On the positive self-similar solutions of the boundary-layer wedge flow problem of a power-law fluid

• Published in: Journal of engineering mathematics Vol. 148; no. 1
• Main Authors: El Amrani, Jamal, Amtout, Tarik, Er-Riani, Mustapha, Lahrouz, Aadil, Settati, Adel
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Asymptotic properties; Boundary layer equations; Computational Mathematics and Numerical Analysis; Fluid flow; Incompressible flow; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Power law; Self-similarity; Shear flow; Shear thickening (liquids); Shear thinning (liquids); Theoretical and Applied Mechanics; Two dimensional flow; Wall shear stresses; Wedge flow; 34B15; Wedge flow; 76D10; Positive solution; 76A05; Power-law fluid; Boundary-layer flow; Normal solution; Existence of solutions
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-024-10394-8

We first study the existence and uniqueness of a positive self-similar solution of the 2D boundary-layer equations of an incompressible viscous power-law fluid when the external flow is accelerating, and then we derive the bounds of the wall shear stress rate. For shear-thickening fluids, we show that the matching with the external flow occurs at a finite distance. Furthermore, we also investigate the asymptotic behaviour at infinity of positive solutions in the case of shear-thinning fluids.