Communications in Numerical Analysis
Volume 2016, No. 1 (2016), Pages 17-36
Article ID cna-00251, 20 Pages
Influence of Hall Current on MHD Flow and Heat Transfer over a slender stretching sheet in the presence of variable fluid properties
K. Vajravelu1 *, K. V. Prasad2, Hanumesh Vaidya2
1Department of Mathematics, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA
2Department of Mathematics, VSK University, Vinayaka Nagar, Ballari-583 105, Karnataka, India
* Corresponding author. Email address: email@example.com
Received: 17 July 2015; Revised: 05 November 2015; Accepted: 20 November 2015
Copyright © 2016 K. Vajravelu, K. V. Prasad and Hanumesh Vaidya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
MHD flow and heat transfer of an electrically conducting fluid over a stretching sheet with variable thickness in the presence of variable fluid properties is analyzed. Wall temperature and the velocity of the stretching sheet are assumed to vary. Also the external magnetic field perpendicular to the sheet and the effects of Hall current are taken into account. The governing nonlinear differential equations are solved numerically by an implicit finite difference scheme. To validate the numerical method, comparisons are made with the available results in the literature for some special cases and the results are found to be in excellent agreement. The effects of physical parameters on the flow and temperature fields are analyzed graphically. The Hall current gives rise to a cross flow and the variable fluid properties have strong effects on the shear stress and the Nusselt number.
Keywords: Numerical solution; variable fluid properties; variable boundary thickness; MHD flow; Hall effects; Nusselt number.
A. Chakrabarti, A. S. Gupta, Hydromagnetic flow and heat transfer over a stretching sheet, Quart Appl. Math, 8 (1979) 73-78.
H. I. Andersson, K. H. Bech, B. S. Dandapat, Magnetohydrodynamic flow of a power law fluid over a stretching sheet, Int. J. Non-Linear Mech, 27 (1992) 929-936.
H. I. Andersson, An exact solution of the Navier-Stokes equations for magnetohydro-dynamic flow, Acta Mech, 113 (1995) 241-244.
K. Vajravelu, J. Nayfeh, Hydromagnetic flow of a dusty fluid over a stretching sheet, Int. J. Nonlinear Mech, 27 (1992) 937-945.
A. Ishak, R. Nazar, I. Pop, Magnetohydrodynamic stagnation point flow towards a stretching vertical sheet, Magnetohydrodynamics, 42 (2006) 77-90.
R. Cortell, Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet, Phys. Lett. A, 357 (2006) 298-305.
E. Sweet, K. Vajravelu, R. A. Van Gorder, I. Pop, Analytical solution for the unsteady MHD flow of a viscous fluid between moving parallel plates, Commun. Non-linear Sci. Numer. Simul, 16 (2011) 266-273.
R. A. Van Gorder, K. Vajravelu, Multiple solutions for hydromagnetic flow of a second grade fluid over a stretching or shrinking sheet, Quarterly of Applied Mathematics, 69 (2011) 405-424.
S. Abbasbandy, R. Naz, T. Hayat, A. Alsaedi, Numerical and analytical solutions for Falkner-Skan flow of MHD Maxwell fluid, Applied Mathematics and Computation, 242 (2014) 569-575.
C. Y. Wang, Exact solutions of the steady state Navier-Stokes equations, Ann. Rev. Fluid Mech, 23 (1991) 159-177.
K. Vajravelu, D. Rollins, Heat transfer in an electrically conducting fluid over a stretching sheet, Int. J. Non-Linear Mech, 27 (1992) 265-277.
I. Pop, T. Y. Na, A note on MHD flow over a stretching permeable surface, Mech. Res. Commun, 25 (1998) 263-269.
T. Fang, J. Zhang, S. Yao, Slip MHD viscous flow over a stretching sheet-an exact solution, Communications in Nonlinear Science and Numerical Simulation, 14 (2009) 3731-3737.
T. Fang, J. Zhang, Closed-form exact solutions of MHD viscous flow over a shrinking sheet, Communications in Nonlinear Science and Numerical Simulation, 14 (2009) 2853-2857.
R. A. Van Gorder, High-order nonlinear boundary value problems admitting multiple exact solutions with application to the fluid flow over a sheet, Applied Mathematics and Computation, 216 (2010) 2177-2182.
A. S. Gupta, Hydromagnetic flow past a porous flat plate with Hall effects, Acta Mechanica, 22 (1975) 281-287.
R. N. Jana, A. S. Gupta, N. Datta, Hall effects on the hydromagnetic flow past an infinite porous flat plate, J. Phys. Soc. Japan, 43 (1977) 1767-1772.
M. A. Hossain, R. I. M. A. Rashid, Hall effects on hydromagnetic free convection flow along a porous flat plate with mass transfer, J. Phys. Soc. Japan, 56 (1987) 97-104.
M. A. Rana, A. M. Siddiqui, N. Ahmed, Hall effect on Hartmann flow and heat transfer of a Burgers' fluid, Phys. Lett. A, 372 (2008) 562-568.
R. C. Chaudhary, A. K. Jha, Heat and mass transfer in elastic-viscous fluid past an impulsively started infinite vertical plate with Hall effect, Latin American Applied Research, 38 (2008) 17-26.
T. Hayat, M. Qasim, Z. Abbas, Homotopy solution for the unsteady threedimensional MHD flow and mass transfer in a porous space, Commun. Nonlinear Sci. Numer. Simul, 15 (2010) 2375-2387.
L. L. Lee, Boundary layer over a thin needle, Phys of Fluids, 10 (1967) 822-828.
T. Fang, J. Zhang, Y. Zhong, Boundary layer flow over a stretching sheet with variable thickness, Appl. Math. Comput, 218 (2012) 7241-7252.
T. C. Chiam, Heat transfer with variable thermal conductivity in a stagnation point flow towards a stretching sheet, Int. Comm. Heat Mass Transfer, 23 (1996) 239-248.
I. A. Hassanien, The effect of variable viscosity on flow and heat transfer on a continuous stretching surface, ZAMM, 77 (1997) 876-880.
M. Subhas Abel, S. K. Khan, K. V. Prasad, Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable fluid viscosity, Int. J. Non- Linear Mech, 37 (2002) 81-88.
K. V. Prasad, K. Vajravelu and P. S. Datti, The effects of variable fluid properties on the hydromagnetic flow and heat transfer over a non-linearly stretching sheet, Int. J. Ther. Sci, 49 (2010) 603-610.
F. C. Lai, F. A. Kulacki, The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium, Int. J. Heat Mass Trans, 33 (1990) 1028-1031.
T. Cebeci, P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer-Verlag, New York (1984).
H. B. Keller, Numerical Methods for Two-point Boundary Value Problems, Dover Publ, New York, (1992).
K. Vajravelu, K. V. Prasad, Keller-box method and its application, HEP and Walter De Gruyter GmbH, Berlin/Boston, (2014).
L. J. Grubka, K. M. Bobba, Heat transfer characteristics of a continuous stretching surface with variable temperature, J. Heat Mass Transfer, 107 (1985) 248-250.
C. H. Chen, Laminar mixed convection adjacent to vertical continuously stretching sheets, Heat Mass Transfer, 33 (1998) 471-476.
M. E. Ali, Heat transfer characteristics of a continuous stretching surface, Heat Mass Transfer, 29 (1994) 227-234.