Analytical solution of a system of magnetohydrodynamic equations in a quasi-one-dimensional approximation for the monotonic variation of the flow velocity along a channel

An analytical solution is obtained for the system of magnetohydrodynamic (MHD) equations in a quasi-one-dimensional approximation for flow regimes with a monotonic variation of the velocity along a MHD channel. The problem of optimal choice of the parameters of an MHD generator for the given ratio of the areas of the outlet and inlet MHD channel cross sections is considered using the resultant analytic solution.