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Flow of a generalized second grade non-Newtonian fluid with variable viscosity. (English) Zbl 1158.76304

Summary: A modified constitutive equation for a second grade fluid is proposed so that the model would be suitable for studies where shear-thinning (or shear-thickening) may occur. In addition, the dependence of viscosity on the temperature follows the Reynolds equation. In this paper, we propose a constitutive relation, \((18)\), which has the basic structure of a second grade fluid, where the viscosity is now a function of temperature, shear rate, and concentration. As a special case, we solve the fully developed flow of a non-Newtonian fluid given by \((11)\), where the effects of concentration are neglected.

MSC:

76A05 Non-Newtonian fluids
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