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Article Dans Une Revue Fractal and Fractional Année : 2022

Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions

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In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shearthickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology
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hal-03817619 , version 1 (17-10-2022)

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Abdellah Bouchendouka, Zine El Abiddine Fellah, Zakaria Larbi, Nicholas O Ongwen, Erick Ogam, et al.. Flow of a Self-Similar Non-Newtonian Fluid Using Fractal Dimensions. Fractal and Fractional, 2022, 6, pp.582. ⟨10.3390/fractalfract6100582⟩. ⟨hal-03817619⟩
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