Studying the Effect of Magnetic Strength and Electrical Conductivity on the Velocity Profile of an MHD Flow in a Rectangular Duct

Omar Yousef Al-Thehabey

doi:10.7176/jetp/10-4-03

Abstract

This document presents the results of an investigation of the impact of variations of electrical conductivity and magnetic field strength on the velocity profile inside a rectangular duct, assuming equilibrium flow. It also presents the physics and the complete theory associated with the MHD, then derive the equations to be utilized for computational analysis of the magnetic field and the velocity profiles.The computational work in this document is based on the assumption that the working fluid is air and it is fully developed in the duct. The finite difference method is used to perform the analysis for 2 distinct cases: the first case is when the magnetic field strength changes, while holding the electrical conductivity constant. The second case is when the electrical conductivity is changing while holding the magnetic field strength constant.It has been found that increasing the magnetic field strength has resulted in decreasing the axial velocity profile, which demonstrated that the magnetic field was pulling the flow to its direction, reducing the flow momentum in the axial direction. It has also been found that the electrical conductivity reduced the velocity profile in the axial direction when that conductivity was increasing, demonstrating that the electric field was also pulling the flow in its direction, reducing the flow momentum in the axial direction. Keywords: MHD, Magnetohydrodynamics, Flow in Rectangular Duct, Magnetic Field, Electrical Conductivity, MHD Flow, MHD Flow Velocity Profile DOI: 10.7176/JETP/10-4-03 Publication date: August 31 st 2020

Highlights

MHD stands for magneto-hydrodynamic, called magneto-gas-dynamics, magneto-aerodynamics or magnetoplasma aerodynamics
It is used to propel vehicles in the air, water, or space, using electric and magnetic fields only, by accelerating an electrically conductive propellant, liquid or gas, the fluid is directed to the rear, which results in accelerating the vehicle forward, as a reaction
Discussion of Results The application was run for two cases: variable magnetic field strength () and variable electrical conductivity

Summary

Introduction

MHD stands for magneto-hydrodynamic, called magneto-gas-dynamics, magneto-aerodynamics or magnetoplasma aerodynamics. Chutia and Deka (2014), studied a steady MHD flow for an incompressible, viscous, electrically conducting fluid in a rectangular duct Their computations have been carried out for several values of the Hartmaan number (H), magnetic Reynolds number (Rm), and the aspect ratio A = b/a, for velocity and induced magnetic field. Shah, Hussain, and Sagheer (2016), presented a numerical analysis of MHD flow of Maxwell fluid with thermal radiation and Joule heating by considering the recently developed Cattaneo-Christov heat flux model which explains the time relaxation characteristics for the heat flux Their results showed stronger magnetic parameter M increased temperature and decreased velocity: temperature profile increases while increasing the radiation parameter and the similar effect of Eckert number is observed on the temperature field, and velocity in the horizontal direction decreases while temperature increases.

Numerical Methods Application

Results

Conclusion