SOLUTION OF THE NON-LINEAR THIRD ORDER PARTIAL DIFFERENTIAL EQUATION OF A STEADY HYDROMAGNETIC FLOW THROUGH A CHANNEL WITH PARALLEL STATIONARY POROUS PLATES

Abstract

This thesis deals with the solution of the non-linear third order partial differential equation of a steady hydromagnetic laminar flow of a conducting viscous incompressible fluid through a channel with two parallel porous plates. The two plates are stationary and there is magnetic field moving at right angle to the electric field. Due to the porous nature of the plates, the fluid is withdrawn through both walls of the channel at the same rate. The specific equations governing the flow are discussed, transformed using dimensionless techniques into a third order partial differential equation, simplified using Taylor’s series expansion and solved by the method of regular perturbation. Expressions for the velocity components and temperature profiles are discussed and represented in form of tables and graphs plotted by use of MATLAB programming software. The velocity profiles parallel (axial) and normal (radial) to the plates as well as the temperature distribution on the fluid are investigated. The results indicate that the radial velocity decreases with increase in Reynolds number while the axial velocity is zero at the walls and increases to the maximum at the centre line depicting the normal free flow velocity of the stream when there is no magnetic field in the fluid flow. The velocity of the fluid decreases with increase in Hartmann number. The temperature of the fluid decreases when Prandtl number increases and Eckert number decreases. This means that when viscous forces increases in the flow the thermal conductivity becomes negligible and thus thermal energy surpasses the kinetic energy of the fluid. The study has its application in hydromagnetic devices where the interaction between velocities profiles, magnetic and electric fields are utilized in the design of various machines, for instance removal of pollutants from plant discharge stream by absorption.