Laminar Non-Newtonian Fluid Flow in Noncircular Ducts and Microchannels

Non-Newtonian fluid flow in noncircular ducts and microchannels is examined. A simple model is proposed for power law fluids based on the Rabinowitsch–Mooney formulation. By means of a new characteristic length scale, the square root of the cross-sectional area, it is shown that dimensionless wall shear stress can be made a weak function of duct shape. The proposed model is based on the solution for the rectangular duct and has an accuracy of $±10%$ or better. The current model eliminates the need for tabulated data or equations for several common shapes found in handbooks, namely, circular tube, elliptic tube, parallel channel, rectangular duct, isosceles triangular duct, circular annulus, and polygonal ducts.