International Journal of Mathematical Archive-4(2), 2013, Available online through ISSN

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1 International Jornal of Mathematical Archive-4(), 3, Available online throgh ISSN CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY FLOW PAST A POROUS PLATE EMBEDDED IN A POROUS MEDIUM IN THE PRESENCE OF HEAT SOURCE K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 Dept. of Science and Hmanities, Sata Institte of Tech and Management, Gajlarega, Vizianagaram, A.P., India Dept of Mathematics, Hind College, Gntr, A.P., India 3 Dept. of Mathematics, Govt. Degree College, Jammalamadg, Kadapa (Dt.), A.P., India (Received on: --; Revised & Accepted on: 8--3) ABSTRACT An attempt has been made to std the two-dimensional MHD free convective oscillator flow of an electricall condcting incompressible viscos flid past an infinite vertical poros plate embedded in a poros medim, throgh which sction occrs with constant velocit and chemical reaction in the presence of a heat sorce. A niform magnetic field is assmed to be applied transversel to the direction of the free stream taking into accont of indced magnetic field. The governing eqations involved in the present analsis are solved b sing the pertrbation method. The velocit, temperatre and concentration fields are stdied for different parameters sch as Grashof nmber (Gr), modified Grashof nmber (Gc), Magnetic field parameter (M), Permeabilit parameter (k), Schmidt nmber (Sc), Prandtl nmber (Pr), heat sorce parameter (Q) and Chemical reaction parameter (Kr), Eckert nmber (Ec) etc. Ke words: MHD, Chemical reaction, Heat Sorce, Poros medim etc. INTRODUCTION: The inflence of magnetic field on viscos incompressible flow of an electricall condcting flid has its importance in man applications sch as extrsion of plastics in the manfactre of raon and nlon, prification of crde oil, plp, paper indstr, textile indstr and in different geophsical cases etc. In man process indstries, the cooling of threads or sheets of some polmer materials is of importance in the prodction line. The rate of cooling can be controlled effectivel to achieve final prodcts of desired characteristics b drawing threads, etc. in the presence of an electricall condcting flid sbject to a magnetic field. MHD plas an important role in agricltre, petrolem indstries, geophsics and in astrophsics. Important applications are in the std of geological formations, in exploration and thermal recover of oil, and in the assessment of aqifers, geothermal reservoirs and ndergrond nclear waste storage sites. MHD flow has application in metrolog, solar phsics and in motion of earth s core. Also it has applications in the field of stellar and planetar magnetospheres, aeronatics, chemical engineering and electronics. In the field of power generation, MHD is receiving considerable attention de to the possibilities it offers for mch higher thermal efficiencies in power plants. Jonah Philliph et al. (6) stdied the effects of thermal radiation and MHD on the nstead free convection and mass transform flow past an exponentiall accelerated vertical plate with variable temperatre. Gireesh Kmar et al. () discssed the effects of chemical reaction on transient MHD convection flow past a vertical srface embedded in a poros medim with oscillating temperatre. Hemanth Poonia and Chadhar (4) analzed the MHD free convection and mass transfer flow over an infinite vertical poros plate with viscos dissipation. Girish Kmar et al. (3) examined the mass transfer effects on MHD flows exponentiall accelerated vertical plate in the presence of chemical reaction throgh poros media. The std of convective flid flow with mass transfer along a vertical poros plate in the presence of magnetic field and internal heat generation receiving considerable attention de to its sefl applications in different branches of science and technolog sch as cosmical and geophsical science, fire engineering, combstion modeling etc. Vajravel (4) stdied natral convection flow along a heated semi-infinite vertical plate with internal heat generation. Corresponding athor: K. Sreelatha * Dept. of Science and Hmanities, Sata Institte of Tech and Management, Gajlarega, Vizianagaram, A.P., India International Jornal of Mathematical Archive- 4(), Feb. 3 84

