On nonlinear oscillations in a MHD-generator

The stability of a flow of incompressible electrically conducting fluid in a channel is considered for the case in which there is an entropy gradient due to Joule dissipation. The device is a Faraday generator, the Hall parameter is zero, and the electrical conductivity of the medium is an exponential function of the temperature. The solution is found by means of a series expansion with allowance for the A4 terms, where A4 is the square of the oscillation amplitude of the dimensionless velocity. Special cases are considered and the effective electrical conductivity of the medium and the effective load factor are calculated