Perturbation Solution for Laminar Flow of Carreau-Extended Non-Newtonian Fluid in Pipe
Non-Newtonian fluids are widely used in industrial production.Based on the complex Carreau-Extended(shorted as Carreau-E)rheological equation with three parameters of yield stress,time constant and power-law index,and the equilibrium relationship of shear stress and pressure drop,motion equation for fully developed,steady and laminar flow of Carreau-E fluid in a pipe was established and its first-order asymptotic solution was derived by using perturbation method.The laws of velocity distribution of different types of fluid flow and the influences of pressure gradient,flow core width,yield stress and time constant on the flow field distribution of the Carreau-E fluid pipe flow were obtained.This study has reference value for the flow characteristics of Carreau-E fluid and other complex non-Newtonian fluids.
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