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

Abstract

The problem of peristaltic transport of a non-Newtonian fluid represented by the constitutive equation for a third grade fluid was analyzed 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 γ<inf>2</inf>+γ<inf>3</inf> (which are the dimensionless material constants) >0 and under some conditions when γ<inf>2</inf>+γ<inf>3</inf><0. Also, the exact range of validity of the perturbation analysis was obtained using the Girolamo Cardano formulas and binomial theorem for both γ<inf>2</inf>+γ<inf>3</inf>>0 and γ<inf>2</inf>+γ<inf>3</inf><0. Finally, we have shown that pumping rate of a third-grade fluid can be greater or less than that 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.