Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

doi:10.1088/1674-1056/23/12/124701

Abstract An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations (PDEs) are converted into a nonlinear self-similar ordinary differential equation (ODE). For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.

Keywords: dual solutions boundary layer flow Maxwell fluid porous shrinking sheet

Received: 12 November 2013
Revised: 03 July 2014
Accepted manuscript online:

PACS:	47.15.-x	(Laminar flows)
	47.50.-d	(Non-Newtonian fluid flows)

Fund: The first author (K. Bhattacharyya) gratefully acknowledges the financial support of National Board for Higher Mathematics (NBHM), DAE, Mumbai, India for pursuing this work. The research of Dr. Alsaedi was partially supported by Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia.

Corresponding Authors: Tasawar Hayat
E-mail: pensy_t@yahoo.com

Cite this article:

Krishnendu Bhattacharyya, Tasawar Hayat, Ahmed Alsaedi Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet 2014 Chin. Phys. B 23 124701


[1]	Crane L J 1970 Z. Angew. Math. Phys. 21 645

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

[3]	Chen C K and Char M I 1988 J. Math. Anal. Appl. 135 568

[4]	Pavlov K B 1974 Magn. Gidrod. 10 146

[5]	Zheng L, Niua J, Zhang X and Ma L 2012 Int. J. Heat Mass Transfer 55 7577

[6]	Zheng L, Wang L, Zhang X and Ma L 2012 Chem. Eng. Commun. 199 1

[7]	Zheng L, Niua J, Zhang X and Gao Y 2012 Math. Comput. Modell. 56 133

[8]	Wang C Y 1990 Q. Appl. Math. 48 601

[9]	Miklavčič M and Wang C Y 2006 Q. Appl. Math. 64 283

[10]	Hayat T, Abbas Z and Sajid M 2007 ASME J. Appl. Mech. 74 1165

[11]	Hayat T, Javed T and Sajid M 2008 Phys. Lett. A 372 3264

[12]	Bhattacharyya K 2011 Front. Chem. Sci. Eng. 5 376

[13]	Bhattacharyya K and Layek G C 2011 Int. J. Heat Mass Transfer 54 302

[14]	Bhattacharyya K, Mukhopadhyay S and Layek G C 2011 Int. J. Heat Mass Transfer 54 308

[15]	Bhattacharyya K 2011 Int. Commun. Heat Mass Transfer 38 917

[16]	Fox V G, Erickson L E and Fan L T 1969 AIChE J. 15 327

[17]	Djukic D S 1974 ASME J. Appl. Mech. 41 822

[18]	Rajagopal K R 1980 Mech. Res. Commun. 7 21

[19]	Rajagopal K R and Gupta A S 1981 Int. J. Eng. Sci. 19 1009

[20]	Rajagopal K R, Na T Y and Gupta A S 1984 Rheol. Acta 23 213

[21]	Fetecau C and Fetecau C 2003 Int. J. Non-Linear Mech. 38 423

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

[23]	Hayat T, Abbas Z and Ali N 2008 Phys. Lett. A 372 4698

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