Numerical solution of shear-thinning and shear-thickening boundary-layer flow for Carreau fluid over a moving wedge
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ORIGINAL ARTICLE
Numerical solution of shear‑thinning and shear‑thickening boundary‑layer flow for Carreau fluid over a moving wedge Ramesh B Kudenatti1 · L. Sandhya2 · N. M. Bujurke3 Received: 2 July 2020 / Accepted: 28 August 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract This paper investigates the linear stability of the flow in the two-dimensional boundary-layer flow of the Carreau fluid over a wedge. The corresponding rheology is analysed using the non-Newtonian Carreau fluid. Both mainstream and wedge velocities are approximated in terms of the power of distance from the leading edge of the boundary layer. These forms exhibit a class of similarity flows for the Carreau fluid. The governing equations are derived from the theory of a non-Newtonian fluid which are converted into an ordinary differential equation. We use the Chebyshev collocation and shooting techniques for the solution of governing equations. Numerical results show that the viscosity modification due to Carreau fluid makes the boundary layer thickness thinner. Numerical results predict an additional solution for the same set of parameters. Thus, a further aim was to assess the stability of dual solutions as to which of the solutions can be realized. This leads to an eigenvalue problem in which the positive eigenvalues are important and intriguing. The results from eigenvalues form tongue-like structures which are rather new. The presence of the tongue means that flow becomes unstable beyond the critical value when the velocity ratio is increased from the first solution. Keywords Boundary layer · Carreau fluid · Dual solutions · Stability analysis · Eigenfunctions
1 Introduction The boundary layer flow over a moving surface occurs in many industrial and manufacturing processes such as polymer extrusion, wire-drawing, metal forming, fibre processing, magnetic tape production, etc., and is used for understanding the aerodynamical properties of the fluids, for example, the wall friction, drag, etc. The fluid surrounding a moving surface plays a significant role in controlling its behaviour while it is in motion. When the surface or polymer sheet is stretched in a non-Newtonian fluid from the fixed point, sufficient care has to be taken in stretching/moving rate so that the surface should not break, and the desired properties are achieved. Moreover, the surface has to be * Ramesh B Kudenatti [email protected] 1
Department of Mathematics, Bengaluru Central University, Central College Campus, Bengaluru 560 001, India
2
Department of Mathematics, Bangalore University, Bengaluru 560 056, India
3
Department of Mathematics, Karnatak University, Dharwad 580 003, India
flat throughout the process. In this case, the non-Newtonian fluid that is surrounded the surface plays a prominent role because the Newtonian fluid fails to provide adequate results. Accordingly, the non-Newtonian fluid (generalized Newtonian fluid) gives satisfactory results in most of the engineering applications. On the other hand, also th
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