Influence of Heat Generation/Absorption and Stagnation point on Polystyrene -TiO 2 /H 2 O Hybrid Nanofluid

: This article focuses on hybrid nanofluid flow induced by stretched surface. The present context covers stagnation point flow of a hybrid nanofluid with the effect of heat generation/absorption. Currently most famous class of nanofluids is Hybrid nanofluid. It contains polystyrene and titanium oxide as a nanoparticles and water as a base fluid. First time attributes of heat transfer are evaluated by utilizing polystyrene-TiO 2 / H 2 O hybrid nanofluid with heat generation/absorption. Partial differential equations are converted into ordinary differential equation by using appropriate transformations for heat and velocity. Homotopy analysis method is operated for solution of ordinary differential equations. Flow and heat are disclosed graphically for unlike parameters. Resistive force and heat transfer rate is deliberated mathematically and graphically. It is deduced that velocity field enhanced for velocity ratio parameter whereas temperature field grows for heat generation/absorption coefficient. To judge the production of any engineering system entropy generation is also calculated. It is noticed that entropy generation grows for Prandtl number and Eckert number while it shows opposite behavior for temperature difference parameter. aerodynamic and


Introduction
Heat transmission plays a vital role in many respects for instance in refrigeration, power generation, thermoelectric devices, heat exchangers, roofing materials, food processing, radiative cooling and thermal energy storage etc. Therefore it is advantageous to enhance the production of heat transfer machines adopted in these areas. Thermal conductivity is the crucial framework in heat transfer problems. Ethylene glycol, water and oils have low thermal conductivity. Nanomaterials like oxides of metals , carbides etc are included in the host fluid for intensification of thermal conductivity. Choi   1 instigated about nanofluids. Hybrid nanofluids seeks the intention of researchers and scientists currently. It consists of two or more non-identical particles having size less than 100nm. Here, we take polystyrene and titanium oxide as nanoparticles due to their wide use in pharmaceuticals, automtive industary, IT equipments(TV, Computers, laptops), food packing industary, construction, household industary, cosmetics, fabrics and textiles. Waini  They include cooling of plates, nuclear reactor cooling, tinning of wires and wire drawing etc. Naganthran et al. [13] described the flow of viscoelastic fluid past a shrinking sheet with oblique stagnation point. They concluded that enhanced mass flux parameter strengthens the heat transfer rate. Consequences of chemical reaction on CNTs along with stagnation point was founded by Khan et al. [14]. Magnified velocity ratio parameter decays the drag force. Ascendancy of Maxwell fluid with suction/injection was illustrated by Ahmed et al. [15]. Porous rotating disk was also considered. Numerical results showed that rotation parameter enhanced the nusselt number at the surface. Moshkin et al. [16] elaborated the flow of unsteady Maxwell fluid by transforming the equations into the Lagrangian coordibates. Weidman [17] contemplated a flow along a rotating plate and revealed the influence of Hiemenz stagnation point on this plate. He gave good comparision with Hannah's consideration. The out turn of Homann stagnation point on a non Newtonian fluid regarding a stable plate was initiated by Mahapatra et al. [18]. They deduced that viscoelastic parameter grows the velocity profile. Azhar et al. [19] studied about heat generation and viscous dissipation of Jeffrey fluid along with stagnation point. Stretching ratio parameter enhanced the drag force as well as Sherwood number. Flow of MHD Carreau fluid induced by stretching surface was instigated by Chu et al. [20]. He examined flow about stagnation point. Both heat and mass will transfer more fastly by increasing velocity ratio parameter. Shah et al [21] takes a Riga plate and found the out turns of stagnation point and mixed convection along with porous medium. Darcy number decays the velocity field while grows the skin friction. Awan et al. [22] assumed MHD second grade fluid with oblique stagnation point. The flow was induced by oscillatory surface. He showed that Sherwood number and heat transfer rate boosts up for larger suction parameter. Conception of entropy in thermodynamic system was prescribed by Rudolf Clausius in 1850s. It is the amount of thermal energy per unit temperature which is unattainable for performing beneficial tasks. The quantity of entropy assembled in irreversible processes is termed as entropy production. For example heat exchange, heat engines, fluid flows, heat pumps, power plants, air conditioners and refrigeneration etc. It determines the execution of thermodynamical system. At first Bejan [23] studied about entropy generation. He explained the significant steps of entropy depreciation. Gholamalipour et al. [24] studied the entropy generation of nanofluid in a permeable annulus. For lesser Darcy and Rayleigh number greater disturbance in entropy producution is noticeable. Dutta et al. [25] considered a rhombic shape closed pattern pervaded by Cu-water nanofluid and investigates about entropy generation. He showed that increment in Ha decays the entropy production rate. Khan et al. [26] discussed the impact of joule heating on casson fluid passing through a revolving cylinder. Entropy generation shows increasing trend for larger Brinkman number. Attributes of entropy production in Newtonian fluid with Darcy model was analyzed by Ambreen et al. [27]. Cho [28] takes a square cavity whose some walls are heated and filled it by Cu-water nanofluid. Along this he considered a porous medium inside the cavity and then measure the entropy production rate. For a fixed Rayleigh number, entropy rate enhanced with enlarged Darcy number. Influence of natural convection in elliptical cavity pervaded by hybrid nanofluid was inspected by Tayebi et al. [29]. Zahid et al. [30] explained that low entropy production occurs for higher Hall parameter. Li et al. [31] examined the thermal radiation effect in a tilted square cavity. He also analyzed the entropy production rate here and found that Rayleig number grows the entropy production rate. Sachica et al. [32] scrutinized the Al 23 O -water nanofluid in a rectangular channel and numerically investigate it. Nano particle volume fraction decreases the entropy generation rate. Extraordinary enhancement in thermal conductivity is noticed for hybrid nanofluids in comparision with ordinary nanofluids. Therefore have innumerable applications in home industary, automative industary, engineering, for cancer treatment, cosmetics, pharmaceuticals, food pakaging, papaer plastics, fabrics, ceramics, paints, food colorants and in soaps as well .
Here the key objective is to discuss the characteristics of polystyrene-TiO 2 /H 2 O hybrid nanofluid flow with heat generation/absorption. Stagnation point is also contemplated in momentum equation. We take advantage of congrous transformations for transmutation of partial differential equations into nondimensionalized ordinary differential equations. Homotopic methodology [33 39]  is executed for series solution. Ramification of incompatible parameters are interpreted graphically. Mathematical expression of drag force is calculated and nusselt number is manifested graphically. Entropy generation rate is also exposed through graphs.