2 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb.-3. Cooke et al. (8) analzed inflence of viscos dissipation and radiation on nstead MHD free convective flow past an infinite heated vertical plate in a poros medim with time dependent sction. Chamkha (6) discssed nstead MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat generation. Ahmed () looked the effects of nstead free convective MHD flow throgh a poros medim bonded b an infinite vertical poros plate. Sharma and Singh () discssed the nstead MHD free convective flow and heat transfer along a vertical poros plate with variable sction and internal heat generation. Sharma et al. () analzed the heat and mass transfer effects on nstead MHD free convective flow along a vertical poros plate with internal heat generation and variable sction. Sondalgekar () investigated the nstead free convection flow along vertical poros plate with different bondar conditions and viscos dissipation effect. Convection in poros medim has important applications in man areas inclding thermal energ storage, flow throgh filtering devices, tilization of geothermal energ, oil extraction, high performance inslation for bildings, paper indstr etc. Hence combined std ma give some vital information which will srel be helpfl in developing other relevant areas. Kishore et al. (7) analzed the effects of thermal radiation and viscos dissipation on MHD heat and mass diffsion flow past an oscillating vertical plate embedded in a poros medim with variable srface conditions. Israel Cooke et al. (5) stdied the inflence of viscos dissipation and radiation on nstead MHD free convection flow past an infinite heated vertical plate in a poros medim with time dependent sction. Chadhar and Arpita Jain (7) discssed the MHD heat and mass diffsion flow b natral convection past a srface embedded in a poros medim. Seethamahalakshmi et al. (9) examined the effects of the chemical reaction and radiation absorption on an nstead MHD convective heat and mass transfer flow fast a semi-infinite vertical moving in a poros medim with heat sorce and sction. Abdel-Nasser Osman et al. () investigated the analtical soltion of thermal radiation and chemical reaction effects on nstead MHD convection throgh poros medim with heat sorce/sink. Chamkha and Khaled (5) looked the effects of hdromagnetic combined heat and mass transfer b natral convection from a permeable srface embedded in flid satrated poros medim. Mass diffsion rates can changed tremendosl with chemical reactions. In majorit cases, a chemical reaction depends on the concentration the concentration of the species itself. A reaction is said to be first order, if the rate of reaction is directl proportional to the concentration itself (Cssler (9)). A few representative areas of interest in which heat and mass transfer combined along with chemical reaction pla an important role in chemical indstries like in food processing and polmer prodction. Chambre and Yong (4) have analzed a first order chemical reaction in the neighborhood of a horizontal plate. Das et al. (, ) have stdied the effect of homogeneos first order chemical reaction on the flow past an implsivel started vertical plate with niform heat flx and mass transfer. Again, the are also discssed the mass transfer effects on moving isothermal infinite vertical plate in the presence of chemical reaction. The dimensionless governing eqations were solved b the sal Laplace Transform techniqe. Sdheer Bab et al. (3) have examined the radiation and chemical reaction effects on an nstead MHD convection flow past a vertical moving poros plate embedded in a poros medim with viscos dissipation. Mthcmaraswam and Klaivel (8) looked the chemical reaction effects on moving infinite vertical plate with niform heat flx and variable mass diffsion The main objective of the present analsis is to std the nstead two-dimensional MHD free convective oscillator flow of an electricall condcting incompressible viscos flid past