Abstract
For a generalized Newtonian fluid the viscosity η* varies with the shear rate\(\dot \gamma *\). Instead of assuming a certain dependence like rheological models do, the viscosity is expanded in a Taylor serie with respect to\(\dot \gamma *\). Based on this expansion a perturbation approach to laminar pipe flow withqw = const. and viscous heating included is formulated. The basic flow (zero order solution) is that of a Newtonian fluid. Higher order terms successively account for the influence of a non-Newtonian fluid. — The asymptotic results compare reasonably well with those of specific rheological models like power law or Ellis model. — The influence of temperature dependent properties (including the viscosity) can be accounted for by the same kind of asymptotic approach. The influence of shear rate as well as temperature dependence thus can be combined in general results valid for all generalized Newtonian fluids.
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