My Limiting Behavior of MHD Flow with Hall Current, Due to a Porous Stretching Sheet
Author(s)
Faiza M. N. El-Fayez*
ABSTRACT
An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions; even at moderate magnetic fields.
An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions; even at moderate magnetic fields.
Cite this paper
El-Fayez, F. (2014) My Limiting Behavior of MHD Flow with Hall Current, Due to a Porous Stretching Sheet. Journal of Applied Mathematics and Physics, 2, 124-130. doi: 10.4236/jamp.2014.25016.
El-Fayez, F. (2014) My Limiting Behavior of MHD Flow with Hall Current, Due to a Porous Stretching Sheet. Journal of Applied Mathematics and Physics, 2, 124-130. doi: 10.4236/jamp.2014.25016.
References
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[1] Crane, L.J. and Angew, Z. (1970) Flow Past a Stretching Plate. Zeitschrift für angewandte Mathematik und Physik ZAMP, 21, 645. http://dx.doi.org/10.1007/BF01587695 [2] Gupta, P.S. and Gupta, A.S. (1977) Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing. Canadian Journal of Chemical Engineering, 55, 744. http://dx.doi.org/10.1002/cjce.5450550619 [3] Andersson, H.I. (1995) An Exact Solution of the Navier-Stokes Equations for Magnetohydrodynamic Flow. Acta Mechanica, 113, 241. http://dx.doi.org/10.1007/BF01212646 [4] Andersson, H.I. (2002) Slip Flow Past a Stretching Surface. Acta Mechanica, 158, 121. http://dx.doi.org/10.1007/BF01463174 [5] Wang, C.Y. (2009) Analysis of Viscous Flow Due to a Stretching Sheet with Surface Slip and Suction. Nonlinear Analysis: Real World Applications, 10, 375. http://dx.doi.org/10.1016/j.nonrwa.2007.09.013 [6] Abel, M.S. and Nandeppanavar, M.M. (2009) Heat Transfer in MHD Viscoelastic Boundary Layer Flow over a Stretching Sheet with Non-Uniform Heat Source/Sink. Communications in Nonlinear Science and Numerical Simulation, 14, 2120. http://dx.doi.org/10.1016/j.cnsns.2008.06.004 [7] Kumar, H. (2011) Heat Transfer over a Stretching Porous Sheet Subjected to Power Law Heat Flux in Presence of Heat Source. Thermal Science, 15, S187. http://dx.doi.org/10.2298/TSCI100331074K [8] Vajravelu, K. and Rollins, D. (2004) Hydromagnetic Flow of a Second Grade Fluid over a Stretching Sheet. Applied Mathematics and Computation, 148, 783. http://dx.doi.org/10.1016/S0096-3003(02)00942-6 [9] Nayfeh, A.H. (1973) Perturbation Methods. John Wiley, New York. [10] Sutton, G.W. and Sherman, A. (1965) Engineering Magnetohydrodynamics. McGraw-Hill, New York. [11] Keller, H.B. (1969) Accurate Difference Methods for Linear Ordinary Differential Systems Subject to Linear Constraints. SIAM Journal on Numerical Analysis, 6, 8. http://dx.doi.org/10.1137/0706002 [12] Pantokratoras, A. (2009) A Common Error Made in Investigation of Boundary Layer Flows. Applied Mathematical Modelling, 33, 413. http://dx.doi.org/10.1016/j.apm.2007.11.009