Relaxation and Retardation Effects on Free Convective Visco-Elastic Fluid Flow Past an Oscillating Plate

An unsteady two dimensional free convective flow of viscoelastic fluid past a flat surface with heat and mass transfer has been investigated.The surface is oscillating with about a mean velocity U 0 .Oscillating temperature and concentration about T ∞ and C ∞ respectively have been considered at the surface.The visco-elastic fluid flow is characterized by Oldroyd-B fluid model having two rheological parameters: relaxation time and retardation time.In the governing fluid flow, a magnetic field of uniform strength B 0 has been applied along the transverse direction to the surface.Governing equations of motion are solved analytically by using perturbation scheme.Analytical expressions for velocity profiles, shearing stress at the surface, temperature and concentration fields are obtained.Results are discussed graphically for various combinations of flow parameters involved in the solution.A special emphasis is given on the effects of relaxation and retardation times.