an infinite vertical poros plate embedded in a poros medim, in which sction occrs with constant velocit and chemical reaction in the presence of a heat sorce. The eqations of continit, momentm, energ and diffsion which govern the flow field are solved to the best possible soltion. Nomenclatre C - dimensionless concentration, [-] CC - concentration, [molmm 3 ] CC ww - species concentration at the plate, [molmm 3 ] CC - species concentration far awa from the plate, [molmm 3 ] cc pp - specific heat at constant pressre, [Jkg - K - ] D - chemical diffsivit, [m s - ] Ec - Eckert nmber, [-] gg xx - acceleration de to gravit, [ms - ] Gc - modified Grashof nmber, [-] Gr - Grashof nmber, [-] BB - applied magnetic field, [-] kk - permeabilit parameter, [-] κκ - thermal condctivit, [Wm - K - ] Pr - Prandtl nmber, [-] 3, IJMA. All Rights Reserved 85

3 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb.-3. pp - pressre, [kgm - s - ] qq - heat flx at the plate, [Wm - ] QQ - heat sorce, [-] Sc - Schmidt nmber, [-] KK rr - chemical reaction, [-] T - dimensionless flid temperatre, [-] TT - flid temperatre, [K] TT - temperatre of the flid far awa from the plate, [K] t - dimensionless time, [-] tt - the time, [s] UU - mean free stream velocit, [ms - ] - dimensionless velocit of the flid at the xx - direction, [-] - velocit of the flid at the xx - direction, [ms - ] vv - velocit of the flid at the - direction, [-] vv - sction velocit, [ms - ] xx - co-ordinate axis along the plate, [-] - co-ordinate axis normal to the plate, [-] Greek smbols αα - absorption coefficient, [m - ] ββ - coefficient of thermal expansion, [K - ] ββ - coefficient of concentration expansion, [(molm -3 ) - ] vv - kinematic viscosit, [m s - ] ρρ - flid densit, [kgm -3 ] σσ - Stefan Boltzman constant, [Wm - K -4 ] ωω - dimensionless freqenc of vibration of the flid, [-] ωω - freqenc of vibration of the flid, [rads - ] FORMULATION OF THE PROBLEM: We consider the nstead two-dimensional MHD free convective oscillator flow of an electricall condcting incompressible viscos flid past an infinite vertical poros plate embedded in a poros medim, throgh which sction occrs with constant velocit and chemical reaction in the presence of a heat sorce. The xx - axis is along the plate in the pward direction and the - axis is normal to it. A niform magnetic field is applied in the direction perpendiclar to the plate. Renolds nmber is mch less than nit and the indced magnetic field is negligible in comparison with the applied magnetic field. It is also assmed that all the flid properties are constant except that of the inflence of the densit variation with temperatre and concentration in the bod force term (Bossinesq s approximation). There is a chemical reaction between the diffsing species and the flid. The foreign mass present in the flow is assmed to be a low level and hence Soret and Dfor effects are negligible. Under these assmptions, the governing eqations of the flow field are: Continit eqation vv = () Momentm eqation ρρ + vv pp tt = ρρgg xx xx + vvvv σσbb + ρρ vv kk ( ) () Energ eqation TT tt + vv TT = κκ TT ρρcc pp + vv CC pp + QQ (TT TT ρρcc ) (3) pp Diffsion eqation CC + vv CC = DD CC tt KK rr (CC CC ) (4) Where and vv are the components of the velocit parallel and perpendiclar to the plate, tt - the time, pp - the pressre, ρρ - the flid densit, gg xx - the acceleration de to gravit, BB - the applied magnetic field, kk - the permeabilit parameter, TT - the flid temperatre, vv- the kinematic viscosit, CC pp - the specific heat at constant pressre, κκ - the thermal condctivit, QQ - the heat sorce, CC - the concentration and DD- the chemical diffsivit, KK rr - the chemical reaction 3, IJMA. All Rights Reserved 86

