Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

Swati Mukhopadhyay^{a}, M. Golam Arif^{b}, M. Wazed Ali Pk^{c}

a Department of Mathematics, The University of Burdwan, Burdwan-713104, W.B., India; b Institute of Business Administration, University of Rajshahi, Rajshahi-6205, Bangladesh; c Department of Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh

Abstract The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell (UCM) model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration (suction) and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration (suction) and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.

Swati Mukhopadhyay, M. Golam Arif, M. Wazed Ali Pk Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction 2013 Chin. Phys. B 22 124701

[1]

Abel M S and Mahesha N 2008 Appl. Math. Model. 32 1965

[2]

Ishak A, Nazar R and Pop I 2008 Heat Mass Transfer 44 921

[3]

Gupta P S and Gupta A S 1977 Can. J. Chem. Eng. 55 744

[4]

Vleggaar J 1977 Chem. Eng. Sci. 32 1517

[5]

Dutta B K, Roy P and Gupta A S 1985 Int. Commun. Heat Mass Transfer 12 89

[6]

Crane L J 1970 ZAMP 21 645

[7]

Liu I C and Andersson H I 2008 Int. J. Thermal Sci. 47 766

[8]

Mukhopadhyay S and Gorla R S R 2012 J. Naval Arch. Marine Engng. 9 123

[9]

Hassanien I A 1996 Appl. Model. 20 779

[10]

Sadeghy K and Sharifi M 2004 Int. J. Nonlinear Mech. 39 1265

[11]

Serdar B and Salih Dokuz M 2006 Int. J. Engng. Sci. 44 49

[12]

Haroun M H 2007 Commun. Nonlinear Sci. Numer. Simul. 12 1464

[13]

Siddiqui A M, Zeb A, Ghori Q K and Benharbit A M 2008 Chaos, Solitons and Fractals 36 182

[14]

Abel M S, Sanjayan E and Nandeppanavar M M 2008 Commun. Nonlinear Sci. Numer. Simul. 13 1808

[15]

Sajid M, Ahmad I, Hayat T and Ayub M 2009 Commun. Nonlinear Sci. Numer. Simul. 14 96

[16]

Heyhat M M and Khabazi N 2010 Proc. IMechE Part C: J. Mech. Eng. Sci. 225 909, DOI:10.1243/09544062JMES2245

[17]

Mukhopadhyay S 2012 Chin. Phys. Lett. 29 054703

[18]

Alim M A, Rahman M M and Karim M M 2008 J. Naval Arch. Marine Eng. DOI: 10.3329/jname.v5i1.1868

[19]

Hayat T, Abbas Z and Sajid M 2006 Phys. Lett. A 358 396

[20]

Hayat T, Fetecau C and Sajid M 2008 Phys. Lett. A 372 1639

[21]

Kumaran V, Banerjee A K, Kumar A V and Vajravelu K 2008 Appl. Math. Comput. 210 26

[22]

Ishak A, Nazar R and Pop I 2009 Chem. Engng. J. 148 63

[23]

Chaudhary M A and Merkin J H 1993 J. Engng. Math. 27 265

[24]

Hayat T, Awais M, Qasim M and Hendi A A 2011 Int. J. Heat Mass Transfer 54 3777

[25]

Andersson H I, Hansen O R and Holmedal B 1994 Int. J. Heat Mass Transfer 37 659

[26]

Kendoush A A 1998 Chem. Engng. Process. 37 223

[27]

Takhar H S, Chamkha A J and Nath G 2000 Int. J. Engng. Sci. 38 1303

[28]

Liu I C 2005 Int. Commun. Heat Mass Transfer 32 1075

[29]

Akyilidiz F T, Bellout H and Vajravelu K 2006 J. Math. Anal. Appl. 320 322

[30]

Cortell R 2007 Chem. Eng. Process.: Process Intens. 46 982

[31]

Mukhopadhyay S and Bhattacharyya K 2012 J. Egyptian Math. Soc. (in press), http://dx.doi.org/10.1016/j.joems.2012.08.019

[32]

Bhattacharyya K, Mukhopadhyay S and Layek G C 2013 Chem. Engng. Commun. 200 1

[33]

Andersson H I, Aarseth J B and Dandapat B S 2000 Int. J. Heat Mass Transfer 43 69

[34]

Dandapat B S, Santra B and Andersson H I 2003 Int. J. Heat Mass Transfer 46 3009

[35]

Dandapat B S, Santra B and Vajravelu K 2007 Int. J. Heat Mass Transfer 50 991

[36]

Elbashbeshy E M A and Bazid M A A 2004 Heat Mass Transfer 41 1

[37]

Sharidan S, Mahmood T and Pop I 2006 Int. J. Appl. Mech. Eng. 11 647

[38]

Ali M E and Magyari E 2007 Int. J. Heat Mass Transfer 50 188

[39]

Tsai R, Huang K H and Huang J S 2008 Int. Commun. Heat Mass Transfer 35 1340

[40]

Chamkha A J, Aly A M and Mansour M A 2010 Chem. Eng. Commun. 197 846

[41]

Abd El-Aziz M 2010 Chem. Eng. Commn. 197 1261

[42]

Mukhopadhyay S 2009 Int. J. Heat Mass Transfer 52 3261

[43]

Mukhopadhyay S 2010 Chin. Phys. Lett. 27 124401

[44]

Mukhopadhyay S 2011 Nucl. Eng. Des. 241 2660

[45]

Bhattacharyya K, Mukhopadhyay S and Layek G C 2011 Chin. Phys. Lett. 28 094702

[46]

Midya C 2012 Chin. Phys. Lett. 29 014701

[47]

Pahlavan A A and Sadeghy K 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1355

[48]

Andersson H I, Bech K H and Dandapat B S 1992 Int. J. Nonlinear Mech. 27 929

[49]

Prasad K V, Sujatha A, Vajravelu K and Pop I 2011 Meccanica DOI:10.1007/s11012-011-9526-x

[50]

Mukhopadhyay S 2009 Int. J. Heat Mass Transfer 52 5213

[51]

Mukhopadhyay S 2011 Nucl. Eng. Design 241 4835

[52]

Sadeghy K, Hajibeygi H and Taghavi S M 2006 Int. J. Nonlinear Mech. 41 1242

[53]

Abel M S, Tawade J V and Nandeppanavar M M 2011 Meccanica DOI:10.1007/s11012-011-9448-7

[54]

Mukhopadhyay S and Vajravelu K 2012 ASME J. Appl. Mech. http://dx.doi.org/10.1115/1.4006260

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