Formulation
Analysis of two dimensional hybrid nanofluid suppressed with polystyrene and titanium oxide (TiO 2 ) particles has carried out.Influence of stagnation point on flow pattern is also discussed. Impact of heat generation/absorption is also figure out. We take stretching velocity Persistent temperature is presumed at both plate surface and ambient fluid.
After implementation of boundary layer approximation the ruling equations appears as: Here u and v are symbolized as velocity constituents x and y respectively.
Equation (1) In these equations A denotes velocity ratio parameter , Pr symbolizes the Prandtl number,  is heat generation/absorption parameter. Algorithmic representation of these quantities are specified as : Its undimensional form is as below here local Reynolds number is symbolized by Re

Entropy generation
Here our principal focus is to evaluate the irreversibilities of a system through entropy generation.Mathematically it is given as

Homotopic solutions
Homotopic method was exposed by Liao [33]. This method is utilized for finding the series solutions of highly non linear problems. Initial gusses and linear approximations are free to choose. They are intimated as follows:

Convergence analysis
Homotopy analysis method is that method which gave us freedom to choose and control the convergance region. Fig. 1

Discussion
Graphical demonstration of influential parameters for flow and heat transmission are given in this portion.Thus figures are portrayed. Effect of velocity ratio parameter A on velocity profile is illustrated in Fig .2. It is noticed that both velocity profile and momentum boundary layer thickness enhanced for increased velocity ratio parameter. Physically magnified ratio parameter prop up the free stream velocity which assists the velocity upgradation. Figs. (3 4).  are plotted for polystyrene particles volume fraction 1  versus velocity and heat profiles. Opposite behavior is detected for velocity and temperature distribution. Velocity profile grows and temperature profile gets steeper. Fig. 5  TiO particles provides significant resistance to the fluid consequently velocity deteriorate. Fig. 6. indicates the impact of titanium oxide   2 TiO particles volume fraction 2  on temperature distribution. Alternate trend is obtained as for velocity field. Nano particles volume fraction strengthens the thermal conductivity of a base fluid. Therefore temperature distribution marked up. Fig. 7. indicates the influence of heat generation/absorption parameter  on temperature profile. Heat generation/ absorption parameter  strengths the thermal boundary layer and temperature profile. In the course of heat generation activity extra heat will be generated and eventually temperature distribution boost. Out turn of Prandtl number on temperature field is displayed in fig. 8. Temperature profile diminishes for intensified Prandtl number Pr. Physically thermal diffusivity fall down for upgraded Prandtl number Pr. So we obtain narrow temperature profile. Figs. (9 10).  displays the heat transfer rate versus Prandtl number Pr and heat generation parameter .
 It is observed that heat transfer rate enhances for Prandtl number Pr as well as heat generation/absorption parameter  . Physically higher Prandtl number reduces the temperature field. Therefore maximum amount of heat will be transferred to the environment. As a result rate of heat transfer increases. Fig. 10. expresses the 3D plot of nusselt number for pertinent parameter. Increment in heat transfer rate has been detected. The reason for this is that enlarged Prandtl number Pr declines the thermal boundary layer which inturns enhances heat transfer rate.
 represents the effect of polstyrene particles volume fraction 1  and titanium oxide particles volume fraction 2  on entropy generation. Results shows that both polystrene particles volume fraction and titanium oxide particles volume fraction enhances the entropy generation rate. To determine the impact of Prandtl number Pr and Eckert number Ec on entropy generation, figs. (13)(14). are sketched. It is noticed that entropy generation rate is a increasing function of Prandtl as well as Eckert number. Actually due to enlarged Eckert number Ec supplementary heat will be induced and therefore entropy generation dominates. Fig. 15. portrayed the footprints of temperature difference parameter  on entropy production rate. Opposite behavior has been perceived as compared to Eckert number. Entropy generation rate diminishes when temperature difference parameter grows.

Conclusions
Influence of heat generation/absorption and stagnation point on hybrid nanofluid are taken into account. Hybrid nanofluid contains Polystyrene and TiO 2 nanoparticles with water as a transiet fluid. The disruptive results for the sophisticated parameters are displayed graphically. The majour outcomes are as persued:  Volume fraction of polystyrene particles 1  enlarged the velocity profile and degrade the temperature profile.  Volume fraction of titanium oxide 2  particles decline the velocity field whereas adverse behavior is detected for temperature field.  Velocity ratio parameter enhanced the velocity field.  Heat generation/absosption parameter emlarged the temperature profile.  Entropy generation intensifies for both polystyrene and titanium oxide parcticles.  Prandtl number Pr and Eckert number Ec also amplifies the entropy generation strength.  Temperature difference parameter decays the entropy generation.
The preference is that the contemporaneous analysis will be extremely beneficial for modeling better flow obstacles specifically in biomedical industary, for cancer treatment, aerodynamic industary, power generation, nuclear reactors and solar thermal absorbers.