Second-order Solutions for Steady Magnetohydrodynamic Channel Flow with Anisotropic Conductivity

Abstract

Further investigation of steady magnetohydrodynamic flow through a straight channel of arbitrary cross section with nonconducting walls is considered, in the presence of anisotropic conductivity due to the Hall effect, where no restriction is made on the Reynolds number or magnetic Reynolds number. An approximate solution is provided by a perturbation expansion in terms of the Hall parameter, assumed small. Corrections are made to the first-order solutions established by Panton and Hosking (1971) and the solutions are then extended to the second order for a square channel. It is found that both the Reynolds number and magnetic Reynolds number terms have a significant influence on the mass transport, the former far outweighing the contribution to the flow established by Tani (1962) for the values of the flow parameters assumed.