4 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb.-3. The bondar conditions are: =, vv = vv, TT = qq, κκ CC = CC ww aaaa = (5) UU = UU + εεee iiww tt, TT TT, CC CC aaaa Where vv is the constant sction velocit and the negative sign indicates that it is towards the plate, qq - the constant heat flx, TT - the flid temperatre far awa from the plate, CC ww - the species concentration at the plate, CC - the species concentration far awa from the plate, UU - the mean free stream velocit, ωω - the freqenc of vibration of the flid, and εε (εε < ) - a constant qantit. For the free stream, eqation () becomes: ρρ dduu ddtt = pp xx ρρ gg xx σσbb UU ρρ vv kk UU (6) On eliminating pp xx between () and (6) we get: ρρ + vv dduu tt = ρρ + gg ddtt xx (ρρ ρρ) + vvvv σσbb + ρρ vv kk UU (tt ) (7) The state eqation is gg xx (ρρ ρρ) = gg xx ρρρρ(tt TT ) + gg xx ρρββ (CC CC ) (8) Where ββ is the coefficient of thermal expansion and ββ is the coefficient of concentration expansion From (7) and (8) we have tt + vv = dduu ddtt + gg xx ββ(tt TT ) + gg xx ββ (CC CC ) + vv σσbb ρρ + vv kk UU (tt ) (9) Eqation () gives: vv = vv (vv > ) () On sbstitting eqation (), in eqations (), (3) and (4) we take: vv tt = dduu + gg ddtt xx ββ(tt TT ) + gg xx ββ (CC CC ) + vv σσbb ρρ TT TT vv tt = + vv kk UU (tt ) κκ TT ρρcc pp + vv CC pp + QQ (TT TT ρρcc ) () pp CC CC vv tt = DD CC KK rr (CC CC ) (3) () Using the transformations: = vv, tt = tt vv vv 4vv CC = CC CC, GGGG = gg xx CC ww CC, =, UU = UU, ωω = 4vvωω UU UU vv ββvvqq kkuu vv3 vv EEEE = kkuu vv, MM = σσbb CC pp vvqq ρρvv, QQ = vv QQ κκvv TT = TT TT vvqq kkvv, GGGG = vvgg xx ββ CC ww CC UU vv, Pr = ρρρρ CC pp, kk, KKKK = KK rr vv vv, SSSS = vv, kk = kk vv DD vv (4) With the help of the non-dimensional qantities (4), eqations ()-(3) redce to: = dddd + GGGGGG + GGGGGG + MM + ( UU) (5) 4 tt 4 dddd kk PPPP 4 SSSS 4 = TT + PPPPPPPP + QQQQ (6) = CC KKKKKKKKKK (7) With the bondar conditions: =, =, CC = aaaa = (8) UU(tt) = + εεee ii ωω tt, TT, CC aaaa 3, IJMA. All Rights Reserved 87

5 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb.-3. SOLUTION OF THE PROBLEM: Eqations (5) (7) are copled, non-linear partial differential eqations and these cannot be solved in closed form. However, these eqations can be redced to a set of ordinar differential eqations, which can be solved analticall. This can be done b representing the velocit, temperatre and concentration of the flid in the neighborhood of the plate as: (, tt) = () + εεee ii ωω tt () + (9) TT(, tt) = TT () + εεee ii ωω tt TT () + () CC(, tt) = CC () + εεee ii ωω tt CC () + () On sbstitting eqations (9)-() in eqations (5)-(7) we get the following sstem of differential eqations: dd + dd MM + dd dddd kk = GGGGTT + GGGGCC + MM + () kk dd + dd dd dddd iiii MM 4 kk = GGGGTT + GGGGCC + iiii + MM + ` (3) 4 kk dd TT dd + PPPP ddtt dddd + QQTT = PPPPPPPP dd dddd (4) dd TT dd + PPPP ddtt dddd iiii 4 PPPPTT + QQTT = PPPPPPPP dd dddd dd dddd (5) dd CC dd + SSSS ddcc dddd KKKKKKKKCC = (6) dd CC dd + SSSS ddcc dddd SSSS iiii 4 KKKK CC = (7) The corresponding bondar conditions (8) are: =, =, ddtt =, ddtt =, CC dddd dddd =, CC = aaaa = (8),, TT, TT, CC, CC aaaa In order to solve the sstem of the differential eqations ()-(7) we pt: () = () + EEEE () (9) TT () = TT () + EEEETT () and () = () + EEEE () (3) TT () = TT () + EEEETT () In this sstem, eqating the coefficients of EEEE and EEEE we get: dd + dd MM + dd dddd kk = GGGGTT + GGGGCC + MM + (3) kk dd dd + dd dddd MM + kk = (GGGGTT + GGGGCC ) (3) dd TT dd + PPPP ddtt dddd + QQTT = (33) dd TT dd + PPPP ddtt dddd + QQTT = PPPPPPPP dd dddd (34) dd + dd dd dddd iiii + MM + 4 kk = iiii + GGGGTT 4 + GGGGCC + MM + (35) kk dd dd + dd dddd iiii 4 + MM + kk = ( GGGGTT + GGGGCC ) (36) dd TT dd + PPPP ddtt dddd iiii 4 PPPP QQ TT = (37) dd TT dd + PPPP ddtt dddd iiii 4 PPPP QQ TT = PPPPPPPP dd dddd dd dddd (38) 3, IJMA. All Rights Reserved 88

6 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb.