[en] 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