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In this paper we studied results of calculation of the direct-flow and swirled, laminar and turbulent flows of liquids and gases in pipes and the channels including sections from a constant and a variable on length by the area of cross-section section. The hydrodynamics and heat transfer of the swirled flows on a method local rotation in the field of a near input in an experimental section and in the conditions of rotation of a wall round the longitudinal axis are investigated in details. At modeling of turbulent transfer of momentum and heat the closing schemes of the second order with the differential equations for the total tensor of Reynolds shear stresses and specific fluxes of heat with the original low-Reynolds basic base from the (k-L-) and (k-τ)-. equations are used. Mechanisms of generation, evolution of recalculated flows, attenuation and development of swirled stream in the direct-flow are analyzed. The correction of algorithm and advantage of model in a prediction of distributions of local and integrated parameters of a complex vortical flow are illustrated by comparisons with experimental data.