-3. The corresponding bondar conditions (8) become: =, =, =, = ddtt =, ddtt =, ddtt =, ddtt = aaaa = dddd dddd dddd dddd CC =, CC =,,, TT, TT, TT, TT aaaa CC, CC (39) Solving the differential eqations (6), (7) and (3) (38), sing bondar conditions (39) we get = αα 5 ee αα + αα 3 ee ββ + αα 4 ee γγ + (4) = αα 3 ee αα + αα 6 ee ββ + αα 7 ee αα + αα 8 ee ββ + αα 9 ee γγ + αα ee (αα +ββ ) + αα ee (ββ +γγ ) + αα ee (γγ +αα ) (4) = ee αα 5 + (4) = αα ee αα 5 + αα 6 ee ββ + αα 7 ee (αα +αα 5 ) + αα 8 ee (ββ +αα 5 ) + αα 9 ee (γγ +αα 5 ) (43) TT = ββ ee ββ (44) TT = ββ 9 ee ββ + ββ 3 ee αα + ββ 4 ee ββ + ββ 5 ee γγ + ββ 6 ee (αα +ββ ) + ββ 7 ee (ββ +γγ ) + ββ 8 ee (αα +γγ ) (45) TT = (46) TT = ββ 5 ee ββ + ββ ee (αα +αα 5 ) + ββ 3 ee (ββ +αα 5 ) + ββ 4 ee (γγ +αα 5 ) (47) CC = ee γγ (48) CC = (49) With the help of (4) (47) the eqations (9) and (3) becomes = αα 5 ee αα + αα 3 ee ββ + αα 4 ee γγ + + EEEE αα 3 ee αα + αα 6 ee ββ + αα 7 ee αα + αα 8 ee ββ + αα 9 ee γγ + αα ee (αα +ββ ) + αα ee (ββ +γγ ) + αα ee (γγ +αα ) (5) TT = ββ ee ββ + EEEE ββ 9 ee ββ + ββ 3 ee αα + ββ 4 ee ββ + ββ 5 ee γγ + ββ 6 ee (αα +ββ ) + ββ 7 ee (ββ +γγ ) + ββ 8 ee (αα +γγ ) (5) = ( ee αα 5 + ) + EEEE αα ee αα 5 + αα 6 ee ββ + αα 7 ee (αα +αα 5 ) + αα 8 ee (ββ +αα 5 ) + αα 9 ee (γγ +αα 5 ) (5) TT = EEEE ββ 5 ee ββ + ββ ee (αα +αα 5 ) + ββ 3 ee (ββ +αα 5 ) + ββ 4 ee (γγ +αα 5 ) (53) Finall from the above eqations (48) (53) and with the help of eqations (9), () and () we obtain the velocit, temperatre and concentration fields are as follows: () = + εε(cos(wwww) + iiiiiiii(wwww)) = αα 5 ee αα + αα 3 ee ββ + αα 4 ee γγ + + EEEE αα 3 ee αα + αα 6 ee ββ + αα 7 ee αα + αα 8 ee ββ + αα 9 ee γγ + αα ee (αα +ββ ) + αα ee (ββ +γγ ) + αα ee (γγ +αα ) ) + εε cos(wwww) + iiiiiiii(wwww) ( ee αα5 + ) +EEEE αα ee αα5 + αα 6 ee ββ + αα 7 ee (αα +αα 5 ) + αα 8 ee (ββ +αα 5 ) + αα 9 ee (γγ +αα 5 ) TT() = TT + εε cos(wwww) + iiiiiiii(wwww) TT = ββ ee ββ + EEEE ββ 9 ee ββ + ββ 3 ee αα + ββ 4 ee ββ + ββ 5 ee γγ + ββ 6 ee (αα +ββ ) + ββ 7 ee (ββ +γγ ) + ββ 8 ee (αα +γγ ) +(cos(wwww) + iiiiiiii(wwww)) EEEE ββ 5 ee ββ + ββ ee (αα +αα 5 ) + ββ 3 ee (ββ +αα 5 ) + ββ 4 ee (γγ +αα 5 ) (55) CC() = CC + εε(cos(wwww) + iiiiiiii(wwww))cc = ee γγ (56) (54) 3, IJMA. All Rights Reserved 89

7 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb.-3. RESULTS AND DISCUSSIONS: The chemical reaction effects on MHD free convective oscillator flow past a poros plate embedded in a poros medim and in the presence of heat sorce have been stdied. The governing eqations are solved b sing pertrbation method and approximate soltions are obtained for velocit, temperatre and concentration fields. The effects of the flow parameters sch as Chemical reaction parameter (Kr), Heat sorce parameter (Q), Prandtl nmber (Pr), Eckert nmber (Ec), Schmidt nmber (Sc), Grashof nmber for heat and mass transfer (Gr, Gc), magnetic parameter or Hartmann nmber (M) and permeabilit parameter (k) on the velocit, temperatre and concentration profiles of the flow field are presented with help of velocit, temperatre and concentration profile. Figs. (a) and (b) illstrate the effect of chemical reaction parameter Kr on velocit and concentration distribtions in the bondar laer. It is noticed from the Fig. (a) that the velocit at the start of the bondar laer increases slowl till it attains the maximm vale, after that the are decreasing and this trend is seen for all the vales of the parameter Kr. From Fig. (b) it can be observed that increasing the vale of the chemical reaction parameter, decreases the concentration of species in the bondar laer, this is de to the fact that destrctive chemical redces the soltal bondar thickness and increases the mass transfer. Figs. (a) and (b) depict the velocit () and temperatre (T) profiles for different vales of the heat sorce parameter Q. It is noticed from the figre (a) that when heat is generated the boanc force increase, which indces the flow rate to increase giving rise to the increase in the velocit profiles. The effect of Q on temperatre profiles are shown in (b). It is clear that the heat generation increases, the temperatre is also increases. Figs. 3(a) and 3(b) are shown that the behavior of the velocit () and temperatre (T) for different vales of the Prandtl nmber Pr. The nmerical reslts show that the effect of increasing vales of Pr reslts in a decreasing velocit. From Fig. 3(b), it is observed that an increase in Pr reslts in a decrease of the thermal bondar laer thickness and in general lower average temperatre within the bondar laer. The reason is that smaller vales of Pr are eqivalent to increase in the thermal condctivit of the flid and therefore heat is able to diffse awa from the heated srface more rapidl for higher