A quasi-onedimensional time dependent model capable of treating MHD compressible flows in linear channels has been adopted. shear stresses and heat losses are taken into account by means fo integral expressions. Electrial boundary conditions related to channel connections (segmented Faraday channels or diagonal conducting sidewall channels) are considered. Three finite difference numerical schemeshave been implemented for the solution of the model equations. MHD supersonic, transonic and subsonic flows can be treated. Variations of the elecric field and current density distribution during transients are calculated in order to evaluate high electrical field locations and current concentrations resulting in occurence of inter-electrode breakdown, local enhance of wall temperature, thermal stresses, corosion and erosion.