Taming Heterogeneity and Complexity of Embedded Control

Analytical Solution of the Problem on a Magnetohydrodynamic Flow in the Initial Part of a Plane Channel in a Transverse Magnetic Field in Oseen Approximation

 

Elena Ligere — Maximilian Antimirov

Department of Engineering MathematicsRiga Technical UniversityRiga LV-1658, Kalku 1, [e-mail]

ABSTRACT. The problem of a flow of conducting fluid in the initial part of a plane channel in transverse magnetic field is solved analytically using Oseen and inductionless approximations. A typical assumption for the solution of similar problems by means of the Oseen approximation is that the velocity and the pressure of the fluid are given at the entrance of the channel. These boundary conditions overdetermine the problem. In the present paper the analytical solution of the problem is obtained with the condition that only the velocity of fluid flowing into the channel through the channel’s lateral side is given. The problem was solved analytically by means of the Fourier transform.Numerical calculations give the M-shaped velocity profiles in the entrance region of the channel at large Hartman numbers. Dependence of the length of the initial part L_init on the Hartman number is analyzed.

KEYWORDS: magnetic fields, boundary conditions, flow control, Fourier transform

1. Introduction

The study of magnetohydrodynamic (MHD) problems on a flow of conducting fluid in a magnetic field has theoretical and practical importance. Applications include control over motion of liquid metal ...