EFFECTS OF RADIATION AND THERMAL DIFFUSION ON MHD HEAT TRANSFER FLOW OF A DUSTY VISCOELASTIC FLUID BETWEEN TWO MOVING PARALLEL PLATES

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1 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve. EFFECTS OF RADIATION AND THERMAL DIFFUSION ON MHD HEAT TRANSFER FLOW OF A DUSTY VISCOELASTIC FLUID BETWEEN TWO MOVING PARALLEL PLATES B. Mallikarjuna Re, D. Chenna Kesavaiah an G. V. Ramana Re Koneru Lakshmaiah (Deeme to be Universit), Vaeswaram, Guntur, Anhra Praesh, Inia Department of H & S, K G Re College of Engineering an Technolog, Chilkur, Moinaba, R R Dist, TS, Inia mallikb@gmail.com ABSTRACT An anticipate outcome of present analsis is effects of raiation an thermal iffusion on MHD heat transfer flow of ust viscous, incompressible, electricall conucting flui between two parallel plates with constant suction on the upper plate an constant injection on the lower plate, first orer chemical reaction, variable temperature an uniform mass iffusion taking into an account. The governing partial ifferential equations which escribe for motion of the problem change into imensionless equations an solve b using perturbation technique. The various analtical quantities for the velocit profiles (for ust flui an ust particles), temperature profiles, concentration profiles an skin friction coefficient are examine an epict graphicall in etail. Kewors: raiation, thermal iffusion, MHD flow, viscoelastic flui. INTRODUCTION Dust flows riven b combine effects of iffusion an thermal iffusion of chemical taxonomic group are encountere in man areas like astrophsical, geophsical an engineering applications. These are consiere in the chemical treatment inustries, power technolog, moisture transport in thermal insulation, foo processing inustries, pore water convection hear salt omes, air craft icing, movement of contaminants in groun water, waste issolution an eliminate in unergroun nuclear waste isposal, ust entrainment in clous in nuclear explosion an manner of functioning of soli fuels in rocket nozzles, etc. Convective flows accompaning temperature an concentration ifferences at as the transfer of heat an mass carr out place have been stuie wiel an istinctl extensions of the problem have been reporte in the literature. In practice, ammonia, water vapor, oxgen, hrogen, helium etc are main gases which are ae in particulate air or implie liquis embee in the ust particles flowing though channels. In such flows, the buoanc forces moves towars within existence ue to temperature with the aition of concentration ifferences MHD channel flows are stuie ue to their important applications in MHD pumps, MHD flow meters an MHD generators etc. in view of the above some of the authors stuie Ashok Kumar an Lal [] consiere effect of oscillator motion of a viscoelastic ust flui passes through a porous meium uner the presence of magnetic fiel, Attia et al. [] Stuie MHD Couette flow an heat transfer of a ust flui with exponential ecaing pressure graient, Chenna Kesavaiah [3] investigate Natural convection heat transfer oscillator flow of an elastico viscous flui form vertical plate, Das [5] has heat transfer to MHD oscillator ust viscoelastic flui flow in an incline channel fille with a porous meium, Gosh et al. [6] prouce the hromagnetic flow of a ust Visco-elastic flui between two infinite parallel plates, Ibrahim Saiu et al. [7] stuies MHD effects on convective flow of ust viscous flui with volume fraction of ust particles, Liu [8] focuse flow inuce b the impulsive motion of an infinite flat plate in a ust gas, Mahura an Kalpana [9] analze thermal effect on unstea flow of a ust viscoelastic flui between two parallel plates uner ifferent pressure graients. The multiphase flui sstems are solicitue with the motion of a liqui or gas containing immiscible having onl a limite abilit to react ientical particles. All multiphase flui sstems foun in nature, flows in rocket tubes, san ust in gas cooling sstems to enhance heat transfer processes, bloo flow in arteries, act of inert soli particles in atmosphere or other suspene particles in sea or ocean beaches are the most common examples of multiphase flui sstems. In this regar some of the researcher are investigate Mahura an Swetha [] Influence of volume fraction of ust particles on ust flui flow through porous rectangular channel, Mohane Ismail an Ganesh [] Unstea Stokes flow of ust flui between two parallel plates through porous meium, Muassar Jalil et al. [] An exact solution of MHD bounar laer flow of ust flui over a stretching surface, Singh an Atul Kumar Singh [3] MHD effects on heat an mass transfer in flow of a ust viscous flui with volume fraction, Om Prakash [4] Effects of thermal iffusion an chemical reaction on MHD flow of ust viscoelastic flui, Saffman [6] observe on the stabilit of laminar flow of a ust gas, Saneep an Saleem [7] MHD flow an heat transfer of a ust nanoflui over a stretching surface in a porous meium. In spite of the above stuies, the namic moel of a two phase conucting flui flow in a nonrotating sstem has receive relativel less attention. The main inten of this paper investigation of the motion of an incompressible viscoelastic flui with embee small spherical inert particles boune b two infinite moving 8863

