ISSN: International Journal of Science, Engineering and Technology Research (IJSETR) Volume 2, Issue 4, April 2013

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1 ISSN: Volume Issue 4 April 3 CHEMICAL REACTION EFFECTS ON MHD FLOW OF CONTINOSL MOVING VERTICAL SRFACE WITH HEAT AND MASS FLX THROGH POROS MEDIM J. Girish Kumr ABSTRACT: This pper is n nlyticl study of the het genertion/bsorption effects on MHD flo of n electriclly conducting incompressible viscous fluid pst n impulsively moving isotherml verticl plte through porous medium in the presence of uniform suction nd tking into the homogeneous chemicl rection of first order. A flo of this type represents ne clss of boundry lyer flo t surfce of finite length. The equtions governing the flo field re solved by nlyticl method. The velocity temperture nd concentrtion hve been evluted for vrition in the different governing prmeters like Mgnetic prmeter (M) Prndtl number (Pr) Schmidt number (Sc) het genertion/bsorption prmeter (Q) therml Grshof number (Gr) solutl Grshof number (Gc). Keyords: MHD Chemicl rection Porous medium Het genertion/bsorption Het nd Mss flux etc. INTRODCTION: The study of nturl convection het nd mss trnsfer phenomenon in porous medi is gining ttention due to its interesting pplictions. Processes involving het nd mss trnsfer in porous medi re often encountered in the chemicl industry in reservoir engineering in connection ith therml recovery process nd in the study of dynmics of J Girish Kumr Deprtment of Mthemtics Government Degree College Jmmlmdugu Kdp A.P. Indi. hot nd slty springs of se. nderground spreding of chemicl stes nd other pollutnts grin storge evportion cooling nd solidifiction re the fe other ppliction res here the combined thermo-solute nturl convection in porous medi is observed. Skidis [] studied the groth of the todimensionl velocity boundry lyer over continuously moving flt plte. Vjrvelu [6] studied the exct solutions for hydrodynmic boundry lyer flo nd het trnsfer over continuous moving horizontl flt surfce ith uniform suction nd internl het genertion/bsorption. Agin Vjrvelu [5] extended the problem to verticl surfce. Het nd Mss trnsfer of MHD flo hve pplictions in meteorology solr physics cosmic strophysics geophysics nd fluid dynmics. Also this process tkes plce in numerous industril pplictions such s polymer production mnufcturing of cermics or glssre nd food processing. Rjeev Jh et l. [9] studied the MHD flo of viscous fluid pst n impulsively moving isotherml verticl plte through porous medium ith chemicl rection. Muthucumrsmy nd Gnesn [8] studied the first order chemicl rection on flo pst n impulsively strted verticl plte ith uniform het nd mss flux. Snkr Reddy et l. [] Het nd mss effects on MHD flo of continuously moving verticl surfce ith uniform het nd mss flux. The study of het genertion or bsorption effects in moving fluids is importnt in fluids undergoing exothermic or endothermic chemicl rections. Het All Rights Reserved 3 IJSETR 88

