AM  Vol.6 No.1 , January 2015
Unsteady Incompressible Flow of a Generalized Oldroyd-B Fluid between Two Oscillating Infinite Parallel Plates in Presence of a Transverse Magnetic Field
Author(s) Dhiman Bose, Uma Basu
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
[1]   Bandeli, R. and Rajagopal, K.R. (1995) Start-Up Flows of Second Grade Fluids in Domains with One Finite Dimension. International Journal of Non-Linear Mechanics, 30, 817-839.
http://dx.doi.org/10.1016/0020-7462(95)00035-6

[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.
http://dx.doi.org/10.1016/j.jnnfm.2008.06.005

[3]   Hayat, T. and Sajid, M. (2007) Homotopy Analysis of MHD Boundary Layer Flow of an Upper-Convected Maxwell Fluid. International Journal of Engineering Science, 45, 393-401.
http://dx.doi.org/10.1016/j.ijengsci.2007.04.009

[4]   Jamil, M. and Khan, N.A. (2011) Slip Effects on Fractional Viscoelastic Fluids. International Journal of Differential Equations, 2011, Article ID 193813.
http://dx.doi.org/10.1155/2011/193813

[5]   Shen, F., Tan, W., Zhao, Y. and Masuoka, T. (2006) The Rayleigh-Stokes Problem for a Heated Generalised Second Grade Fluid with Fractional Derivative Model. Nonlinear Analysis: Real World Application, 7, 1072-1080.
http://dx.doi.org/10.1016/j.nonrwa.2005.09.007

[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.
http://dx.doi.org/10.1016/j.amc.2007.12.045

[7]   Wenchang, T., Wenxiao, P. and Mingyu, X. (2003) A Note on Unsteady Flows of a Viscoelastic Fluid with the Fractional Maxwell Model between Two Parallel Plates. International Journal of Non-Linear Mechanics, 38, 645-650.
http://dx.doi.org/10.1016/S0020-7462(01)00121-4

[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

 
 
Top