2 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve. parallel plates in the presence of transverse magnetic flui uner the thermal iffusion an raiation effect. The flow is prouce b time varing pressure graient. The velocit fiels of the flui flow an ust particles are etermine b perturbation metho. MATHEMATICAL FORMULATION Consier the unstea laminar ust flow of incompressible, viscous, slightl conucting, viscoelastic flui with uniform istribution of the ust particles between two heate porous infinite moving parallel plates with the subject to the affect of uniform magnetic fiel normal to the flow fiel with heat source uner the effects of thermal iffusion, raiation an chemical reaction. The ust particles are uniforml istribute in a porous meium an aopte in orer to eceive to be spherical in shape an uniform in size. The number of ensit of the ust particles is taken as a constant throughout the flow. Originall, when t the temperature an concentration of the ust fluis is axis is T an C respectivel. When t the temperature profiles an concentration profiles are evaluate to Tw an Cw respectivel. Regaring these assumptions the flow will be a parallel flow in which the streamlines are along the x axis as shown below: u u KN () g T T g C C K v u Bu u K m v K u v () Q K T qr T T T T C p C p C p (3) C T T D Kr C C DT (4) The initial an bounar conitions of the problem t : u v, T T t : u v, T T Tw T e at, (5) e u v, T T Tw T e at C C Cw C e at C C Cw C at for for The raiative heat flux of the equation (3) in the spirit of Cogle et al. [4] Where I Kiw in the wall an qr 4 T T I eb, where K iw is the absorption T eb Planck s function Introuce the following non imensional quantities T To C Co a t u v, t, u, v, T, C,a Tw T Cw C Introucing these non imensional quantities, equations () (4) reuce to u u u GrT GmC E v u M u (6) t w K v W u v T T Pr S R T C C T Sc KrSc C S T (7) (8) (9) Initial an bounar conitions of equation (5) accoring to new sstem become, t : T : u v, T t : u v, T T Tw T e at for u v, T e at, C e at () for where u ust flui phase velocit, v ust particle velocit, t time, ensit of the flui, P pressure of flui, x coorinate axis in the irection of the flow, g acceleration ie to gravit, volumetric thermal expansion coefficient, mean free path of iffusing particles, coorinate axis normal to the plate, A Darc number, t time, N Number ensit of ust particles, T temperature of flui, T Initial temperature, C concentration of flui, initial uniform concentration at T, concentration of ust particle), M B mn C (mass (Hartmann 8864

