Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes - Rhameez S. Herbst; Charis Harley; Kumbakonam R. Rajagopal (Fluids)
The flow of an incompressible power-law fluid through a convergent channel is considered, where the viscosity is chosen to be pressure dependent. Instead of utilizing the classical similarity transformation traditionally employed when considering Jeffery-Hamel flow, allowing for purely radial solutions for the velocity field, we allow for flow in both the radial and angular directions. We develop a numerical scheme that conserves the pressure-dependent viscosity at each cell in the computational grid. We recover the classical solution to the problem, and through our numerical solutions, we observe not only that the tangential velocities are not negligible, but also that flow reversal occurs, as illustrated by solutions with varying flow regimes. Decreasing the angle of the channel causes the magnitude of the velocity to decrease, while shorter channels lead to an increase in the magnitude of the radial and tangential velocities. In the case of the latter, this could indicate that in shorter channels, the tangential velocity has a larger impact on the occurrence of flow reversal. For more varied flow regimes, the magnitude of the radial and tangential velocities increases.