vales of Pr. Hence in the case of smaller Prandtl nmbers as the thermal bondar laer is thicker and therefore the rate of heat transfer is redced. The inflence of the viscos dissipation parameter i.e., the Eckert nmber (Ec) on velocit and temperatre are shown in Fig. 4(a) and 4(b). The velocit and temperatre both are increases with increasing Eckert nmber. It expresses the relationship between the kinetic energ in the flow and the enthalp. It embodies the conversion of kinetic energ in to internal energ b work done against the viscos flid stresses. Greater viscos dissipative heat cases a rise in the temperatre as well as the velocit. The effects of Schmidt nmber on the velocit () and concentrations (C) are displas in Figs. 5(a) and 5(b). As the Schmidt nmber increases, the concentration decreases. This cases the concentration boanc effects to decrease ielding a redction in the flid velocit. Redctions in the velocit and concentration distribtions are accompanied b simltaneos redctions in the velocit and concentration bondar laers. The velocit profiles for different vales of the thermal Grashof nmber Gr are described in Fig. 6(a). It is observed that an increase in Gr leads to arise in the vales of velocit. Hence the positive vales of Gr correspond to cooling of the plate. In addition, it is observed that the velocit increases rapidl near wall of the plate as Grashof nmber increases and then decas to the free stream velocit. For the case of different vales of the soltal Grashof nmber Gc, the velocit profiles in the bondar laer are shown in Fig. 6(b). It is observed that an increase in Gc, leads to a rise in the vales of velocit. The inflence of magnetic parameter or Hartmann nmber M, on the velocit () is shown in Fig.7. An increase in M redces the velocit. The application of a transverse magnetic field to an electricall condcting field gives rise to a resistive tpe of force called Lorentz force. This force has the tendenc to slow down the flid. This trend is apparent from Fig.7. Fig. 8 depicts the velocit profiles for different vales of permeabilit parameter k. Clearl as k increases the peak vale of velocit across the bondar laer tends to increase rapidl near wall of the poros plate CONCLUSIONS We smmarize below the following reslts of phsical interest on the velocit, temperatre and concentration distribtion of the flow field.. A growing magnetic parameter or Prandtl nmber or Schmidt nmber or chemical reaction parameter retards the velocit of the flow field at all points.. The effect of increasing Grashof nmber or modified Grashof nmber or permeabilit parameter or Eckert nmber or Heat sorce is to accelerate velocit of the flow field at all points. 3, IJMA. All Rights Reserved 9

8 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb A growing Prandtl nmber decreases temperatre of the flow field at all points 4. The Eckert nmber or Heat sorce increase the leads to increase the temperatre at all points. 5. The growing Schmidt nmber or Chemical reaction parameter decreases the concentration of the flow field at all points. REFERENCES. Abdel-Nasser A Osman Abo-Dahad S M and Mohamed R A., Analtical soltion of thermal radiation and chemical reaction effects on nstead MHD convection throgh poros media with heat sorce/sink, Mathematical Problems in Engineering, Vol., Article ID 58, pp.-8,.. Ahmed S., Effects of nstead free convective MHD flow throgh a poros medim bonded b an infinite vertical poros plate, Bll. Cal. Math. Soc., 9, pp.57-5, Basanth Kmar Jha and Ravindra Prasad., Free convection and mass transfer effects on the flow past an accelerated vertical plate with heat sorce, Mechanics Research Commnications, Vol. 7, pp , Chambre PL and Yong JD., On the diffsion of chemicall reactive species in a laminar bondar laer flow, The Phsics of flids, Vol., pp , Chamkha A J and Khaled A R., Hdromagnetic combined heat and mass transfer b natral convetion from a permeable srface embedded in flid satrated poros medim, International Jornal of Nmerical methods for Heat and Flid Flow, (5), pp ,. 6. Chamkha AJ., Unstead MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption, Int. J. Sci. Engg., 3 (4), pp ,. 