UNSTEADY-FLOW OF A NON-NEWTONIAN FLUID DOWN AN OPEN INCLINED CHANNEL

The unsteady flow of a Walters fluid (Model B') down an open inclined channel under gravity has been investigated analytically. The exact solution of velocity distribution has been obtained by using Laplace transform and Finite Fourier Sine Transform techniques. A uniform tangential stress is applied at the free surface in the direction of flow. The velocity distribution has been obtained taking different forms of time dependent pressure gradient g(t) viz. (i) constant, (ii) exponentially decreasing function of time, and (iii) Cosine function of time. It has been observed that the unsteady flow will never occur in case of a Newtonian fluid when the pressure gradient is taken to be constant, but the opposite behaviour is observed in the non-Newtonian fluid case. The fluid flow ultimately becomes steady under the exponential decreasing form of the pressure gradient in both non-Newtonian and Newtonian fluids.