2 ISSN: Volume Issue 4 April 3 genertion effects my lter the temperture distribution nd consequently the prticle deposition rte in nucler rectors electric chips nd semiconductor fers. Ptil nd Kulkrni [7] studied the effects of chemicl rection on free convective flo of polr fluid through porous medium in the presence of internl het genertion. Effect of viscous dissiptive het nd uniform mgnetic field on the free convective flo through porous medium ith het genertion/bsorption s studied by Amkiri nd Ogulu []. Hdy et l. [3] hve nlyzed the MHD free convection flo long vy surfce ith het genertion or bsorption effect. Gireesh Kumr nd Rmkrishn [4] hve discussed the MHD flo of viscous fluid pst n impulsively moving isotherml plte through porous medium ith chemicl rection nd het genertion/bsorption. Motivted by ll these orks e contemplte to study the chemicl rection nd het genertion/bsorption effects on MHD flo of n electriclly conducting incompressible viscous fluid pst n impulsively moving isotherml verticl plte through porous medium in the presence of uniform het nd mss flux. The equtions governing the flo re solved by using the nlyticl method. The velocity temperture nd concentrtion hve been evluted ith vrying prmeters like mgnetic prmeter Prndtl number Schmidt number het genertion/bsorption prmeter therml Grshof number nd solutl Grshof number. FORMLATION OF THE PROBLEM: Consider the stedy to-dimensionl lminr incompressible flo of chemiclly recting viscous fluid on continuously moving verticl surfce in the presence of uniform mgnetic field ith het genertion uniform het nd mss flux effects issuing slot nd moving ith uniform velocity u in fluid t rest. Let the x-xis be tken long the direction of motion of the surfce in the uprd direction nd y-xis is norml to the surfce. The temperture nd concentrtion levels ner the surfce re rised uniformly. The induced mgnetic field viscous dissiption re ssumed to be neglected. No under the usul Boussinesq s pproximtion the flo field is governed by the folloing equtions. Continuity eqution u v x y Momentum eqution u v u v g T T x y u B y Energy eqution () * g C C u u K T T C p u v x y p T k y Q Diffusion Eqution C C C u v D k C l x y y The initil nd boundry conditions u u u v v const. T q y k T T C C C j y D T s y () T (3) (4) t y (5) Where u v re velocity components in x nd y directions respectively. g is the ccelertion due to grvity is volumetric coefficient of therml * expnsion is the volumetric coefficient of expnsion ith concentrtion T is the temperture of the fluid C is the species concentrtion T is the ll temperture C is the concentrtion t the plte T is the free stem temperture fr y from the plte C is the free stem concentrtion in fluid All Rights Reserved 3 IJSETR 88

3 ISSN: Volume Issue 4 April 3 fr y from the plte is the kinemtic viscosity D is the species diffusion coefficient k is the chemicl rection l prmeter. The term T T Q is ssumed to be the mount of het generted or bsorbed per unit volume. Q is constnt hich my tke on either positive or negtive vlues. When the ll temperture T exceeds the free stem temperture T the source term represents the het source hen Q nd het sink hen Q. The first term nd second term on the right hnd side of the momentum eqution () denote the therml nd concentrtion buoyncy effects respectively. prmeter Q is the het genertion/bsorption prmeter. METHOD OF SOLTION: The study of ordinry differentil equtions () () nd (3) long ith their initil nd boundry conditions (4) hve been solved by using the method of ordinry liner differentil equtions ith constnt coefficients. We get the folloing nlyticl solutions for the velocity temperture nd concentrtion 6 4 A3e A e Ae (5) 4 T e (6) 4 (7) C e In order to rite the governing equtions nd the boundry conditions the folloing non-dimensionl