Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(2): 024702    DOI: 10.1088/1674-1056/22/2/024702
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

Krishnendu Bhattacharyyaa, Tasawar Hayatb, Ahmed Alsaedic
a Department of Mathematics, The University of Burdwan, Burdwan-713104, West Bengal, India;
b Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;
c Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Abstract  In this analysis, the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in presence of wall mass transfer is studied. Using similarity transformations, the governing equations are converted to an ordinary differential equation and then solved analytically. The introduction of magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has major impact in the stretching sheet case. The similarity solution is always unique in the stretching case, and in the shrinking case the solution shows dual nature for certain values of the parameters. For stronger magnetic field, the similarity solution for the shrinking sheet case becomes unique.
Keywords:  magnetohydrodynamic boundary layer      Casson fluid      stretching/shrinking sheet      wall mass transfer      analytic solution  
Received:  30 May 2012      Revised:  28 July 2012      Accepted manuscript online: 
PACS:  47.15.Cb (Laminar boundary layers)  
  47.50.-d (Non-Newtonian fluid flows)  
  47.65.-d (Magnetohydrodynamics and electrohydrodynamics)  
Corresponding Authors:  Krishnendu Bhattacharyya     E-mail:  krish.math@yahoo.com; krishnendu.math@gmail.ocm

Cite this article: 

Krishnendu Bhattacharyya, Tasawar Hayat, Ahmed Alsaedi Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer 2013 Chin. Phys. B 22 024702

