The flow in a helical duct is characterized by increased fluid mixing, accomplished by the inducement of a secondary flow in the plane normal to the helix centerline. Two independent phenomena interact to produce this secondary flow. First, the curvature of the duct (i.e. its torroidal nature) causes Dean's type recirculation. Second, the torsion due to the non-planarity of the helix causes additional mixing. The secondary flow alters the axial velocity profile and increases the pressure drop compared to a straight duct. Imposing a rectangular cross section on such a duct complicates the analysis compared to a circular or elliptical cross section. A series solution based on curvature is introduced. The components of the series are determined using appropriate eigenfunction expansions. However, the resulting low order solution is limited to low Dean number flows. The analytical solution is useful for flows where curvature (torroidal ducts) or curvature and torsion (helical ducts) are important.