A similarity transformation is given, which reduces the partial, nonlinear differential equations describing a compressible, polytropic plasma flow across an azimuthal magnetic field in a duct with plane inclined walls to an ordinary nonlinear differential equation of second order. The latter is solved rigorously in terms of a hyperelliptic integral. The form of the plasma flow fields in pure outflows (diffuser) is discussed analytically in dependence of the Reynolds(R)and Hartmann(H)numbers and the polytropic coefficient(&ggr;)for given duct angles&thgr;0. The realizable Mach numbers are shown to be eigenvalues of the nonlinear boundary‐value problem,M = M(R, H, &ggr;, &thgr;0).