Powell-Eyring Nanofluid Flow through a Permeable Stretching Surface with n th Order Chemical Reaction

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1 International Journal of Engineering Science Invention (IJESI) ISSN (Online): , ISSN (Print): Volume 7 Issue Ver. III April 018 PP 88-9 Poell-Eyring Nanofluid Flo through a Permeable Stretching Surface ith n th Order Chemical Reaction S.Anuradha 1, R.Praveena 1 Professor& Head, PG & Department Of Mathematics, Hindusthan College of Arts & Science, Coimbatore-8 Research Scholar, PG & Department Of Mathematics, Hindusthan College of Arts & Science, Coimbatore-8 Corresponding auther: S.Anuradha Abstract: Investigation Of non-netonian Nanofluid flo through a permeable stretching surface ith nth order chemical reaction has been analyzed in this present article. Mathematical modeling has been formulated for continuity, momentum, energy and concentration equations. The governing partial differential equations are transformed into coupled nonlinear ordinary differential equations ith the help of similarity transformation and then solved by using MATLAB s built in solver bvpc. The non-dimensional parameters Prandtl number (pr), Leis number (Le), Thermophoresis parameter (Nb), Bronian motion parameter (Nt), fluid parameters ( are studied ith help of graphs. Keyords Poell Eyring Nanofluid, Stretching Surface, Chemical Reaction Date of Submission: Date of acceptance: I. INTRODUCTION Non-Netonian fluid flo over a stretching surface due to its industrial applicationshas received significant attention. Such interest is fueled by engineering applications in a number of fields as continuous casting of metal, filaments, crystal groing, and extrusion of polymers, glass fiber production, paper production, and process of condensation of metallic plates. Entropy production determines the performance of thermal machines such as heat pumps, and air conditioners, poer plants, heat engines, refrigerators,. It also plays a key role in the thermodynamics of irreversible processes. During the recent years of nanotechnology brought out a multidimensional change to its useful applications in industry and engineering process. A nanofluid is a base fluid ith a nanometer sized particles. Abolbashari et al. [1] and they investigated entropy analysis of MHD unsteady in nano-fluid flo past a stretching permeable surface. Abbas et al. [] have described by an entropy generation on nanofluid flo through a horizontal plate. Bhatti et al.[3-9] have purposed a ne numerical simulation of MHD stagnation-point flo over a permeable stretching/shrinking sheet in porous media ith heat transfer and the various studies to visualized to analyze numerical simulation of entropy generation on MHD toards a effects of thermo-diffusion and thermal radiation on Williamson nanofluid over an boundary layer flo over a permeable shrinking/ stretching sheet and also discussed by Numerical simulation of entropy generation ith thermal radiation on MHD Carreau nanofluid on MHD Eyring Poell nanofluid through a permeable stretching surface. Mohammad et al. [10] examined that the entropy generation of nanofluid due to Peristaltic MHD blood flo as a practical tool of optimization for non-netonian flo through a permeable stretching surface using SLM. Munnaaar et al. [11] have investigated the analysis of entropy generation in the flo of peristaltic nanofluids in channels ith compliant alls. Muhammad et al [1] studied Entropy generation as a practical tool of optimization for non-netonian nanofluid flo through a permeable stretching surface using SLM. Qing et al. [13] have derived an entropy generation on MHD Casson nanofluid flo over a porous stretching/ shrinking surface. Rashidi et al. [1-15] have studied entropy generation in steady MHD flo due to a rotating porous disk in a nanofluid. And also Investigation of entropy generation in MHD and slip flo over a rotating porous disk ith variable properties. Sheikholeslami et al. [16] have been discussedmhd free convection of AlO3 ater nanofluid considering thermal radiation. Muhammed MubashirbBhatti et al.[17] studied entropy generation on non-netonian nanofluid flo through a permeable stretching surface. This paper is extension of Muhammed MubashirbBhatti et al.[17] for non-netonian Eyring-Poel nanofluid through a permeable stretching sheet ith nth order chemical reaction. Mathematical modeling has been formulated for continuity, momentum, energy and concentration equations. The governing partial differential equations are transformed into coupled nonlinear ordinary differential equations ith the help of similarity transformation and then solved by MATLAB s built in solver bvpc. 88 Page

2 II.MATHEMATICAL FORMULATION We considered a Mathematical model by Muhammed MubashirbBhatti et al.[17] in hich Eyring Poell nanofluid of boundary layer flo past a permeable stretching surface. This paper investigated nth order chemical reaction for Eyring Poell nanofluid of boundary layer flo over a stretching surface.in this study also, Cartesian coordinate has been considered as x-axis along the direction of the sheet and y-axis along normal to it and near a stagnation point at y = 0. T and C are all temperature and concentration respectively. Ambient temperature and concentration are T and C respectively. Assume velocity of the sheet along x- direction as u ax. The governing partial differential equations of Eyring Poell nanofluid model are as follos: u v 0 x y u u 1 u 1 u u due 3 e x y BC y BC y y dx u v u T T T C T D T T qr 1 Q0 u v D ( ) B T T x y y y y T y y cp c p C C C D T u v D T ( ) n B Kr C C x y y T y The corresponding boundary conditions are defined as u u, v v, T T, C C at 0 y (5) u u, 0,, e v T T C Cas y (6) Using the similarity transformation variables u ' u T T C C y, u u f ( ), v f ( ),,, x x T T C C The radiative flux is defined as 1 T qr 3k y (8) Where 1 is the Stefan Boltzmann constant and k is Rosseland mean absorption coefficient. We assume that the temperature differences ithin the flo are sufficiently small such that expressed as a linear combination of temperature. Expanding higher order terms yields: T T T 3T 3 * 3 qr 16 T T y 3k0 y Using the above, Equations () to (6) becomes ''' '' ''' ' '' 1 f 1 f f f ff 0 1 Pr (1) () (3) () (7) T may be T about T in Taylor s series and neglecting (11) eff f N N ( ) Q 0 (1) '' ' ' ' ' b t '' ' Nt '' n Lef K 0 (13) Nb Their corresponding boundary conditions are (9) (10) 89 Page

3 ' ' f (0) S, f (0), f ( ) 1, (1) (0) 1, ( ) 0, (15) (0) 1, ( ) 0, (16) Where the non-dimensional parameters are ax 3 Pr DB ( C C) DT ( T T) 1 Pr eff, Le, Nb, Nt,, 16R DB T BC x C 1 3 III. RESULTS AND DISCUSSION Mathematical modeling has been formulated for continuity, momentum, energy and concentration equations. The governing partial differential equations are transformed into coupled nonlinear ordinary differential equations ith the help of similarity transformation and then solved by using MATLAB s built in solver bvpc. The physical parameters involved in the governing flo problem have explained ith help of graphs. Figures 1- depict velocity profile for various values of fluid parameters γ, β. It is observed that increasing values of γ decreases the velocity profile hile the result is reverse ith variation of fluid parameter β. It is evident from the figures 3 and that increasing values of thermophoresis parameter Nt increase both temperature and concentration profiles.thermophoresis parameter Nt enhances thickness of the boundary layer. Figures 5 and 6 shos the variation of Bronian parameter Nb ith temperature and concentration profiles. Increment in Bronian parameter Nb enhances temperature profile and reduces the concentration profile. Figures 7, 8 and 9 illustrate velocity, temperature and concentration profiles against various values of Leis number and nth order chemical reaction parameter. Increasing Leis number diminish the temperature and concentration profiles. The order of chemical reaction enhances the separation process of species of rarer and lighter particles. (17) 90 Page

