AJCM  Vol.4 No.3 , June 2014
Effects of Hall Current on MHD Boundary Layer Second-Order Viscoelastic Fluid Flow Induced by a Continuous Surface with Heat Transfer
ABSTRACT

Effects of Hall current on heat transfer and magnetohydrodynamic (MHD) boundary layer flow induced by a continuous surface in a parallel free stream of a second-order viscoelastic fluid are studied for uniform suction/injection by taking viscous dissipation into account. Complex nonsimilar solutions to the stream function and temperature are developed by means of an elegant technique, known as homotopy analysis method (HAM). Convergence of the solutions is ensured with the help of -curves. Graphical and tabular results for the effects of Hall current reveal that it has a significant influence on: complex velocity, complex temperature, magnitude of the shear stress at the surface, magnitude of the rate of heat transfer at the surface and on boundary layer thickness.


Cite this paper
Zaman, H. , Shah, M. , Khan, F. and Javed, Q. (2014) Effects of Hall Current on MHD Boundary Layer Second-Order Viscoelastic Fluid Flow Induced by a Continuous Surface with Heat Transfer. American Journal of Computational Mathematics, 4, 143-152. doi: 10.4236/ajcm.2014.43013.
References
[1]   Cramer, K. and Pai, S. (1973) Magnetofluid Dynamics for Engineers and Applied Physicists. McGraw-Hill, New York.

[2]   Zaman, H. (2013) Hall Effects on the Unsteady Incompressible MHD Fluid Flow with Slip Conditions and Porous Walls. Applied Mathematics and Physics, 1, 31-38.

[3]   Ayub, M., Zaman, H. and Ahmad, M. (2010) Series Solution of Hydromagnetic Flow and Heat Transfer with Hall Effect in a Second Grade Fluid over a Stretching Sheet. Central European Journal of Physics, 8, 135-149.
http://dx.doi.org/10.2478/s11534-009-0110-0

[4]   Ahmad, M., Zaman, H. and Rehman, N. (2010) Effects of Hall Current on Unsteady MHD Flows of a Second Grade Fluid. Central European Journal of Physics, 8, 422-431. http://dx.doi.org/10.2478/s11534-009-0083-z

[5]   Hayat, T., Zaman, H. and Ayub, M., (2010) Analytic Solution of Hydromagnetic Flow with Hall Effect over a Surface Stretching with a Power Law Velocity. Numerical Methods for Partial Differential Equations, 27, 937-959.
http://dx.doi.org/10.1002/num.20562

[6]   Hayat, T., Naz., R. and Asghar, S. (2004) Hall Effects on Unsteady Duct Flow of a Non-Newtonian Fluid in a Porous Medium. Applied Mathematics and Computation, 157, 103-114. http://dx.doi.org/10.1016/j.amc.2003.08.069

[7]   Asghar, S., Mohyuddin R.M. and Hayat, T. (2005) Effects of Hall Current and Heat Transfer on Flow Due to a Pull of Ecentric Rotating Disks. International Journal of Heat and Mass Transfer, 48, 599-607.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2004.08.023

[8]   Khan, M., Asghar S. and Hayat, T. (2009) Hall Effect on the Pipe Flow of a Burgers’ Fluid: An Exact Solution. Nonlinear Analysis: Real World Applications, 10, 974-979. http://dx.doi.org/10.1016/j.nonrwa.2007.11.016

[9]   Abo-Eldahab, E.M. and Elbarbary, M.E. (2001) Hall Current Effect on Magnetohydrodynamic Free Convection Flow past a Semi-Infinite Vertical Plate with Mass Transfer. International Journal of Engineering Science, 39, 1641-1652.
http://dx.doi.org/10.1016/S0020-7225(01)00020-9

[10]   Abo-Eldahab, E.M. and Abd El Aziz, M. (2004) Hall Current and Ohmic Heating Effects on Mixed Convection Boundary Layer Flow of a Micropolar Fluid from a Rotating Cone with Power Law Variation in Surface Temperature. International Communications in Heat and Mass Transfer, 31, 751-762.
http://dx.doi.org/10.1016/S0735-1933(04)00062-4

[11]   Debnath, L., Ray, S.C. and Chatterjee, A.K. (1979) Effects of Hall Current on Unsteady Hydromagnetic Flow past a Porous Plate in a Rotating Fluid System. ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, 59, 469-471.
http://dx.doi.org/10.1002/zamm.19790590910

[12]   Sakiadis, B.C. (1961) Boundary Layer Behavior on Continuous Solid Surfaces. AIChE Journal, 7, 26-28.
http://dx.doi.org/10.1002/aic.690070108

[13]   Liao, S.J. (2003) Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall, CRC Press, Florida. http://dx.doi.org/10.1201/9780203491164

[14]   Liao, S.J. (1992) The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problem. Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai.

[15]   Liao, S.J. (2012) Homotopy Analysis Method in Nonlinear Differential Equations. Springer-Verlag Berlin Heidelberg.
http://dx.doi.org/10.1007/978-3-642-25132-0

[16]   Liao, S.J. (2013) Advances in the Homotopy Analysis Method. World Scientific Publishing Company, Singapore.

[17]   Liao, S.J. (2009) Notes on the Homotopy Analysis Method: Some Definitions and Theorems. Communications in Nonlinear Science and Numerical Simulation, 14, 983-997.

[18]   Ayub, M., Zaman, H., Sajid, M. and Hayat, T. (2008) Analytical Solution of Stagnation-Point Flow of a Viscoelastic Fluid towards a Stretching Surface. Communications in Nonlinear Science and Numerical Simulation, 13, 1822-1835.
http://dx.doi.org/10.1016/j.cnsns.2007.04.021

[19]   Zaman, H. and Ayub, M. (2010) Series Solution of Unsteady Free Convection Flow with Mass Transfer along an Accelerated Vertical Porous Plate with Suction. Central European Journal of Physics, 8, 931-939.
http://dx.doi.org/10.2478/s11534-010-0007-y

[20]   Hady, F.M. and Gorla, R.S.R. (1998) Heat Transfer from a Continuous Surface in a Parallel Free Stream of Viscoelastic Fluid. Acta Mechanica, 128, 201-208. http://dx.doi.org/10.1007/BF01251890

[21]   Zaman, H., Hayat, T., Ayub, M., Gorla, R.S.R. (2011) Series Solution for Heat Transfer from a Continuous Surface in a Parallel Free Stream of Viscoelastic Fluid. Numerical Methods for Partial Differential Equations, 27, 1511-1524.
http://dx.doi.org/10.1002/num.20593

 
 
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