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

• Published in: Fractal and fractional 2022-10, Vol.6 (10), p.582
• Main Authors: Bouchendouka, Abdellah, Fellah, Zine El Abiddine, Larbi, Zakaria, Ongwen, Nicholas O., Ogam, Erick, Fellah, Mohamed, Depollier, Claude
• Format: Article
• Language: English
• Subjects: Acoustics; Blood flow; Exact solutions; Fluid dynamics; Fluid flow; fractal dimensions; Fractal geometry; Fractals; Hydrology; Industrial applications; Mechanics; Newtonian fluids; Non Newtonian fluids; non-Newtonian fluid; noninteger dimensional space; Ostwald ripening; Physics; Power law; power-law fluid; Rheological properties; Rheology; self-similar fluid; Self-similarity; Shear; Shear strain; Shear stress; Shear thickening (liquids); Shear thinning (liquids); Thickening; Velocity; Velocity distribution; Viscosity
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract6100582

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 shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology.