Unsteady MHD free Convective flow in a Rotating System with Soret Effect on n th order chemical reaction S.Anuradha 1 K.Sasikala 2

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1 Vol. 7Issue 1, January 018, ISSN: Ipact Factor: Journal Hoepage: Eail: Double-Blind Peer Revieed Refereed Open Access International Journal - Included in the International Serial Directories Indexed & Listed at: Ulrich's Periodicals Directory, U.S.A., Open J-Gage as ell as in Cabell s Directories of Publishing Opportunities, U.S.A Unsteady MHD free Convective flo in a Rotating Syste ith Soret Effect on n th order cheical reaction S.Anuradha 1 K.Sasikala Abstract Keyords: Magnetohydronaics (MHD); Soret Effect; Rotating syste; Theral Diffusion; Cheical reaction;. An Investigation on Soret effect ith n th order cheically reactive MHD free convection flo through a porous ediu in a rotating syste is carried out in this present study. Siilarity transforations are used to convert the governing nonlinear boundary layer equations into ordinary differential equations and solved it nuerically. The nuerical solutions of various diensionaless paraeters on the velocity, teperature, concentration profiles, skin friction, Nusselt nuber, Sherood nuber have been studied through graphs. The present study concluded that Soret Effect on n th order cheical reaction play ajor role in any industrial applications. Copyright 018 International Journals of Multidisciplinary Research Acadey. All rights reserved. Author correspondence: 1 Professor & Head in Departent of Matheatics, Hindusthan College of Arts & Science, Coibatore,Tailnadu,India,Eail:anu.prasanthi@gail.co. Assistant Professor in Departent of atheatics, Hindusthan College of Arts & Science, Coibatore,Tailnadu,India 1. Introduction Investigations on an unsteady MHD free convective heat and ass transfer flo over a porous ediu find variety of applications in odern etal-orking processes and anufacturing processes. Soe of the applications are the laination, hot rolling, crystal groing, purification of olten etals, eltspinning processes and ire draing etc. Fro odel studies on the Dufour and soret effect of MHD free convective flos have been ade by several investigators. Raptis et al., (1985) obtained the unsteady free convection flo through a porous ediu ith a sei-infinite vertical porous plate [1]. Dursunkaya et al., (199) investigated the steady natural convection fro a vertical surface ith the effects of diffusion-thero and theral-diffusion []. Kafoussias et al., (1995) reported the teperature dependent viscosity on ixed free-forced convective and ass transfer flo ith theral-diffusion and diffusion-thero effects [3]. Lavanya et al., (004) analyzed the to-diensional steady MHD free convection flo along a vertical porous plate ith theral radiation, heat generation, viscous dissipation and cheical reaction, Dufour and Soret effects [4]. Ala and Rahan (005) as established the on steady MHD free convective heat and ass transfer flo past a sei-infinite vertical porous plate ith Dufour and Soret effects [5]. On nuerical study of MHD cobined free-forced convective and ass transfer flo past a sei-infinite vertical plate in the presence of dufour and soret effect as reported by Ala (006) [6]. Ala et al., (006) exained an unsteady MHD free convective flo past a vertical porous plate in a porous ediu ith the presence of heat and ass transfer effect [7]. Nazul Isla and Mahud Ala (007) investigated the steady MHD free convection heat and and ass transfer fluid flo through a porous ediu ith theral diffusion and diffusion thero past a sei-infinite vertical porous plate in a rotating syste [8]. Eunuel et al., (008) discussed the cobined heat and ass transfer of a steady MHD convective and slip flo due to a rotating disk ith the effects of Theral-diffusion and diffusion theros, viscous dissipation and ohic heating [9]. Anjali Devi and Ua Devi (011) studied the MHD slip flo ith theral radiation over a porous rotating infinite disk in the presence of Soret and Dufour effects [10]. Shara and Borgohain (014) explained the effects of Soret and Dufour on heat and ass transfer of a binary fluid ixture in porous ediu over a rotating disk [11]. In vie of the above studies, an investigation on Soret effect ith n th order cheically 11 Eail: ijesj@gail.co

2 ISSN: Ipact Factor: reactive MHD free convection fo through a porous ediu in a rotating syste is carried out in this present study.. Matheatical Model Consider tie dependent, to diensional, MHD free convection heat and ass transfer flo in a rotating syste of an electrically conducting viscous fluid through a porous ediu along an infinite vertical porous plate y=0. The flo direction x and y axis are taken along the plate and noral to it. The teperature and the concentration at the plate are defined as T and C here B is agnetic field and the fluid is assuerd to be slightly conducting therefore the effect of agnetic Reynolds nuber hich is very sall and less than unity. Hence the induced agnetic field is negligible. The governing boundary layer equations of oentu, energy, and concentrations are ritten as follos; The continuity equation v 0 y The oentu equations u u * u B0 u v g0 ( T T) g0 C C u t y y K B0 v u t y y K The energy equation T T k T Dk C v qr T T t y c y c c y The concentration equation T p s p C C C Dk T v D KrC C t y y T y T Subject to the folloing boundary conditions, t 0, u 0, v 0, 0,T T,C C for all values of y. t 0, u U 0, v vt, 0, T T, C C, at at y 0 6 t 0, u 0, v 0, 0, T T, C C, at at y 7 We introduce a siilar paraeter hich is the tie dependent length scale, v t v 0, ct, 0 hen t 0, t Introducing the folloing non-diensionl variables to find a siilarity solution y u T T C C, f, g,, U U T T C C 0 0 Where e use the folloing physical quantities, r g T T g C C B G G M R * 0 0 0,,, U0 U0 cp Dk C C T Dk T T T 0 Pr, Df, Sc, Sr, k c c T T D T C C n s p By introducing the above non-diensional varibles, equations ()-(5) becoe f f G G Kf Mf Rg 0 r g g Kg Mg Rf Eail: ijesj@gail.co

3 ISSN: Ipact Factor: Pr Pr Df PQ r r 0 1 n S S S S K 0 13 c c r c r The corresponding boundary conditions are, f 1, g 0, 1, 1, at , 0, 0, 0, 15 f g at 3. Nuerical Analysis In this present article, e investigatigated unsteady MHD free convective and ass transfer flo through a porous ediu ith theral diffusion, dufour effect and soret effect on nth order cheical reaction past an infinite vertical porous plate in a rotating syste. The governing boundary layer equations ()-(5) are transfored to ordinary differential equations (10)-(13) by using siilarity transforation. Then they are solved by using Runge-Kutta 6 th order Schee. The obtained nuerical results are illustrated graphically for various non-diensional paraeters on velocity, teperature, concentration profiles, skin friction, Nusselt nuber, Sherood nuber.. 4. Results and Discussion It is very iportant to study the influence of various diensionless paraeters ingrained in the flo odel on velocity, teperature and concentration. The physical paraeters involved in the flo proble is Prandtl nuber(pr), Dufour nuber(df), Activation energy (E), Fitted rate constant(n), teperature difference paraeter(δ) and reaction rate(σ). Graphs are shoed to describe the behavior of the flo fields ith different values of flo paraeters. Fig 1, Fig., and Fig.3 are ade for the flo velocity, teperature and concentration profiles against the Prandtl nuber(pr). It reveals that the velocity and teperature field develops but reverse effect on concentration profile ith the hike in Pr. Fig.4, Fig.5, and Fig.6 visualized the variations of Skin friction, Nusselt nuber and Sherood nuber of the fluid under the influence of Prandtl nuber(pr). It is evident that, inflating the values of Pr causes depreciation in Skin friction and nusselt nuber and enhances the Sherood nuber profiles. Fig.7, Fig.8, and Fig.9 elucidate the diensionless velocity, teperature ad concentration distribution for different values of Dufour nuber(df). It is noticed that the velocity and teperature fields are enlarge but the concentration field reduced ith the iproveent in Df. Fig.10, Fig.11, and Fig.1 exhibit the Skin friction, Nusselt nuber and Sherood nuber distribution for various values of Df. It is established that rising values of Df increases the Skin friction and nusselt nuber profiles but reverse trend has been observed in the Sherood nuber Eail: ijesj@gail.co

4 ISSN: Ipact Factor: Conclusion This study is an investigation of unsteady MHD free convective and ass transfer flo through a porous ediu ith theral diffusion, dufour effect and soret effect on nth order cheical reaction past an infinite vertical porous plate in a rotating syste. The results are as follos; The velocity and teperature field develops but reverse effect on concentration profile ith the hike in Pr. Increasing the values of Pr causes depreciation in Skin friction and nusselt nuber and enhances the Sherood nuber profiles. The velocity and teperature fields are enlarge but the concentration field reduced ith the iproveent in Df. Increasing values of Df increases the Skin friction and nusselt nuber profiles but reverse trend has been observed in the Sherood nuber. References [1]. Raptis. A and Perdikis. P.C., (1985), Unsteady Flo Through a Porous Mediu in the Presence of Free Convection, Int.Co.Heat Mass Trans., 1, pp []. Dursunkaya.Z and Worek W.M., (199), Diffusion-Thero and Theral-Diffusion Effects in Transient and Steady Natural Convection fro Vertical Surface, Int. J. Heat Mass Trans., 35(8), pp [3]. Kafoussias N.G., Willias E.M., (1995), Theral-Diffusion and Diffusion-Thero Effects on Mixed Free-Forced Convective and Mass Transfer Boundary Layer Flo ith Teperature Dependent Viscosity,Int.J. Engng. Sci., 33, pp [4]. Lavanya.B and Leela Ratna.,(004), Dufour and Soret effects on Steady MHD Free Convective Flo Past a Vertical Plate Ebedded in a Porous Mediu ith Cheical Reaction, Radiation Heat generation and Viscous Dissipation, Advances in Applied Science Research, 5, pp [5]. Ala M. S and M.M. Rahan., (005), Dufour and soret effect on MHD Free Convective Heat and Mass Transfer Flo past a Vertical Flate Plate Ebedded in a Porous Mediu, J. Naval Architecture and Marine Engng, (1), pp [6]. Ala M.S.,(006), Dofour and Soret Effects on Steady MHD Cobined Free-Forced Convective and Mass Transfer Flo Past a Sei-infinite Vertical Plate,Thaasat Int. J. Sci. Technol., 11, pp Eail: ijesj@gail.co

5 ISSN: Ipact Factor: [7]. Ala M. S., Rahan.M.M and Saad M. A.,(006), Dufour and Soret effects on Unsteady MHD Free Convection and Mass Transfer Flo Past a Vertical Porous Plate in a Porous Mediu,Nonlinear Analysis Modelling and Control, 11, pp [8]. Nazul Isla and Md.Mahud Ala., (007), Dufour and Soret Effects on Steady MHD Free Convection and Mass Transfer Fluid Flo Through a Porous Mediu in a Rotating Syste, Journal of Naval Architecture and Marine engineering, 4, pp [9]. Eunuel.O., Jonathan. S., and Robert. H., (008), Theral-Diffusion and Diffusion-Thero Effects on Cobined Heat and Mass Transfer of a Steady MHD Convective and Slip Flo due to a Rotating Disk ith Viscous Dissipation and ohic hating, Int. Coun. Heat Mass Transfer, 35, pp [10]. Anjali Devi. S.P and Ua Devi R., (011), Soret and Dufour Effects on MHD Slip Flo ith Theral Radiation over a porous Rotating Infinite disk, Counication in Nonlinear Science and Nuerical Stiulation, 16(4), pp [11]. Shara B.R and Borgohain. D., (014), Influence of Cheical Reaction, Soret and Dufour Effects on Heat and Mass Transfer of a Binary Fluid Mixture in Porous Mediu over a Rotating Disk, IOSR Journal of Matheatics, 10(6), pp Eail: ijesj@gail.co