3 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve. Gr number), Kr K g Tw T (Grashof (chemical reaction parameter), number), R 4 I m (raiation parameter) W (relaxation time K g Cw C parameter for particles), Gm K E (viscoelastic (moifie Grashof number), Q parameter), Sc (Schmit number), S (Heat D KT C p source parameter), Pr (Prantl number), KT D T T k K, ST T w (thermal iffusion Cw C u, t u u, t e at v, t v v, t e at () T, t T T, t e at C, t C C, t e at Substituting equation () in to the equations (6) (9) an equating harmonic an non harmonic terms get the flowing set of equations u u GrT GmC ae u u w () v GrT GmC (3) u v & u v aw (4) T S R T (5) parameter) T S R a Pr T (6) SOLUTION OF THE PROBLEM Solve the sstem of equations (6) (9) subject to the bounar conitions () accoring to Pop [5] assume that C Kr Sc C ST T (7) C Kr a Sc C ST T (8) where ashes represents ifferentiation w. r. t. to The initial an bounar conition are reuce to u v u v, T C, T C u v u v, T C, T C Solve the equations () (8) uner the initial an bounar conitions (9) we get the solution at (9) at u, t A3 A4 Cosh A3 A4 Cosh 3 Cosh e at A5 A6 A5 A6 Cosh 3 v, t A3 A4 Cosh A3 A4 3 Cosh e at A5 A6 A3 A4 Cosh 3 aw T, t at e 8865

4 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve. C, t A 3 at A e A A 3 Skin Friction Let f an p be the skin friction for ust flui an ust particles respectivel then we have f u u Pr. From these figures it is evient that the velocit profiles ecreases with increasing values of Prantl number. The effects of heat source parameter A3 A4 tanh A3 tanh A4 tanh e at A5 A6 tanh A5 tanh A6 3 tanh 3 f number A3 A4 tanh A3 tanh A4 tanh on velocit profiles (ust flui an ust particles) are foun in figures 9(a) an 9(b), we notice that the velocit (ust flui an ust particles) ecreases with increasing values of heat source parameter. Thermal iffusion parameter e at A5 A6 tanh A5 tanh A6 3 tanh 3 aw RESULTS AND DISCUSSIONS The graphical presentations variations of velocit profiles (for ust flui an ust particles), temperature profiles, concentration profile an skin friction for ust flui has been analze. Figures (a) an (b) etermine the velocit for both (ust flui an ust particles) of S ST effects are shown in figure (a) an (b) for velocit profiles for both ust flui an ust particles observe, it is being perceive the velocit ecreases in both ust flui an ust particles as increasing values of iffusion parameter. It is known that the raiation parameter R plas an important role in is foun that the velocit increases with an increasing values of chemical reaction parameter. Figures 3(a) an 3(b) epicte velocit profiles (for ust flui an ust flow phenomena because; it is a measure of the relative magnitue of viscous bounar laer thickness to the thermal bounar laer thickness. In view of the above the variation of velocit profiles illustrate in figures (a) an (b), it is notice that the velocit reuces as increasing values of raiation parameter for both ust flui as well as ust particles. Figures (a) an (b) shown the variation of velocit profiles for viscoelastic particles) of various values of Schmit number parameter istinct values of the chemical reaction parameter Kr, it Sc, from this figure it is clear that, an increases in the values of Schmit number the velocit increases in both ust flui as well as ust particles. The velocit profiles for both (ust flui an ust particles) are observe form figures 4(a), 4(b) an 5(a), 5(b) of thermal Grashof number Gr an mass Grashof number Gm. It is E, it is reail apparent that an increases the viscoelastic parameter the velocit of ust flui an ust particles also increases. Temperature profiles have been plotte in figures (3) to (5) inicate the effects of R, Prantl number Pr an heat source parameter S. From these figures foun that the raiation parameter ecie that velocit profiles increases where as increases in the values of thermal Grashof number an mass Grashof number. This is an account of the buoanc effects enter more significant an as consier like. It implies that, heaviest flui is entraine out of the free stream ue the having strength buoanc effects as thermal Grashof number or mass Grashof number increases. This confirms the ownwar flow to a thin region near the plates. Figures 6(a) an 6(b) preicte the velocit for ifferent values of temperature profiles ecreases in with increasing values of raiation parameter an Prantl number, but the reverse effect observe in heat source parameter. In the concentration fiel the chemical reaction parameter effects are much influence. This profile have the common feature that the concentration profiles ecreases in a monotone fashion form the surface to a zero value far awa in the free stream. Concentration profile for the the porosit parameter increasing in porosit parameter the velocit also shown in figure (6), we notice that an increasing the chemical reaction parameter the temperature profiles increases. Effect of Hartman number ecreases. K. We observe that an M evience to a resistive tpe of force similar to rag force, which tens to resist the retaring flow of viscoelastic flui flow. From figures 7(a) to 7(b) clear that an increasing values of Hartman numbers the velocit ecreases for both (ust flui an ust particles). This is because increasing Hartman number the opposing Lorentz force increases resulting in the ecrease of the flui velocit. The velocit profiles for ust flui an ust particles are shown in figures 8(a) an 8(b) for ifferent values of Prantl ifferent values of chemical reaction parameter The Schmit number Kr Sc effect are on temperature profiles are observe in Figure-7, where as Schmit number increases the temperature profiles also increases. From figure (8) etermine that the temperature profiles for ifferent values of the heat source parameter S, it is observe that increases in the heat source parameter the temperature profiles ecreases. For various values of iffusion parameter ST on temperature profiles inicate in Figure-9, it is evient 8866

