RESEARCH ARTICLE

Magnetohydrodynamic slip flow and diffusion of a reactive solute past a permeable flat plate with suction/injection

  • Krishnendu BHATTACHARYYA ,
  • G. C. LAYEK
Expand
  • Department of Mathematics, The University of Burdwan, West Bengal, Burdwan-713104, India

Received date: 22 Feb 2011

Accepted date: 20 Aug 2011

Published date: 05 Dec 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

The magnetohydrodynamic (MHD) boundary layer slip flow and solute transfer over a porous plate in the presence of a chemical reaction are investigated. The governing equations were transformed into self-similar ordinary differential equations by adopting the similarity transformation technique. Then the numerical solutions are obtained by a shooting technique using the fourth order Runge-Kutta method. The study reveals that due to the increase in the boundary slip, the concentration decreases and the velocity increases. On the other hand, with an increase in the magnetic field and mass suction, both boundary layer thicknesses decreased. As the Schmidt number and the reaction rate parameter increases, the concentration decreases and the mass transfer increases.

Cite this article

Krishnendu BHATTACHARYYA , G. C. LAYEK . Magnetohydrodynamic slip flow and diffusion of a reactive solute past a permeable flat plate with suction/injection[J]. Frontiers of Chemical Science and Engineering, 2011 , 5(4) : 471 -476 . DOI: 10.1007/s11705-011-1130-z

Acknowledgments

The Authors are thankful to the reviewers for their valuable comments and suggestions. One of the authors (K. Bhattacharyya) gratefully acknowledges the financial support from the National Board for Higher Mathematics (NBHM), DAE, Mumbai, India to pursue this work.
1
Blasius H. Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z Math U Phys, 1908, 56: 1-37

2
Pohlhausen E. Der Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner Reibung und kleiner Wärmeleitung. Zeitschrift für Angewandte Mathematik und Mechanik, 1921, 1(2): 115-121

3
Howarth L. On the solution of the laminar boundary layer equations.In: Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1938, 164(919): 547-579

4
Abu-Sitta A M M. A note on a certain boundary-layer equation. Applied Mathematics and Computation, 1994, 64(1): 73-77

5
Wang L. A new algorithm for solving classical Blasius equation. Applied Mathematics and Computation, 2004, 157(1): 1-9

6
Cortell R. Numerical solutions of the classical Blasius flat-plate problem. Applied Mathematics and Computation, 2005, 170(1): 706-710

7
Bataller R C. Radiation effects in the Blasius flow. Applied Mathematics and Computation, 2008, 198(1): 333-338

8
Sparrow E M, Cess R D. The effect of a magnetic field on free convection heat transfer. International Journal of Heat and Mass Transfer, 1961, 3(4): 267-274

9
Gupta A S. Laminar free convection flow of an electrically conducting fluid from a vertical plate with uniform surface heat flux and variable wall temperature in the presence of a magnetic field. Zeitschrift für Angewandte Mathematik und Physik, 1962, 13(4): 324-333

10
Riley N. Magnetohydrodynamic free convection. Journal of Fluid Mechanics, 1964, 18(04): 577-586

11
Watanabe T, Pop I. Hall effects on magnetohydrodynamic boundary layer flow over a continuous moving flat plate. Acta Mechanica, 1995, 108(1-4): 35-47

12
Damseh R A, Duwairi H M, Al-Odat M. Similarity analysis of magnetic field and thermal radiation effects on forced convection flow. Turkish Journal of Engineering and Environmental Sciences, 2006, 30: 83-89

13
Lai F C, Kulacki F A. Non-Darcy mixed convection along a vertical wall in a saturated porous medium. Journal of Heat Transfer, 1991, 113(1): 252-255

14
Postelnicu A. Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Heat and Mass Transfer, 2007, 43(6): 595-602

15
Bhattacharyya K, Layek G C. Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing. Chemical Engineering Communications, 2010, 197(12): 1527-1540

16
Beavers G S, Joseph D D. Boundary conditions at a naturally permeable wall. Journal of Fluid Mechanics, 1967, 30(01): 197-207

17
Martin M, Boyd I. Momentum and heat transfer in laminar boundary layer with slip flow. Journal of Thermophysics and Heat Transfer, 2006, 20(4): 710-719

18
Aziz A. Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(3): 573-580

19
Andersson H I. Slip flow past a stretching surface. Acta Mechanica, 2002, 158(1-2): 121-125

20
Wang C Y. Flow due to a stretching boundary with partial slip—an exact solution of the Navier-Stokes equations. Chemical Engineering Science, 2002, 57(17): 3745-3747

Outlines

/