow and entropy generation in an inclined duct with separation considering Brownian motion effects. Atashafrooz, M.,(2019), Interaction effects of an inclined magnetic field and nanofluid on forced convection heat transfer and flow irreversibility in a duct with an abrupt contraction. They took into account the thermal radiation and Joule heating effects. The effect of rising microbe density by cause of Peclet and Lewis numbers was examined by Acharya et al. (2016). The Keller box method was used to investigate the numeral solutions, which revealed that as the Peclet number increased, the concentration of microorganisms decreased. Shaw et al. (2018) nonlinear differential equations must be solved representing the movement of gyrotactic motile creatures and nanofluid, researchers used a spectrum relaxation technique. This bio convection flow was studied using a spherical submerged in a permeable material. Kuznetsov (2012) revealed the unpredictability of both non-oscillatory and oscillatory circumstances for nanofluid flows, with creatures that are oxytactic resulting in density stratification due to creatures with oxytactic motion or nanoparticle disposal.  in this work, Arrhenius activation energy, viscous dissipation, and joule heating are taken into consideration as we examine the improvements in electrically conducting Casson fluid generated by a porous elongated surface.  the current study intends to examine the characteristics of thermophoresis and Brownian motion-induced heat and mass transport processes in a liquid thin film of Casson Nano fluid across an extended sheet. In the current study, first-order chemical reaction, radiation, a continuous heat source, and an oscillating vertical wall embedded in a porous media are used to study the thermophysical properties of a Casson fluid. Vijaya N.et al (2018)  The major objective of this study to explore nanofluid flow in the presence of Gyrotactic Microbes on the stretching surface. The aspects of magnetic field and activation energy are also incorporated to study these special types of flows. Graphical portrayal is depicted using the powerful bvc4c via MATLAB software.

PHYSICAL MODEL DESCRIPTION
In this paper the study of nanofluids and gyrotactic microorganisms through the magnetic field and activation energy. Nanoparticles volume fractions are 1% more efficient than microorganisms. Motion of microorganisms are interrupted by nanoparticles. Solid nanoparticles mixed together, and microorganisms is prefix to the general fluid to achieve the appropriate bio convection stability. An atmosphere temperature, concentration of the fluid and microorganisms far from the surface of stretching sheet is revealed in the figure1. In the x-axis represents the flow direction with velocity component u. The y-axis is aligned with the sheet's velocity components . In the sheet was confined with the porous media take nanoparticles and gyrotactic microorganisms in it. Microorganisms moving around cause the bio convection to occur. In relation to the Nano entities, the microorganisms migrated separately.
Where Ω= where Ω is the motile microbes' parameter, Le is the Lewis number, Pe is the Peclet number, Ec is the Eckert number, N U is the Brownian motion, Nt is the thermophoresis parameter, Pr is the Prandtl number, Sc is the bio convection Schmidt number, I is the porosity parameter, and M is the Magnetic field, σ is chemical reaction parameter, E is activation energy parameter, δ is temperature difference additionally, dimensionless coordinates of technical interest like skin friction, Nusselt and Sherwood numbers and regional density index of motile microbes may be defined as

NUMERICAL SOLUTIONS
Using boundary layer theory, the PDEs (1) to (5) that regulate the flow of nanofluids issues are turned into nonlinear coupled ODEs. When it comes to boundary conditions (14), These strongly linked, ODEs. (10) to (13) are numerically solved using MATLAB's famed BVP4C solver. The BVP4C solver is based on a three-stage Lobatto IIIa collocation algorithm, with a collocation polynomial that produces a C1 continuous solution that is fourth-order accurate over the entire domain

Runge -Kutta method
Before going to apply the Runge-Kutta method, first apply the PDEs into ODEs of first order. Let us consider : = , . = f , W = J , The boundary conditions are

