In the present work a model for the two-dimensional time dependent description of the magneto-fluid dynamics in the channel of an MHD (magnetohydrodynamic) generator is described. The numerical code obtained from it can be used for the analysis of the MHD channel operation, during the design procedure and for numerical experiments. The model is based on a time dependent two-dimensional description of the fluid dynamics iteratively coupled to a steady state two-dimensional description of the electrodynamics. In the plasma flow considered the magnetic field diffusion dominates over the magnetic field convection. A semi-implicit finite difference pressure scheme has been utilized for the solution of the fluid dynamic problem. The turbulence behavior is taken into account. The electrodynamics is described by a second order elliptic partial differential equation, obtained from the Maxwell equations and generalized Ohm’s law, and solved by means of an exponential fitting finite difference method. The model has been validated by the comparison of its results with experimental data. Two regime conditions and a transient caused by the interruption of the seeding injection, have been analyzed.