Unsteady Hydromagnetic Flow of Viscoelastic Fluid down an Open Inclined Channel

Abstract: In this paper, we study the unsteady hydromagnetic flow of a Walter's fluid (Model B') down an open inclined channel of width 2a and depth d under gravity, the walls of the channel being normal to the surface of the bottom under the influence of a uniform transverse magnetic field. A uniform tangential stress is applied at the free surface in the direction of flow. We have evaluated the velocity distribution by using Laplace transform and finite Fourier Sine transform technique. The velocity distribution has been obtained taking different form of time dependent pressure gradient g(t), viz., i) constant ii) exponential decreasing function of time and iii) Cosine function of time. The effects of magnetic parameter M, Reynolds number R and the viscoelastic parameter K are discussed on the velocity distribution in three different cases.