Magnetohydrodynamic entry flow for a plane channel in an axial magnetic field

Abstract

An integral solution is described for flow of an electrically conducting fluid in a plane channel in a magnetic field which is aligned with the direction of the mean flow. It is shown that the presence of the magnetic field retards the development of the velocity profile by producing Lorentz forces which oppose the movement of fluid from the viscous wall region to the core. Solutions are presented for the entry length as a function of the magnetic interaction parameter. Solutions are also given for the dependence of the frictional component of the pressure drop on the magnetic field strength. The transverse pressure gradient produced by Lorentz forces is discussed for a typical case.