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5 IV. CONCLUSIONS The nonlinear governing equations are continuity, momentum, energy and concentration hich are solved ith the help of similarity transformation. The expressions of the emerging parameters analyzed numerically and graphically. It can be concluded as follos: Increasing values of γ decreases the velocity profile hile the result is reverse ith variation of fluid parameter β. Increasing values of thermophoresis parameter Nt increase both temperature and concentration profiles. Increment in Bronian parameter Nb enhances temperature profile and reduces the concentration profile. Increasing Leis number diminish the temperature and concentration profiles. The order of chemical reaction enhances the separation process of species of rarer and lighter particles. REFERENCES [1] Abolbashari MH, Freidoonimehr N, Nazari F, Rashidi MM., Entropy analysis for an unsteady MHD flo past a stretching permeable surface in nano-fluid, Poder Technol. (01); 67: [] Abbas T, Ayub M, Bhatti MM, Rashidi MM, AliMES., Entropy generation on nanofluid flo through a horizontal rigaplate, Entropy (016); 18(6)3. [3] Bhatti MM, Abbas T, Rashidi MM., A ne numerical simulation of MHD stagnation-point flo over a permeable stretching/shrinking sheet in porous media ith heat transfer, Iran. J.Sci. Technol, Trans. A: Sci. (016); 1 7. [] Bhatti MM, Rashidi MM., Numerical simulation of entropy generation on MHD nanofluid toards a stagnation point flo over a stretchingsurface,int.j.appl.comput.math. (016); [5] Bhatti MM, Rashidi MM., Effects of thermo diffusion and thermal radiation on Williams on nanofluid over a porous shrinking/stretching sheet, J. Mol.Liq. (016); 1: [6] Bhatti MM, Rashidi MM., Entropy generation ith nonlinear thermal radiation in MHD boundary layer flo over a permeable shrinking/ stretching sheet: numerical solution, J. Nanofluids (016); 5()53 8. [7] Bhatti MM, Abbas T, Rashidi MM, AliMES., Numerical simulation of entropy generation ith thermal radiation on MHD Carreau nanofluid toards a shrinking sheet, Entropy (016);18(6)00. [8] Bhatti MM, Abbas T, Rashidi MM, AliMES, Yang Z., Entropy generation on MHD Eyring Poell nanofluid through a permeable stretching surface,entropy (016);18(6). [9] Mohammad Mehdi rashidi, Muhammad Mubashir Bhatti, Munaar aliabbas, Mohammed el-sayedali., Entropy generation on MHD nanofluid blood flo due to peristaltic aves, Entropy (016); 18,117; doi: /e [10] Munaaraliabbas, Yanqinbai, Mohammad Mehdi rashidi, Muhammad MubashirBhatti., Analysis of entropy generation in the flo of peristaltic nanofluids in channels ith compliant alls, Entropy (016); 18, 90;doi: /e [11] Muhammad MubashirBhatti, Tehseen Abbas, Mohammad Mehdi Rashidi., Entropy generation as a practical tool of optimisation for non-netonian nanofluid flo through a permeable stretching surface using SLM, Journal of Computational Design and Engineering (017); 1 8 [1] Qing J, Bhatti MM, Abbas MA, Rashidi MM, AliMES., Entropy generation on MHD Casson nanofluid flo over a porous stretching/ shrinking surface, Entropy (016); 18()13. [13] Rashidi MM, Abelman S, Freidoonimehr N., Entropy generation due to MHD flo insteady rotating porous disk in a nanofluid, International journal of heat and mass transfer 6(013) [1] Rashidi MM, Nasser Kaviani, Abelman S., Investigation of entropy generation in MHD and slip flo over a rotating porous disk ith variable properties, Int. J.Heat Mass Transf. (01); 70: [15] Sheikholeslami M, Gorji-bandpy, GanjiDD, Rana P, Soheilsoleimani., Entropy generation of nanofluid in presence of magnetic field using Lattice Boltzmann Method, Physica A: Stat.Mech.Appl. (015); 17: Page