Peristaltic motion of a Carreau fluid in an asymmetric channel

Mathematical modeling and analytical solution are presented for the flow of an incompressible Carreau fluid in an asymmetric channel with sinusoidal wall variations. The peristaltic wave train on the channel walls has different amplitudes and phase. A long wavelength approximation is adopted to solve the flow problem. The explicit forms for the stream function, axial pressure gradient and pressure drop over a wavelength are obtained using a perturbation technique for a small Weissenberg number. The pumping characteristics, axial pressure gradient and trapping phenomena has been mainly discussed. Comparison is made between the results for the Newtonian and Carreau fluids.