7. Chadhar R C and Arpita Jain., MHD heat and mass diffsion flow b natral convection past a srface embedded in a poros medim, Theoretical Applied Mechanics, Vol. 36, No., pp.-7, Cooke C. 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Heat Mass Transfer, 46, pp. 35-3, Cssler EL., Diffsion mass transfer in flid sstems, Cambridge Universit Press, Das UN Deka RK and Sondalgekar VM., Effects on mass transfer on flow past an implsivel started infinite vertical plate with constant heat flx and chemical reaction, Foshing im ingenicrwesen, Vol. 6, pp , Das UN Deka RK and Sondalgekar VM., Effects on mass transfer on flow past an implsivel started infinite vertical plate with a chemical reaction, The Blletin GUMA, Vol. 5, pp.3-, Gireesh Kmar J Ramakrishna S and Sivaiah M., Effects of chemical reaction on transient MHD convection flow past a vertical srface embedded in a poros medim with oscillating temperatre, Ultra Scientist, Vol. (3) M, pp , Girish Kmar J Kishore PM and Ramakrishna S., Mass transfer effects on MHD flows exponentiall accelerated isothermal vertical plate in the presence of chemical reaction throgh poros media, Advances in Applied Sciences Research, 3(4), pp.34-4,. 4. Hemanth Poonia and Chadhr R.C., MHD free convection and mass transfer flow over an infinite vertical poros plate with viscos dissipation, Theoreq. Appl. Mech., Vol. 37(4), pp.63-87,. 5. Israel Cooke C Ogl A and Ombo Pepple VM., The inflence of viscos dissipation and radiation on nstead MHD free convection flow past an infinite heated vertical plate in a poros medim with time dependent sction, Int. J. Heat Mass Transfer, 46, 3, pp.35-3, Jonah Philliph K Rajesh V and Vijaa Kmar Varma S., Effects of thermal radiation and MHD on the nstead free convection and mass transform flow past an exponentiall accelerated vertical plate with variable temperatre, International Jornal of Mathematical Archive, Vol. 3(4), pp ,. 7. Kishore PM Rajesh V and Vijaakmar Verma S., The effects of thermal radiation and viscos dissipation on MHD heat and mass diffsion flow past an oscillating vertical plate embedded in a poros medim with variable srface conditions, Theoret. Appl. Mech., Vol.39, No., pp.99-5,. 8. Mthcmaraswam, R., and Klaivel, T., Chemical reaction effects on moving infinite vertical plate with niform heat flx and variable mass diffsion, Forschng im-ingenierwesen, 68, pp.-4, Seethamahalakshmi Ramana Redd G V and Prasad B D C N., Effects of the chemical reaction and radiation absorption on an nstead MHD convective heat and mass transfer flow past a semi-infinite vertical moving in a poros medim with heat sorce and sction, IOSR Jornal of Engineering, Vol., Isse, pp.8-36,.. Sharma PR Dadkeech IK and Grminder Singh., Heat and mass transfer effects on nstead MHD free convective flow along a vertical poros plate with internal heat generation and variable sction, Int. J. of Math Archive, 3(5), pp. 63-7,.. Sharma PR Singh G., Unstead MHD free convective flow and heat transfer along a vertical poros plate with variable sction and internal heat generation, Int. J. Appl. Math and Mech., 4, pp. -8, 8.. Sondalgekar VM., Viscos dissipation effect on nstead free convective flow past an infinite vertical poros plate with constant sction, Int. J. Heat Mass Transfer, 5, pp.53-6, Sdheer Bab M Sata Naraana PV Sankar Redd T and Umamaheswara Redd D., Radiation and chemical reaction effects on an nstead MHD convection flow past a vertical moving poros plate embedded in a poros medim with viscos dissipation, Advances in Applied Science Research, (5), pp.6-39,. 3, IJMA. All Rights Reserved 9

