Magneto-Fluid-Mechanic Channel Flow. II. Theory

Abstract

A semi-empirical theoretical analysis is presented describing the fully established turbulent channel flow of an electrically conducting fluid in the presence of a transverse and uniform magnetic field. The channel is assumed to be electrically insulated and of such geometry that two-dimensional flow prevails. The magnetic Reynolds number is assumed to be small so that the distortion of the externally imposed magnetic field is negligible. The paper establishes that a straightforward generalization of Prandtl's mixing length concept providing for the damping of the turbulent fluctuation is sufficient in predicting skin friction coefficients and velocity profiles over the whole range of Reynolds and Hartmann numbers for which experimental data are available.