quntities re introduced. yv C Pr k kl Kr v p qv kv j v * vg vg u kv Gr Gc u uv uv v K pv vq Sc k Q D v C pv B v T T C C M T C v qv j v kv kv () In vie of () the equtions () (9) nd (4) re reduced to the folloing nondimensionl form d d M d d k GrT GcC () d T dt Pr QPrT d d () d C dc Sc KrScC d d (3) The corresponding initil nd boundry conditions in non-dimensionl form re T C t (4) T C s Where Gr is the therml Grshof number Gc is the solutl Grshof number Pr is the fluid Prndtl number Sc is the Schmidt number nd Kr is the chemicl rection The computed solution for the velocity is vlid t some distnce from the slot even though suction is pplied from the slot onrd. This is due to the ssumption tht velocity field is independent of the distnce prllel to the plte. The fluids considered in this study re ir (Pr =.7) nd ter (Pr = 7.). RESLTS AND DISCSSION: A representtive set of numericl results is shon grphiclly in figures to illustrte the influence of physicl prmeter viz. Chemicl rection prmeter (Kr =.5) Mgnetic prmeter (M =.) Prndtl number (Pr =.7) Schmidt number (Sc =.6) Permebility prmeter (k = ) therml Grshof number (Gr = nd Gr = -) solutl Grshof number (Gc = nd Gc = -) Het genertion prmeter (Q =.) on velocity temperture nd concentrtion profiles on todimensionl incompressible nd chemiclly recting flo of viscous fluid on continuously moving verticl plte in the presence of mgnetic field ith het genertion. The therml Grshof number Gr nd solutl Grshof number Gc represents here the effects of free convection currents nd receives positive All Rights Reserved 3 IJSETR 883

4 ISSN: Volume Issue 4 April 3 zero or negtive vlues. The cse Gr < nd Gc < corresponds physiclly to n externlly heted surfce s the free convection currents re moving tords the surfce. The cse Gr > nd Gc > corresponds to n externlly cooled surfce nd the cse Gr = nd Gc = corresponds to bsence of the free convection currents. From figures nd e observe tht hen Gr > Gc > nd Gr < Gc < n increse in mgnetic prmeter (M) nd het genertion prmeter (Q) leds to fll the velocity Figure - : Velocity profile hen Sc =.6 Pr =.7 Q = Kr =.5 k = M =. Gr = -. Gc = -. M =. Gr = -. Gc = -. M = 3. Gr = -. Gc = -. M = 4. Gr = -.. Gc = -. M =. Gr =. Gc =. M =. Gr =. Gc =. M = 3. Gr =. Gc =. M = 4. Gr =. Gc = Figure - 3: Velocity profile hen M =. Q =. Pr =.7 Sc =.6 k = Kr =. Gr =. Gr =. Kr =.5 Gr =. Gc =. Kr =. Gr =. Gc =. Kr =. Gr = -. Gc = -. Kr =.5 Gr = -. Gc = -. Kr =. Gr =. Gc =. Figure - 4: Velocity profile hen M =. Sc =.6 Q =. Kr =.5 Pr =.7 k = Gr =. Gc =. k = Gr =. Gc =. k = Gr =. Gc =. k = Gr = -. Gc = -.. k = Gr =-. Gc = -. k = Gr = -. Gc = Figure - : Veocity profile hen M =. Pr =.7 Sc =.6 Kr =.5 k = Q =. Gr = -. Gc = -. Q =.. Gr = -. Gr = -. Q = 3. Gr = -. Gc = -. Q = 4. Gr = -. Gc = -. Q =. Gr =. Gc =. Q =. Gr =. Gc =. Q = 3. Gr =. Gc =. Q = 4. Gr =. Gc = From figure 3 it is noticed tht hen Gr > nd Gc > n increse in chemicl rection prmeter (Kr) cuses to decrese in velocity. It is lso observed from the figure 4 hen increse in permeble prmeter (k) leds to increse in velocity for both positive nd negtive cses of Gr nd Gc From figure 5 it is noticed tht n increse in therml Grshof number nd solutl Grshof number cuses to increse in velocity in both positive nd negtive of Gr nd Gc. It is lso observed from the figure 6 hen increse in Schmidt prmeter (Sc) leds to decrese in velocity for both positive nd negtive cses of Gr nd Gc. Figure - 5: Velocity profile hen M =. Q =. Pr =.7 Sc =.6 k = Kr =.5.5 Gr =. Gc =. Gr =. Gc = 4. Gr = 4. Gc = 4. Gr = -. Gc = -. Gr = -. Gc = -4. Gr = -4. Gc = All Rights Reserved 3 IJSETR 884

