Critical analysis of generalized Newtonian fluid flow past a non‐linearly stretched curved surface: A numerical solution for Carreau model

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 104; no. 2
• Main Authors: Ali, Nasir, Khan, Muhammad Waris Saeed, Saleem, Shahzad
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.02.2024
• Subjects: Boundary layer flow; Boundary layer thickness; Constitutive relationships; Curvature; Equations of motion; Fluid flow; Newtonian fluids; Ordinary differential equations; Parameters; Partial differential equations; Skin friction; Velocity distribution
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.202300100

The underlying intention of the present work is to elaborate the boundary layer flow of Carreau fluid over a non‐linear stretching curved surface. Firstly, we derived the equation of motion for a two‐dimensional curved surface using the Carreau constitutive relation. Employing the well‐known approximations of the boundary layer theory (order of magnitude analysis), the terms of higher and next order have been neglected. We developed an appropriate similarity transformation that reduced the considered partial differential equation into an ordinary differential equation (self‐similar formulation). The MATLAB built‐in function usually known as bvp5c is utilized to get the numerical solution of the considered problem. The impact of the power‐law index (n), Weissenberg number (We)$( {We} )$ and curvature parameter (k) on velocity profile and skin friction are analyzed through several graphs and tables. The obtained results are also verified by employing the shooting method through Maple software. The results reveal that both boundary layer thickness and velocity profile increase by enlarging the dimensionless curvature parameter of the curved surface. The underlying intention of the present work is to elaborate the boundary layer flow of Carreau fluid over a non‐linear stretching curved surface. Firstly, we derived the equation of motion for a two‐dimensional curved surface using the Carreau constitutive relation. Employing the well‐known approximations of the boundary layer theory (order of magnitude analysis), the terms of higher and next order have been neglected. We developed an appropriate similarity transformation that reduced the considered partial differential equation into an ordinary differential equation (self‐similar formulation).…