In this paper, slip phenomena in a capillary tube, a narrow slit andan annulus are modeled using both the power law and the Oldroyd con-stitutive equations. On the basis of this analysis, new expressions for slip velocity, flowenhancement and frictional tesistance were obtained. It is predicted thatwhen the slip does occur, the velocity profile, volumetric flow rate andpressure drop are very different from those under nonslip conditions. Asthe slip velocity increases, the velocity profile becomes flatter and is ex-pected to significantly influence heat and mass transfer rates. These cal-culations provide a basis for subsequent calculation of these heat and masstransport rates.