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Unsteady Incompressible Flow of a Generalized Oldroyd-B Fluid between Two Oscillating Infinite Parallel Plates in Presence of a Transverse Magnetic Field

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ABSTRACT
In this paper an attempt has been made to study the unsteady incompressible flow of a generalized Oldroyd-B fluid between two oscillating parallel plates in presence of a transverse magnetic field. An exact solution for the velocity field has been obtained by means of Laplace and finite Fourier sine transformations in series form in terms of Mittage-Leffler function. The dependence of the velocity field on fractional as well as material parameters has been illustrated graphically. The velocity fields for the classical Newtonian, generalized Maxwell, generalized second grade and ordinary Oldroyd-B fluids are recovered as limiting cases of the flow considered for the generalized Oldroyd-B fluid.
 
Cite this paper
Bose, D. and Basu, U. (2015) Unsteady Incompressible Flow of a Generalized Oldroyd-B Fluid between Two Oscillating Infinite Parallel Plates in Presence of a Transverse Magnetic Field. Applied Mathematics, 6, 106-115. doi: 10.4236/am.2015.61011.
 
References
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[2]Fetecau, C., Fetecau, C., Karman, M. and Vieru, D. (2009) Exact Solutions for the Flow of a Generalized Oldroyd-B Fluid Induced by a Constantly Accelerating Plate between Two Side Walls Perpendicular to the Plate. Journal of Non-Newtonian Fluid Mechanics, 156, 189-201.
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[6]Vieru, D., Fetecau, C. and Fetecau, C. (2008) Flow of a Generalized Oldroyd-B Fluid Due to a Constantly Accelerating Plate. Applied Mathematics and Computation, 201, 834-842.
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[8]Vieru, D., Fetecau, C. and Fetecau, C. (2010) Unsteady Flow of a Generalized Oldroyd-B Fluid Due to an Infinite Plate Subject to a Time-Dependent Shear Stress. Canadian Journal of Physics, 88, 675-687.
http://dx.doi.org/10.1139/P10-055                                                                                           eww150113lx
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