5 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve. Sc that an increase in iffusion parameter the temperature that the skin friction for Schmit number profiles ecreases. The effects of raiation parameter Grashof number Gr, it is etermine b that skin R on temperature profiles are inicate in figure (), form this figure notice that an increases in raiation parameter reuces the temperature profiles. Figure () pretening versus friction increases where the Schmit number increases. APPENDIX S R, Kr Sc, S R a Pr, 3 K a Sc ST ST M, M a A A,, w aw K 3 K A3 Gr AGm, A4 Gm A, 3 A5 Gm A Gr AGm, A Kr=5.,.,5.,. Dust Velocit (v) a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Pr=.76; ST=.; Sc=.65; Gr=.; S=.;R= Kr=5.,.,5.,. Flui Velocit (u) Flui Velocit (u) Figure (b): Velocit Profiles for ifferent values of Kr a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Pr=.7; ST=.; Sc=.65;Gr=.; S=.; R=..4 Sc=.,.,3., Figure (a): Velocit Profiles for ifferent values of Kr -. - a=.;m=.;t=.;w=.5;e=.;k-=.;gm=. Kr=.; Pr=.7; ST=.; Gr=.; S=.; R= Figure 3(a): Velocit Profiles for ifferent values of Sc 8867

6 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve Sc=.,.,3.,4. Dust Velocit (v) Dust Velocit (v) Gr=.,.,3.,4.. a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; Pr=.76; ST=.; Gr=.; S=.; R= a=.;m=.;t=.;w=.5;e=.;k-=.;gm=. Kr=.; Pr=.76; ST=.; Sc=.65; S=.; R= Figure 5(b): Velocit Profiles for ifferent values of Gr Figure 3(b): Velocit Profiles for ifferent values of Sc Flui Velocit (u) Flui Velocit (u) Gm=.,.,3., K=.,.,3.,4.. a=.;m=.;t=.;w=.5;e=.;k=.;kr=. Pr=.7; ST=.; Sc=.65; Gr=.;S=.;R= Figure 4(a): Velocit Profiles for ifferent values of Gm a=.;m=.;t=.;w=.5;e=.;gm=.;kr=. Pr=.7; ST=.; Sc=.65; Gr=.; S=.;R= Dust Velocit (V) Dust Velocit (v) s.4.3 Gm=.,.,3., Figure 6(a): Velocit Profiles for ifferent values of K.3 K=.,.,3.,4... a=.;m=.;t=.;w=.5;e=.;k=.;kr=. Pr=.76; ST=.; Sc=.65;Gr=.;S=.;R= a=.;m=.;t=.;w=.5;e=.;gm=.;kr=. Pr=.76; ST=.; Sc=.65; Gr=.; S=.; R= Figure 6(b): Veloct Profiles for ifferent values of K Flui Velocit (u) Flui Velocit (u) Figure 4 (b): Velocit Profiles for ifferent values of Gm Gr=.,.,3.,4..4. a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; Pr=.7; ST=.; Sc=.65; S=.;R= Figure 5(a): Velocit Profiles for ifferent values of Gr a=.;t=.;w=.5;e=.;k=.;gm=.;kr=. Pr=.7; ST=.; Sc=.65; Gr=.; S=.; R=.. M=.,4.,6., Figure 7(a): Veloct Profiles for ifferent values of M 8868

