Laplace Transform Solution Of Hydromagnetic Steady Flow Of Viscous Incompressible Fluid Between Two Parallel Infinite Plates

Abstract

This project aims at getting the solution of hydro magnetic steady flow of viscous incompressible fluid between two parallel infinite plates using the Laplace transform method. The upper plate is moving with constant velocity and the lower plate is held stationary under the influence of inclined magnetic field. We shall convert the boundary conditions of the fluid flow into initial conditions. The initial conditions are determined and the problem is solved by use of Laplace Transform. In chapter one, we shall major in the definition of Hydromagnetic steady flow together with where it can be applied. In chapter two we shall introduce the Laplace Integrals and Laplace transforms as well as some of their properties. Finally in chapter three, we shall develop the equations governing the hydromagnetic flow and in this chapter we shall obtain these basic equations. We shall also get the solution of the hydromagnetic steady flow of viscous incompressible fluid between two parallel infinite

plates using the Laplace transform and discus the results which are presented in form of a graph for selected Hartmann numbers.