TITLE:
Unsteady Incompressible Flow of a Generalized Oldroyd-B Fluid between Two Oscillating Infinite Parallel Plates in Presence of a Transverse Magnetic Field
AUTHORS:
Dhiman Bose, Uma Basu
KEYWORDS:
Oldroyd-B Fluid, Exact Solution, Mittage-Lefller Function, Fractional Derivative, Transverse Magnetic Field
JOURNAL NAME:
Applied Mathematics,
Vol.6 No.1,
January
12,
2015
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.