RESULTS AND DISCUSSIONS
In this paper propose that, the effect of activation energy on nanoparticles through the porous media. With the help of physical representations numerical results are explore. The system of equations from (10 -13) by using the boundary conditions (14). The velocity, temperature, concentration, motile microbe's density distributions, and heat and mass transfer allocations can be analyzed by using a number of estimates parameters, in Fig. (2) -(20) and table. M=2, m=1, I =0.5, Pr=3.2, L = 0.5, M =0.5, Ec=0.5, Le=1, n=0.1, E=2, =0.1, = 1, Ω=1, Sc=1, Pe=0.3. In Fig. 2 the velocity profiles are increase if upgrading the values of M. Magnetic field produces Lorentz force opposes nanofluid velocity results decreases in the thickness boundary layer, but it is increases it formed contradictory because of the nature of the greater strength of the fluid. The velocity profiles in porous term are depicted in Fig. 3, elevating the values of porosity parameters the velocity profiles are increased. Because the porous media has little impact on heat or mass transport. the region is the size of the microorganisms is larger than the size of pore size of the medium, so the moment of the microorganisms are not affected by the porous media having small permeability. When the porosity of the medium is increased, it offers superior solutions for bio convection parameters than when the porosity is decreased. It's worth noting that when porosity is high, the density of microorganisms is more stable. The values of Positive constant for nonlinear stretching sheet m are increased the velocity depictions are enhanced it is depicted in Fig. 4, the temperature, the concentration and the motile microbe's density distributions are decreased depicts in Fig. 5,  Fig. 14 and Fig. 19 respectively. Fig. 6 illustrates if the values of Prandtl number increases profiles of temperature is decline. By the definition of Pr raising the values of Pr results in either a larger momentum diffusivity or a lower thermal diffusivity, which reduces the thickness of the thermal layer. The temperature profiles are increasing for escalates the values of Ec. It is shown in Fig. 7. The heat transfer is more in the fluid as the values of the Eckert number raises. This event alters the thickness of the boundary layer and raises the temperature.            The values of N^ and N U developed the temperature profiles are increases it is shown in the Figs. 8 & 9. The boundary layer's temperature differential created the thermophoretic force, which plays a role in the diffusion of nanoparticles from an area of higher temperature to one of lower temperature causes enhance in the thickness of the thermal and solutal boundary layer.
Brownian motion is the random nanoparticle movement in the base fluid and is greater influence by its base fluid's tangent moving atoms. Brownian motion is related to the size of nanoparticles. In Fig. 10 it depicts that the Lewis number escalates the concentration profiles are declined. Le is defined as the product of thermal diffusivity and mass diffusivity. So, a thermal concentration boundary layer results from a rise in the Lewis number, which causes increased thermal diffusivity and decreased mass diffusivity. In Fig. 11 the concentration profiles increases if temperature difference parameter increases the behaviour of temperature difference parameter on because of the increase in the temperature difference between the wall and the surrounding area, thickness decreases and a thinner concentration profile appears. Fig. 12 depicts the function of concentration by varying the infinite activation energy E. The illustration makes it clear that concentration profiles are escalating function of E. Enhancing E at lower temperatures leads to a slower constant reaction rate and, ultimately, a smaller response. This improves the concentration solvent. The demeanour of non-dimensional rate constant and constant fitted rate n over concentration field are shown in Figs. 13 and 15. Examined is the fact that increased and n values produce an increase and decrease in concentration boundary layer thickness that eventually improves concentration respectively. The effect of Schmidt number for the bio convection of motile organisms Fig. 16 illustrates this. The increasing values of Schmidt number Sc are connected with a diminishing concentration profile. The density of motile microorganism declines as the rate of viscous diffusion escalates. Fig. 17 clarifies that increasing the values of Peclet number the values of density of microorganism concentration profiles are diminishes. Microorganisms swimming up the upper surface of the fluid cause bio convection. The action of microorganisms in this problem is caused by viscous drag and gravitational torques. An upgrade in the Peclet number's values Pe improves the rate of advective transport associated with dispersion while simultaneously increasing the flux of self-swimming motile microorganisms. The velocity of swimming motile microorganisms is produced by the bio convection Peclet number in the fluid, which causes a slowing regarding thickness of the motile organisms approaching the exterior. The concentration difference of microorganism's parameter are increases then the density of microorganism concentration profiles is diminishing this is seen in Fig.  18. The density of motile microorganisms is significantly affected by bio convection factors. A layer of heated fluid condenses on top of a layer of colder fluid at the boundary, this is known as thermal or temperature inversion. Thermal inversion (reversal) is caused by the viscous dissipation effect, which causes more heat to be created near the boundary. This is why certain graphs (slightly) depart from the imposed border restrictions.
In table 1 it is considering the difference of base paper and present paper there is very small variation in the articles. In present article comparing the Porous term differences.

CONCLUSIONS
This paper studies the Gyrotactic nanofluids and microbes flow via porous medium. A stream is taking in the nonlinear stretching sheet. According to this test's results, the use of gyrotactic microorganisms and nanoparticles are said to drive the flow toward uniformity and stability. The important outcomes are given in the following: i)In this article Porosity parameter need not affected because microorganism size is more than the size of pores. ii) An escalates in the motile microbe's parameter and bio convection he Schmidt number increases. As bio convection parameters rise, however, a declining tendency in the density profiles of mobile microorganisms is seen.
iii) The magnetic field and porosity parameters are increased the velocity profiles are increased. iv) Thermophoresis, Brownian motion, Eckert number these parameters are increases the profiles of temperatures are increased and Prandtl number rises the temperature profiles are diminishing. v) The concentration profiles are decreases if the Lewis number, reaction rate parameter, temperature difference parameter, power constant n are rises. The Activation energy parameter values are increases then the concentration profiles are increased. vi) Schmidt number, Peclet number, concentration difference of microorganisms these parameters are increases then density of motile microorganism's profiles are decreases.