Peristaltic Flow of a Third-Grade Fluid in a Planar Channel

The problem of peristaltic transport of a non-Newtonian fluid represented by the constituve equation for a third grad fluid was analysed for the case of planar channel with harmonically undulating extensible wall, under zero Reynolds number and long wavelength approximation. New exact analytical solution of the non-linear equation resulting from the momentum equation was given when γ2 + γ3(which are the dimensionless material constants)>0 and under some conditions when γ2 + γ3<0. Also, the exact range of validity of the perturbation analysis was obtained using the Girolamo Cardano formulas and binomial theorem for both γ2 +γ3>0 and γ2+ γ3<0. Finally, we have shown that pumping rate of a third-grade fluid can be greater or less than for a Newtonian fluid having a shear viscosity same as the lower-limiting viscosity of non-Newtonian material depending on the value of the material constants, amplitude ratio and flow rate.n/