7 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve M=.,4.,6.,8. Dust Velcoit (v) Dust Velocit (v).4.3. a=.;t=.;w=.5;e=.;k=.;gm=.;kr=. Pr=.76; ST=.; Sc=.65; Gr=.; S=.; R=. S=.,.4,.6, a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; Pr=.76; ST=.; Sc=.65;Gr=.;R= Figure 9(b): Veloct Profiles for ifferent values of S Figure 7(b): Veloct Profiles for ifferent values of M Flui Velcoit (u) Flui Velocit (u) a=.;m=.;t=.;w=.5;e=.;k-=.;gm=. Kr=.; ST=.; Sc=.65; Gr=.; S=.; R= ST=.,.,.3,.4.5. Pr=.,.,3., a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; Pr=.7; Sc=.65; Gr=.;S=.;R= Figure (a): Veloct Profiles for ifferent values of S Figure 8(a): Veloct Profiles for ifferent values of Pr T..6 ST=.,.,.3,.4.5 Dust Velocit (v).5 Dust Velocit (v) Pr=.,.,3., a=.;m=.;t=.;w=.5;e=.;k=.;gm= a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; ST=.; Sc=.65; Gr=.; S=.;R= Kr=.; Pr=.76; Sc=.65; Gr=.; S=.;R= Figure (b): Veloct Profiles for ifferent values of S T Figure 8(b): Veloct Profiles for ifferent values of Pr Flui Velocit (u).35.4 Flui Velocit (u).35.3 S=.,.4,.6,.8.5. a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; Pr=.7; ST=.; Sc=.65; Gr=.;S=.. a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; Pr=.7; ST=.; Sc=.65; Gr=.;R= Figure (a): Veloct Profiles for ifferent values of R.5 - R=.,.4,.6, Figure 9(a): Veloct Profiles for ifferent values of S 8869

8 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve a=.,s=.,t=.,r=..5 Dust Velocit (v). Temperature Pr=.7,.76,.8,.9.5 R=.,.4,.6, a=.;m=.;t=.;w=.5;e=.;k=.;gm=. Kr=.; Pr=.76;ST=.; Sc=.65; Gr=.; S= Figure (b): Velocit Profiles for ifferent values of R Figure (4).: Temperature Profiles for ifferent values of Pr a=.,t=.,r=.,pr=.76 Temperature Flui Velocit (U).5 E=.,.,3.,4. a=.,m=.,t=.,w=.5,r=.,k=.,gm=. Kr=.,Pr=.76,ST=., Sc=.65,Gr=., S=.. S=.,4.,6., Figure (a): Velocit profiles for ust flui ifferent values of E Figure (5).: Temperatur Profiles for ifferent Values of S.7..8 E=.,.,3., a=.,m=.,t=.,w=.5,r=.,k=.,gm=. Kr=.,Pr=.76,ST=., Sc=.65,Gr=., S=.. - a=.;sc=.65;t=.;st=.;pr=.7;r=.;s=..4 Concentration Dust Velocit (V).6. Kr=.,.,3., Figure (b): Velocit profies for ust particles ifferent values f E Figure (6): Concentration Profiles for ifferent values of Kr.5 a=.,s=.,t=.,pr= a=.;t=.;st=.;kr=.5; Pr=.7;R=.;S=. R=.,.,3., Concentration Temperature Figure (3).: Temperature Profiles for ifferent values of R -. Sc=.,.4,.6, Figure (7): Concentration Profiles for ifferent values of Sc 887

