Unsteady Hydromagnetic Flow of Viscoelastic Fluid down an Open Inclined Channel

TL;DR

This study investigates the unsteady flow of a viscoelastic fluid under magnetic influence in an inclined open channel, analyzing velocity profiles for various time-dependent pressure gradients using mathematical transforms.

Contribution

It introduces a detailed mathematical analysis of viscoelastic fluid flow with magnetic effects in an inclined channel, considering different pressure gradient functions.

Findings

Velocity distribution varies with magnetic parameter M, Reynolds number R, and viscoelastic parameter K.

Different pressure gradients significantly influence flow behavior.

Mathematical solutions obtained for various time-dependent pressure functions.

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.