5 T ISSN: Volume Issue 4 April 3 T C C..8.6 Figure - 6: Velocity profile hen M =. Q =. Pr =.7 Kr =.5 k = Sc =.6 Gr =. Gc =. Sc =. Gr =. Gc =. Sc =. Gr =. Gc =. Sc =.6 Gr = -. Gc = -. Sc =. Gr = -. Gc = -. Sc =. Gr = -. Gc = Figure - 9: Temperture profile hen Q =. Pr =.7 Pr =. Pr = From figure 7 it is noticed tht n increse in Prndtl number (Pr) decrese in velocity in both positive nd negtive of Gr nd Gc. It is lso observed from the figure 8 hen increse in het genertion prmeter (Q) leds to decrese in temperture Figure - 7: Velocity profile hen M =. Sc =.6 Kr =.5. k = Q =. Figure - 8: Temperture profile hen Pr =.7 Pr =.7 Gr = -. Gc = -. Pr =. Gr = -. Gc = -. Pr = 7. Gr = -. Gc = -. Pr =.7 Gr =. Gc =. Pr =. Gr =. Gc =. Pr = 7. Gr =. Gc =. Q = Q = Q = 3 Q = From the figure 9 hen increse in Prndtl number (Pr) leds to decrese in temperture. It is lso observed from the figure hen increse in chemicl rection prmeter (Kr) leds to decrese in concentrtion. From the figure hen increse in Schmidt number (Sc) leds to decrese in concentrtion. APPENDIX Sc Sc Pr Sc Sc Pr A Figure - : Concentrtion profile hen Sc =.6 Figure - : Concentrtion profile hen Kr =.5 4KrSc 4KrSc 4Q Pr Pr 4 A 4 M k 4 M k Kr =.5 Kr =. Kr =.5 Kr =. Sc =.6 Sc =. Sc = Q All Rights Reserved 3 IJSETR 885

6 ISSN: Volume Issue 4 April 3 Gr A M k Gc A M A 3 A A k REFERENCES:. A. R. C. Amkiri nd A. Ogulu The effect of viscous dissiptive het nd uniform mgnetic field on the free convective flo through porous medium ith het genertion/bsorption Europen Journl of Scientific Reserch vol. 5 No. 4. pp B. C. Skidis Boundry lyer behvior on continuous solid surfce AIChE. J. vol. 7 pp F. M. Hdy R. A. Mohmed nd A. Mhdy MHD free convection flo long verticl vy surfce ith het genertion or bsorption effect Int. Comm. Het Mss Trnsfer vol. 33() pp J. Gireesh Kumr nd S. Rmkrishn MHD flo of viscous fluid pst n impulsively moving verticl plte through porous medium ith chemicl rection nd het genertion/bsorption ltr Scientist of Physicl Sciences vol. () pp K. Vjrvelu Hydromgnetic convection t continous moving surfce Act Mech vol. 7 pp K. Vjrvelu Hydromgnetic flo nd het trnsfer over continuous moving porous flt surfce Act Mech. vol. 64 pp P. M. Ptil nd P. S. Kulkrni Effects of chemicl rection on free convective flo of polr fluid through porous medium in the presence of internl het genertion Int. J. Therm. Sci. vol.47(8) pp R. Muthucumrsmy nd P. Gnesn First-order chemicl rction on flo pst n impulsively strted verticl plte ith het nd mss flux Act Mech 47 pp Rjeev Jh Devendr Kumr nd R. K. Shrivstve Act Cienci Indic Vol. XXXII M No. p T. Snkr Reddy M. Gnnesr Reddy nd N. Bhskr Reddy Het nd mss trnsfer effects on MHD flo of continuously moving verticl surfce ith uniform het nd mss flux Act Cienci Indic Vol. XXXIV M No. p J Girish Kumr: Completed M. Sc. from Sri Venktesr niversity Tirupti Andhr Prdesh B. Ed. from Sri Krishn Devry niversity Annthpur Andhr Prdesh Ph. D. from Sri Venktesr niversity Tirupti Andhr Prdesh nd M. Tech. from Achry Ngrjun niversity Guntur Andhr Prdesh Indi. Present orking s Lecturer in Mthemtics Deprtment of Mthemtics Government Degree College Jmmlmdugu Kdp(Dt.) A.P. Indi. All Rights Reserved 3 IJSETR 886