AbstractImportant flow enhancement effects take place when the motion of a non‐Newtonian fluid is driven either by pressure gradients pulsating around a non‐zero mean or by longitudinal and transversal boundary waves superposed on Poiseuille flow. Flow enhancement in the latter case is an order of magnitude larger than in the former. A regular perturbation in terms of the amplitude of the oscillation is used and closed form formulas given for mass transport rates at the lowest significant order. In particular it is shown that a mean flow may be generated even when the pressure gradients oscillate around a zero mean or the boundary waves are superposed on a fluid at rest if the frequencies of two superposed waves are in certain rat