9 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve. REFERENCES.5 [] Ashok Kumar an M Lal. 7. Effect of oscillator motion of a viscoelastic ust flui passes through a porous meium uner the presence of magnetic fiel, International Journal of Engineering an Technolog. 9(4): Concentration.5 a=.;sc=.65;t=.;st=.;kr=.5;pr=.7;r=.. S=.,.,3., Figure (8): Concentration Profiles for ifferent values of S.. Concentration [3] Chenna Kesavaiah D, Satanaraana P V, Suhakariah A an Venkataramana S. 3. Natural convection heat transfer oscillator flow of an elastico viscous flui form vertical plate. International Journal of Research in Engineering an Technolog. (6): a=.;sc=.65;t=.;kr=.5;pr=.7;r=.;s=. ST=.,.,.3,.4, Figure (9): Concentration Profiles for ifferent values of S [5] Das U J. 7. Heat transfer to MHD oscillator ust viscoelastic flui flow in an incline channel fille with a porous meium. Latin American Applie Research. 47: Concentration a=.;sc=.65;t=.;st=.;kr=.5;pr=.7;s=. [6] Gosh N C, Gosh B C an Debnath L. The hromagnetic flow of a ust Visco-elastic flui between two infinite parallel plates, Computers an Mathematics with Applications. 39: R=.,.,3., [4] Cogl A C, Vincentr W C an Gilles S E A Differential approximation for raiative transfer in a non-gra gas near equilibrium. AIAA Journal. 6: T.5.5 [] Attia H A, Al-kais A M A an Ewis K M.. MHD Couette flow an heat transfer of a ust flui with exponential ecaing pressure graient, Tamkang Journal of Science an Engineering. 4(): Figure (): Concentration Profiles for ifferent values of R [7] Ibrahim Saiu, Waziri M Y, Abubakar Roko an Hamisu Musa.. MHD effects on convective flow of ust viscous flui with volume fraction of ust particles, ARPN Journal of Engineering an Applie Sciences. 5(): [8] Liu J T C Flow inuce b the impulsive motion of an infinite flat plate in a ust gas, Austronautica Acta. 3: S=.,4.,6., ust Particles ( ) Skin friction p 4.4 ust Flui ( ) f [9] Mahura K R an Kalpana G. 3. Thermal effect on unstea flow of a ust viscoelastic flui between two parallel plates uner ifferent pressure graients. International Journal of Engineering an Technolog. (): a=., M=5., t=., w=.5, Sc=. Kr=.,Gm=5.,K=,Pr=.7,E= Gr Figure ().: Skin friction for ifferent values of S versus Gr [] Mahura K R an Swetha D S. 7. Influence of volume fraction of ust particles on ust flui flow 887

10 VOL. 3, NO., NOVEMBER 8 ISSN Asian Research Publishing Network (ARPN). All rights reserve. through porous rectangular channel. International Journal of Mathematics Tren an Technolog. 5(5): [] Mohane Ismail A an Ganesh S. 4. Unstea Stokes flow of ust flui between two parallel plates through porous meium. Applie Mathematical Sciences. 8(5): 4-49 [] Muassar Jalil, Saleem Asghar an Shagufta Yasmeen. 7. An exact solution of MHD bounar laer flow of ust flui over a stretching surface, Hinawi Mathematical Problems in Engineering, Article ID 37469, 5 pages. [3] N P Singh an Atul Kumar Singh.. MHD effects on heat an mass transfer in flow of a ust viscous flui with volume fraction, Inian Journal of Pure an Applie Phsics. 39: [4] Om Prakash, Devenra Kumar an Dwivei Y K.. Effects of thermal iffusion an chemical reaction on MHD flow of ust viscoelastic (Walter s liqui moel B) flui, J. Electromagnetic Analsis an Applications. : [5] Pop I Effects of thermal iffusion an chemical reaction on MHD flow of ust visco-elastic (Walter s liqui moel-b) flui, Rev. Roum. Phsics.3: 4. [6] Saffman P G. 96. On the stabilit of laminar flow of a ust gas. Journal of Flui Mechanics. 3(): -8. [7] Saneep N an Saleem S. 7. MHD flow an heat transfer of a ust nanoflui over a stretching surface in a porous meium, Joran Journal of Civil Engineering. () 887

Magnetic Field and Chemical Reaction Effects on Convective Flow of

Communications in Applied Sciences ISSN 221-7372 Volume 1, Number 1, 213, 161-187 Magnetic Field and Chemical Reaction Effects on Convective Flow of Dust Viscous Fluid P. Mohan Krishna 1, Dr.V.Sugunamma