Flow reversals of a non-Newtonian fluid in an expanding channel

Abstract

The flow of an incompressible power-law fluid through convergent–divergent channels is considered where the choice of the viscosity is such that the zero-shear rate viscosity is neither zero nor infinity for any finite value of the power-law exponent. Rather than employing the classical similarity transformation employed by Jeffery and Hamel implying purely radial solutions for the velocity field, we instead consider flow in both the radial and angular directions, under three sets of boundary conditions. This work is in contrast to the earlier study by Mansutti and Rajagopal (1991). wherein the viscosity could be zero or infinity for certain values of the power-law exponent. While seeking solutions to nonlinear differential equations, when seeking similarity solutions, one ought to be cognizant that the equations might have solutions in addition to the similarity solution that is being sought. We observe that the tangential velocity does indeed play a role in the flow regime of the fluid, with flow reversal also present for certain values of α. In the case of traction boundary conditions, we also observe a change in the flow characteristics.