9 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb Vajravel K., Natral convection at a heated, semi-infinite vertical plate with internal heat generation, Acta Mech., 34, pp.53-59, 979. APPENDIX αα = + +4 MM+ kk, αα = +4 MM+ kk, αα 3 = GGGG ββ ββ + ββ MM+ kk, αα 4 = GGGG γγ + γγ MM+ kk, αα 5 = [ + αα 3 + αα 4 ], αα 6 = αα 8 = αα = GGGGββ 4 (ββ ) + (ββ ) MM+ kk, αα 9 = GGGGββ 7 (γγ +ββ ) +(γγ +ββ ) MM+ kk, αα = GGGGββ 9 ββ + ββ MM+ kk, αα 7 = GGGGββ 5 (γγ ) + (γγ ) MM+ kk, αα = GGGGββ 3 (αα ) + (αα ) MM+ kk, GGrrββ 8 (γγ +αα ) +(γγ +αα ) MM+ kk αα 3 = [αα 6 + αα 7 + αα 8 + αα 9 + αα + αα + αα ], GGGGββ 6 (αα +ββ ) +(αα +ββ ) MM+ kk, αα 4 = + +4 iiii 4 +MM+ kk, αα 5 = +4 iiii 4 +MM+ kk, αα 6 = GGGGββ 5 ββ + ββ iiii 4 +MM+, kk αα 7 = αα 9 = GGGGββ (αα +αα 5 ) +(αα +αα 5 ) iiii 4 +MM+ kk, αα 8 = GGGGββ 3 (ββ +αα 5 ) +(ββ +αα 5 ) iiii 4 +MM+ kk GGGGββ 4 (γγ +αα 5 ) +(γγ +αα 5 ) iiii 4 +MM+ kk, αα = [αα 6 + αα 7 + αα 8 + αα 9 ] ββ = PPPP + PPPP +4( QQ), ββ = PPPP PPPP +4( QQ), ββ 3 = PPPPPPPP (αα αα 5 ) (αα ) +PPPP (αα )+QQ, ββ 4 = PPPPPPPP (ββ αα 3 ) (ββ ) +PPPP (ββ )+QQ, ββ 5 = PPPPPPPP (γγ αα 4 ) (γγ ) +PPPP (γγ )+QQ, ββ 6 = 4PPPPPPPP αα αα 3 αα 5 ββ (αα +ββ ) +PPPP (αα +ββ )+QQ, ββ 7 = 4PPPPPPPP ββ γγ αα 3 αα 4 (ββ +γγ ) +PPPP (ββ +γγ )+QQ, ββ 8 = 4PPPPPPPP αα γγ αα 4 αα 5 (αα +γγ ) +PPPP (αα +γγ )+QQ, ββ 9 = ββ [αα ββ 3 + ββ ββ 5 + γγ ββ 5 + (αα + ββ )ββ 6 + (ββ + γγ )ββ 7 + (αα + γγ )ββ 8 ] ββ = PPPP + PPPP +4 iiii ββ = ββ 4 = 4 PPPP QQ, ββ = PPPP PPPP +4 iiii PPPPPPPP αα αα 5 αα 5 (αα +αα 5 ) +PPPP (αα +αα 5 ) iiii 4 PPPP QQ, ββ 3 = PPPPPPPP γγ αα 4 αα 5 (γγ +αα 5 ) +PPPP (γγ +αα 5 ) iiii 4 PPPP QQ, 4 PPPP QQ, PPPPPPPP ββ αα 3 αα 5 (ββ +αα 5 ) +PPPP (ββ +αα 5 ) iiii 4 PPPP QQ ββ 5 = ββ [ββ (αα + αα 5 ) + ββ 3 (ββ + αα 5 ) + ββ 4 (γγ + αα 5 )] γγ = SSSS+ SSSS +4KKKKKKKK γγ 4 = SSSS SSSS +4 ii ωω 4 KKKK SSSS, γγ = SSSS SSSS +4KKKKKKKK, γγ 3 = SSSS + SSSS +4 ii ωω 4 KKKK SSSS, 3, IJMA. All Rights Reserved 9

10 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb.-3. GRAPHS.6.4 Kr =. Kr =. Kr = Figre - (a): Velocit profile for different vales of chemical reaction parameter Kr when Gr = 5, Gc =, Ec =., Pr =.7, Sc =., M =., k =., Q = Kr =. Kr =. Kr = 5. C Figre - (b): Concentration profile for different vales of chemical reaction parameter Kr when Sc = Q = -.5 Q =.5 Q =. Q = Figre - (a): Velocit profile for different vales of Heat sorce parameter Q when Gr = 5, Gc =, Ec =., Pr =.7, Sc =., M =., k =., Kr =.. 3, IJMA. All Rights Reserved 93

11 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb Q = -.5 Q =.5 Q =. Q =.5 Temperatre Figre - (b): Temperatre profile for different vales of Heat sorce parameter Q when Gr = 5, Gc =, Ec =., Pr =.7, Sc =., M =., k =., Kr = Pr =.7 Pr =. Pr = Figre - 3(a): Velocit profile for different vales of Prandtl nmber Pr when Gr = 5, Gc =, Ec =., Kr =., Sc =., M =., k =., Q = Pr =.7 Pr =. Pr = 7.. Temperatre Figre - 3(b): Temperatre profile for different vales of Prandtl nmber Pr when Gr = 5, Gc =, Ec =., Kr =., Sc =., M =., k =., Q =.5. 3, IJMA. All Rights Reserved 94

12 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb Ec =. Ec =. Ec = Figre - 4(a): Velocit profile for different vales of Eckert nmber Ec when Gr = 5, Gc =, Kr =., Pr =.7, Sc =., M =., k =., Q =.5. 4 Ec =. Ec =. Ec =. Temperatre Figre - 4(b): Temperatre profile for different vales of Eckert nmber Ec when Gr = 5, Gc =, Kr =., Pr =.7, Sc =., M =., k =., Q = Sc =. Sc =.5 Sc = Figre - 5(a): Velocit profile for different vales of Schmidt nmber Sc when Gr = 5, Gc =, Ec =., Pr =.7, Kr =., M =., k =., Q =.5. 3, IJMA. All Rights Reserved 95

13 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb Sc =. Sc =.5 Sc =.75 C Figre - 5(b): Concentration profile for different vales of Schmidt nmber Sc when Kr =. 3.5 Gr = 5. Gr =. Gr = 5. Gr = Figre - 6(a): Velocit profile for different vales of Grashof nmber Gr when Gc =, Kr =., Ec =., Pr =.7, Sc =., M =., k =., Q =.5..5 Gc =. Gc = 5. Gc =. Gc = Figre - 6(b): Velocit profile for different vales of modified Grashof nmber Gc when Gr = 5, Kr =., Ec =., Pr =.7, Sc =., M =., k =., Q =.5. 3, IJMA. All Rights Reserved 96

14 K. Sreelatha *, B. Rami Redd and J. Girish Kmar 3 / CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE OSCILLATORY / IJMA- 4(), Feb M =. M = 5. M =. M = Figre - 7: Velocit profile for different vales of magnetic parameter M when Gr = 5, Gc =, Kr =., Ec =., Pr =.7, Sc =., k =., Q = k =. k =. k =. k = Figre - 8: Velocit profile for different vales of permeabilit parameter k when Gr = 5, Gc =, Kr =., Ec =., Pr =.7, Sc =., M =., Q =.5. Sorce of spport: Nil, Conflict of interest: None Declared 3, IJMA. All Rights Reserved 97