[1] Pavlov K B 1974 Magnetohydrodynamics 10 146
[2] Chakrabarti A and Gupta A S 1979 Quart. Appl. Math. 37 73
[3] Andersson H I 1992 Acta Mech. 95 227
[4] Andersson H I, Bech K H and Dandapat B S 1992 Int. J. Non-Linear Mech. 27 929
[5] Vajravelu K and Rollins D 1992 Int. J. Non-Linear Mech. 27 265
[6] Andersson H I 1995 Acta Mech. 113 241
[7] Kumaran V and Ramanaiah G 1996 Acta Mech. 116 229
[8] Pop I and Na T Y 1998 Mech. Res. Commun. 25 263
[9] Chamkha A J 2000 Chem. Eng. J. 76 159
[10] Ishak A, Nazar R and Pop I 2006 Magnetohydrodynamics 42 77
[11] Ishak A, Nazar R and Pop I 2007 Magnetohydrodynamics 43 83
[12] Fang T, Zhang J and Yao S 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3731
[13] Eerdunbuhe and Temuerchaolu 2012 Chin. Phys. B 21 035201
[14] Salem A M and Fathy R 2012 Chin. Phys. B 21 054701
[15] Fang T and Aziz A 2010 Z. Naturforsch. 65a 1087
[16] Bhattacharyya K and Layek G C 2011 Chem. Eng. Commun. 198 1354
[17] Qasim M, Hayat T and Hendi A A 2011 Heat Transfer Asian Res. 40 641
[18] Hayat T, Qasim M and Mesloub S 2011 Int. J. Numer. Methods Fluids 66 963
[19] Mukhopadhyay S 2010 Chin. Phys. Lett. 27 124401
[20] Bhattacharyya K, Mukhopadhyay S and Layek G C 2011 Chin. Phys. Lett. 28 094702
[21] Wang C Y 1990 Quart. Appl. Math. 48 601
[22] Miklavčič M and Wang C Y 2006 Quart. Appl. Math. 64 283
[23] Fang T and Zhang J 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2853
[24] Fang T, Zhang J and Yao S 2010 Chin. Phys. Lett. 27 124702
[25] Hayat T, Abbas Z, Javed T and Sajid M 2009 Chaos, Solitons and Fractals 39 1615
[26] Fang T 2009 Int. J. Heat Mass Transfer 51 5838
[27] Noor N F M, Kechil S A and Hashim I 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 144
[28] Fang T, Yao S, Zhang J and Aziz A 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 1831
[29] Bhattacharyya K 2011 Chin. Phys. Lett. 28 074701
[30] Bhattacharyya K and Pop I 2011 Magnetohydrodynamics 47 237
[31] Fang T, Zhang J and Yao S 2009 Chin. Phys. Lett. 26 014703
[32] Ali F M, Nazar R, Arifin N M and Pop I 2011 Int. J. Numer. Meth. Fluids 67 1310
[33] Bhattacharyya K 2011 Front. Chem. Sci. Eng. 5 376
[34] Wang C Y 2008 Int. J. Non-Linear Mech. 43 377
[35] Mahapatra T R, Nandy S K and Gupta A S 2011 ASME J. Appl. Mech. 78 021015
[36] Bhattacharyya K and Layek G C 2011 Int. J. Heat Mass Transfer 54 302
[37] Bhattacharyya K, Mukhopadhyay S and Layek G C 2011 Int. J. Heat Mass Transfer 54 308
[38] Bhattacharyya K 2011 Chin. Phys. Lett. 28 084702
[39] Bhattacharyya K 2011 Int. Commun. Heat Mass Transfer 38 917
[40] Fan T, Xu H and Pop I 2010 Int. Commun. Heat Mass Transfer 37 1440
[41] Rosali H, Ishak A and Pop I 2011 Int. Commun. Heat Mass Transfer 38 1029
[42] Bhattacharyya K and Vajravelu K 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 2728
[43] Rohni A M, Ahmad S and Pop I 2012 Int. J. Heat Mass Transfer 55 1888
[44] Bhattacharyya K, Arif M G and Ali Pk W 2012 Acta Tech. 57 1
[45] Bachok N, Ishak A and Pop I 2012 Int. J. Heat Mass Transfer 55 2102
[46] Bhattacharyya K, Mukhopadhyay S, Layek G C and Pop I 2012 Int. J. Heat Mass Transfer 55 2945
[47] Rosali H, Ishak A and Pop I 2012 Int. Commun. Heat Mass Transfer 39 826
[48] Fox V G, Erickson L E and Fan L T 1969 AIChE J. 15 327
[49] Wilkinson W 1970 Chem. Eng. J. 1 255
[50] Djukic D S 1974 ASME J. Appl. Mech. 41 822
[51] Rajagopal K R 1980 Mech. Res. Commun. 7 21
[52] Rajagopal K R and Gupta A S 1981 Int. J. Eng. Sci. 19 1009
[53] Rajagopal K R, Na T Y and Gupta A S 1984 Rheol. Acta 23 213
[54] Dorier C and Tichy J 1992 J. Non-Newtonian Fluid Mech. 45 291
[55] Jafar K, Nazar R, Ishak A and Pop I 2011 Magnetohydrodynamics 47 61
[56] Fredrickson A G 1964 Principles and Applications of Rheology (Englewood Cliffs, N J: Prentice-Hall)
[57] Mustafa M, Hayat T, Pop I and Aziz A 2011 Heat Transfer Asian Res. 40 563
[58] Liao S J 2003 J. Fluid Mech. 488 189
[59] Hayat T, Javed T and Sajid M 2008 Phys. Lett. A 372 3264
[60] Hayat T, Abbas Z and Ali N 2008 Phys. Lett. A 372 4698
[61] Hayat T, Iram S, Javed T and Asghar S 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 2932
[62] Ishak A, Lok Y Y and Pop I 2010 Chem. Eng. Commun. 197 1417
[63] Yacob N A, Ishak A and Pop I 2011 Comput. Fluids 47 16
[64] Bachok N, Ishak A and Pop I 2011 Magnetohydrodynamics 47 237
[65] Ishak A, Lok Y Y and Pop I 2012 Chem. Eng. Commun. 199 142
[66] Yacob N A and Ishak A 2012 Meccanica 47 293
[67] Mustafa M, Hayat T, Pop I and Hendi A 2012 Z. Naturforsch 67a 70
[68] Nakamura M and Sawada T 1988 ASME J. Biomechanical Eng. 110 137
[1] Nonlinear tunneling through a strong rectangular barrier
Zhang Xiu-Rong, Li Wei-Dong. Chin. Phys. B, 2015, 24(7): 070311.
[2] Heat transfer analysis in the flow of Walters’B fluid with a convective boundary condition
T. Hayat, Sadia Asad, M. Mustafa, Hamed H. Alsulami. Chin. Phys. B, 2014, 23(8): 084701.
[3] Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux
Swati Mukhopadhyay, Iswar Chandra Mandal. Chin. Phys. B, 2014, 23(4): 044702.
[4] Casson fluid flow and heat transfer over a nonlinearly stretching surface
Swati Mukhopadhyay. Chin. Phys. B, 2013, 22(7): 074701.
[5] Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing
Swati Mukhopadhyay. Chin. Phys. B, 2013, 22(11): 114702.
[6] Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects
Swati Mukhopadhyay, Krishnendu Bhattacharyya, Tasawar Hayat. Chin. Phys. B, 2013, 22(11): 114701.
[7] Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation
Zhao Guo-Zhong, Yu Xi-Jun, Xu Yun, Zhu Jiang, Wu Di. Chin. Phys. B, 2010, 19(8): 080204.
[8] Variational iteration method for solving compressible Euler equations
Zhao Guo-Zhong, Yu Xi-Jun, Xu Yun, Zhu Jiang. Chin. Phys. B, 2010, 19(7): 070203.
[9] New approximate solution for time-fractional coupled KdV equations by generalised differential transform method
Liu Jin-Cun, Hou Guo-Lin. Chin. Phys. B, 2010, 19(11): 110203.
No Suggested Reading articles found!