Non‐newtonian flow through open channels

Abstract

A general method is proposed for prediction of the flow rate and maximum velocity in the isothermal, steady, uniform, laminar flow of any incompressible, time‐independent non‐Newtonian fluid in straight open channels of arbitrary cross section. The method requires only a knowledge of two geometric coefficients and a function of shear stress, used to characterize the behavior of the fluid model. The slip effect at the solid boundary has been taken into consideration. Numerical values of the geometric parameters have been determined for flow through an inclined plane of infinite width, semi‐circular, semi‐elliptical, rectangular, and 90° and 60° symmetric triangular open channels. Applications have been made to various non‐Newtonian fluid models such as the power‐law, Bingham, Ellis, Meter and the Reiner‐Rivlin general model. Numerical examples are presented. A generalization of the Fanning friction factor — Reynolds number is also presented. The problem of determining the point of transition from laminar to turbulent flow in the general case is examined, as is the problem of prediction of the friction factor in turbulent flow.

Incompressible Non-Newtonian Fluid Flows

“…Therefore, this approach necessitates the knowledge of only one parameter (β) as opposed to the two geometric parameters, namely, a and b in the method of Kozicki et al . (1966) and Kozicki and Tiu (1967), albeit a similar suggestion was also made by Miller (1972) and Liu (1983). Finally, for the limiting case of a circular pipe, evidently β=3 thereby leading to a=(1/4) and b=(3/4) and the two definitions of the Reynolds number coincide, as expected.…”

“…Perhaps the most systematic and successful friction factor analysis is that provided by Kozicki et al . (1966Kozicki et al . ( , 1967 .…”

Friction factor-Reynolds number relationship for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes

“…Here, the f¼K/Re line based on the Kozicki and Tiu (1967) Re definition for a power law or a Bingham plastic fluid, Eq. (5) or Eq.…”

“…The database for non-Newtonian flow in rectangular channels was extended by Haldenwang et al (2004) to include their limited study on non-Newtonian flow in semi-circular and trapezoidal channels. They looked at the efficiency of the definitions of the Reynolds number due to Haldenwang et al (2002) and those of Kozicki and Tiu (1967) in correlating the laminar flow data on the f vs Re plot for these channel shapes. For the range of shapes and fluids studied, they concluded that the f¼K/Re line using the simpler Reynolds number proposed by Haldenwang et al (2002) adequately predicts their experimental data in the laminar flow regime, provided the correct flow curve model is used to take account of the rheology of the test fluid used.…”

Flow of molten poly(ethylene terephthalate) through packed beds of glass beads

“…Several papers have been published recently, however, concerning experimental investigations of the flow of polymeric systems through porous media (1, 5, 6, 9, 10, 13, I?, 16,18,20,21,23,24). Of the experimental work noted, only that of Griskey and Gregory (13) and Siskovic, Gregory, and Griskey (21 ) considered flows of molten polymers.…”