In this paper, the Magnetohydrodynamic (MHD) Flow of
Viscous Fluid over a Nonlinear Stretching Sheet is investigated numerically.
The partial differential equations governing the flow are reduced to a non
linear ordinary differential equations by using similarity transformations. The
resulting
transformed equations are numerically solved by an explicit finite difference
scheme known as the Keller Box Method. The velocity profiles are determined
and the effects of the magnetic parameter and non linear stretching parameter
on the flow characteristics are investigated. In addition to this the numerical
results for the local skin friction coefficients are computed. Comparison with
the exact solution and previously reported analytic solutions is made and
excellent agreement is noted. Moreover, the velocity profile obtained by Keller
box method is in a better agreement to the exact solution than by the Homotopy
Analysis Method. It is also found that, an increase in the magnetic parameter
or non-linearity parameter causes a decrease in the velocity profile and
velocity distribution.
Cite this paper
Yirga, Y. and Tesfay, D. (2014). Magnetohydrodynamic Flow of Viscous Fluid over a Non-Linearly Stretching Sheet. Open Access Library Journal, 1, e1030. doi: http://dx.doi.org/10.4236/oalib.1101030.
Crane, L.J.
(1970)
Flow past a Stretching Plate. Zeitschrift
für angewandte Mathematik und Physik ZAMP, 21, 645-647. http://dx.doi.org/10.1007/BF01587695
Brady, J.F. and Acrivos, A.
(1981)
Steady Flow in a Channel or Tube with Accelerating Surface Velocity. An
exact solution to the Navier-Stokes Equation with Reverse Flow. Journal of Fluid Mechanics, 112, 127-150. http://dx.doi.org/10.1017/S0022112081000323
Nadeem, S. (2009) Anwar
Hussain: MHD Flow of a Viscous Fluid on a Nonlinear Porous Shrinking Sheet with
Homotopy Analysis Method. Applied
Mathematics and Mechanics (Engl.
Ed.), 30,
1569-1578.
Nadeem, S. and
Lee, C. (2012) Boundary Layer Flow of Nanofluid over an Exponentially
Stretching Surface. Nanoscale
Research Letters, 7, 94. http://dx.doi.org/10.1186/1556-276X-7-94
Sharidan, S., Mahmood, T. and Pop, I. (2006) Similarity Solutions for the Unsteady Boundary
Layer Flow and Heat Transfer Due to a Stretching Sheet. International Journal of Applied Mechanics and Engineering, 11, 647-654.
Cortell, R. (2007) Viscous Flow and Heat Transfer over a Nonlinearly
Stretching Sheet. Applied
Mathematics and Computation (Elsevier), 184,
864-873. http://dx.doi.org/10.1016/j.amc.2006.06.077
Alinejad, J.
and Samarbakhsh, S. (2012) Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous
Dissipation. Journal of Applied Mathematics(Hindawi
Publishing Corporation), 2012, Article ID: 587834.
Devi, C.D.S., Takhar, H.S.
and Nath, G. (1991) Unsteady
Mixed Convection Flow in Stagnation Region Adjacent to a Vertical Surface. Heat and Mass Transfer, 26, 71-79.
Andersson, H.I.,
Aarseth, J.B.
and Dandapat, B.S.
(2000) Heat Transfer in a Liquid Film on an Unsteady Stretching Surface. International Journal of Heat and Mass
Transfer, 43, 69-74. http://dx.doi.org/10.1016/S0017-9310(99)00123-4
Nazar, R., Amin, N.
and Pop, I. (2004) Unsteady Boundary Layer Flow Due to Stretching Surface in a
Rotating Fluid. Mechanics Research Communications, 31, 121-128. http://dx.doi.org/10.1016/j.mechrescom.2003.09.004
Elbashbeshy, E.M.A. and Bazid, M.A.A. (2004) Heat Transfer over an Unsteady Stretching
Surface. Heat and Mass Transfer, 41, 1-4. http://dx.doi.org/10.1007/s00231-004-0520-x
Ishak, A., Nazar,
R. and Pop, I. (2009) Heat Transfer over an Unsteady Stretching Permeable
Surface with Prescribed Wall Temperature. Nonlinear
Analysis: Real World Applications,
10, 2909-2913. http://dx.doi.org/10.1016/j.nonrwa.2008.09.010
Wubshet, I., Shankar,
B. and Nandeppanavar, M.M. (2013) MHD
Stagnation Point Flow
and Heat Transfer Due to Nanofuid towards Astretching Sheet. International Journal of Heat and Mass
Transfer, 56, 1-9.
Turkyilmazoglu, M. and Pop, I. (2013) Heat and Mass Transfer of Unsteady Natural
Convection Flow of
Some Nano- fluids
Past Avertical Infinite Flat Plate with Radiation Effect. International Journal of Heat and Mass
Transfer, 59, 167-171. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.009
Xu, H., Pop,
I. and You,
X.C. (2013) Flow
and Heat Transfer in a Nano-Liquid Film over an Unsteady Stretching Surface. International Journal of Heat and Mass
Transfer, 60, 646-652. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.01.046
Karmishin, A.V., Zhukov,
A.I. and Kolosov, V.G. (1990) Methods of Dynamics Calculation and Testing for
Thin- Walled
Structures.
Mashinostroyenie, Moscow.
Keller, H.B. (1971) A New Difference Scheme for Parabolic Problems.
In: Hubbard,
B.,
Ed., Numerical Solutions of Partial
Differential Equations, II, Academic Press, New York, 327-350.
Hayat, T., Hussain, Q.
and Javed, T. (2007) The Modified Decomposition Method and Pade
Approximation for the MHD Flow over a Non-Linear Stretching Sheet. Nonlinear Analysis: Real World Applications, 10, 966-973.
Ghotbi, A.R. (2009) Homotopy
Analysis Method for Solving the MHD Flow over a Non-Linear Stretching Sheet. Communications in Nonlinear Science and
Numerical Simulation, 14, 2653-2663.