This article deals with the steady flows of incompressible,conducting,viscous fluids through ducts under an imposed azimuthal magnetic field.The equations determining the velocity profile and the induced magnetic field are derived. By means of these equations,we can find a new sort of exact solutions of the magnetohydrodynamics. We discuss, in detail, the flows in a circular segment cross-section duct with insulating walls,and derive the analytical expressions for the velocity profile and the induced magnetic field.The volume flow through the duct, which depends on the Hartmann number, is given. The schematic analyses of the results are also included.