ORIGINAL PAPER
A New Analytical Procedure for Solving the Non-Linear Differential Equation Arising in the Stretching Sheet Problem
 
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1
Department of Mathematics, Bangalore University Central College Campus Bangalore 560 001, Karnataka, INDIA
 
2
Department of Mathematics, Government First Grade College for Women Hassan 573 201, Karnataka, INDIA
 
3
Department of Energy and Process Engineering Norwegian University of Science and Technology 7491 Trondheim, NORWAY
 
 
Online publication date: 2013-09-06
 
 
Publication date: 2013-08-01
 
 
International Journal of Applied Mechanics and Engineering 2013;18(3):955-964
 
KEYWORDS
ABSTRACT
The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem
 
REFERENCES (22)
1.
Andersson H.I. (1992): MHD flow of a viscoelastic fluid past a stretching surface. - Acta Mech., vol.95, pp.227-230.
 
2.
Andersson H.I. (1995): An exact solution of the Navier-Stokes equation for magneto hydrodynamic flow. - Acta Mech. vol.113, pp.241-244.
 
3.
Andersson H.I. (2002): Slip flow past a stretching surface. - Acta Mech., vol.158, pp.121-125.
 
4.
Ariel P.D. (1994): MHD flow of a viscoelastic fluid past a stretching sheet with suction. - Acta Mech .,vol.105, pp.49-56.
 
5.
Crane L.J. (1970): Flow past a stretching plate. - J. Appl. Math. Phys. (ZAMP), vol.21, pp.645-647.
 
6.
Dandapat B.S., Singh S.N. and Singh R.P. (2004): Heat transfer due to permeable stretching wall in presence of transverse magnetic field. - Arch. Mech., vol.56(2), pp.127-141.
 
7.
Fisher E.G. (1976): Extrusion of Plastics. - 3rd Edition. London: Newnes-Butter World.
 
8.
Gupta P.S. and Gupta A.S. (1977): Heat and mass transfer on a stretching sheet with suction or blowing. - Can. J. Chem. Eng. vol.55, pp.744-746.
 
9.
Kumaran V. and Ramanaiah G. (1996): A note on the flow over a stretching sheet. - Acta Mech ., vol.119, pp.229 -233.
 
10.
Liao S.J. (2003): On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. - J. Fluid Mech., vol.488, pp.189-212.
 
11.
Liao S.J. and Pop I. (2004): Explicit analytic solution for similarity boundary layer equations. - Int. J. Heat and Mass Transfer, vol.47, pp.75-85.
 
12.
Magyari E. and Keller B. (2000): Exact solutions for self- similar boundary-layer flows induced by permeable stretching walls. - Euro. J. Mech. B / fluids. vol.19, pp.109-122.
 
13.
Magyari E. and Keller B. (2001): The wall jet as limiting case of a boundary-flow induced by a permeable stretching surface. - J. Appl. Math. Phys. (ZAMP), vol.52, pp.696-703.
 
14.
Magyari E., Pop I. and Keller B. (2003): New analytical solutions of a well-known boundary value problem in fluid mechanics. - Fluid Dyn. Res, vol .33, pp.313-317.
 
15.
Pavlov K.B. (1974): Magnetohydrodynamic flow of an incompressible viscous liquid caused by deformation of plane surface. - Magnetnaya Gidrodinamica, vol.4, pp.146-147.
 
16.
Rajagopal K.R., Na T.Y. and Gupta A.S. (1984): Flow of a viscoelastic fluid over a stretching sheet. - Rheo. Acta, vol.23, pp.213-215.
 
17.
Sakiadis B.C. (1961): Boundary layer behaviour on continuous solid surfaces, II: The boundary layer on a continuous flat surface. - A.I.Ch.E. J. vol.7, pp.221-225.
 
18.
Siddappa B. and Abel M.S. (1986): Viscoelastic boundary layer flow past a stretching plate with suction and heat transfer. - Rheol. Acta. vol.25, pp.319-320.
 
19.
Siddheshwar P.G. (2004): A new analytical procedure for solving the stretching sheet problem. - International Conference on Recent Trends in Applied Mathematics, March, 24-26, Gulbarga University, India.
 
20.
Siddheshwar P.G., Sekhar G.N. and Chan A.T. (2005): MHD flow over a nonlinearly stretching sheet. - Vignana Bharathi-Bangalore University Journal, vol.17, pp.76-81.
 
21.
Siddheshwar P.G.and Mahabaleswar U.S. (2005): Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet. - Int. J. Non-Linear Mech., vol.40, pp.807-820.
 
22.
Vajravelu K. (2001): Viscous flow over a nonlinearly stretching sheet. - Appl. Maths. Compu.,vol.124, pp.281-288.
 
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