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Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

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Abstract

A Jeffery-Hamel (J-H) flow model of the non-Newtonian fluid type inside a convergent wedge (inclined walls) with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical (numerical) solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

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Authors and Affiliations

  1. Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Ramat-Aviv, 69978, Israel

    J. Nagler

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  1. J. Nagler
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Nagler, J. Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction. Appl. Math. Mech.-Engl. Ed. 38, 815–830 (2017). https://doi.org/10.1007/s10483-017-2206-8

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  • DOI: https://doi.org/10.1007/s10483-017-2206-8

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