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.
Highlights
The magneto hydrodynamic flow problem between two parallel plates has shown immense attention during the last several decades
In this paper we have presented the flow of a generalized Oldroyd-B fluid between two oscillating infinite parallel plates
The fluid velocity increases and there are points of local minimum and local maximum in the velocity curves which are oscillatory in nature
Summary
The magneto hydrodynamic flow problem between two parallel plates has shown immense attention during the last several decades. (2015) Unsteady Incompressible Flow of a Generalized Oldroyd-B Fluid between Two Oscillating Infinite Parallel Plates in Presence of a Transverse Magnetic Field. Shen et al [5] studied the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative model. Vieru et al [6] discussed the flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate. Wenchang et al [7] investigated unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates. Vieru et al [8] studied the unsteady flow of a generalized Oldroyd-B fluid due to an infinite plate subject to a time-dependent shear stress. In the present paper we consider the flow of a generalized Oldroyd-B fluid between two oscillating infinite parallel plates in presence of transverse magnetic field. The exact solution for the velocity field is obtained by using the method of integral transformations and the dependence of the said field on the material as well as fractional calculus parameters is illustrated graphically
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