Unsteady stagnation-point boundary layer flows of power-law fluids over a porous flat plate
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Unsteady stagnation‑point boundary layer flows of power‑law fluids over a porous flat plate S. Dholey1 Received: 7 January 2020 / Accepted: 20 August 2020 © Springer Nature Switzerland AG 2020
Abstract The problem of unsteady stagnation-point flows of power-law fluids over a porous flat plate with mass transfer is considered with a view to examine the rheological behaviors of the fluids. This study is completely based on the four physical parameters, namely, flow strength parameter a, mass transfer parameter d, unsteadiness parameter 𝛽 and non-Newtonian power-law index n. For d = 0 , the numerical results of this analysis reveal the existence of two types of solutions - one is attached flow solution (AFS) and the other is reverse flow solution (RFS) in a definite range of n ( 0 < n ≤ 2 ) when (a, 𝛽) = (1, −1) . The present analysis confirms that the velocity profile for any dilatant fluid (n > 1) matches smoothly with the free stream velocity for a suitable amount of blowing d(< 0) depending upon the values of n. We will also discuss the asymptotic behaviors of the boundary layer flows for large values of d, i.e., for d → ±∞ . The asymptotic analysis ensures the existence of the above two solutions for large values of suction d > 0 , whereas the boundary layer solution is terminated after a certain value of blowing d < 0 , dependent on the values of 𝛽(< 0) and n. Below this critical value of blowing d, this unsteady flow problem also provides us with a solution which does not appear to have a boundary layer character. Keywords Unsteady · Power-law fluids · Porous surface · Dual solutions · Asymptotic solutions
1 Introduction Unsteady boundary layer flows of power-law fluids over flat surfaces represent one of the most classical problems in the practical fluid dynamics. There are numerous avenues in chemical, mechanical, biomedical, mineral and food processing engineering applications where the proper knowledge for settling the flows of non-Newtonian fluids are required to set up the new design techniques in many fluid dynamic devices. Many fluids of practical interest are non-Newtonian and their characteristic features are completely different from that of the viscous Newtonian fluids. However, the use of non-Newtonian fluids have an increasing demand in modern technology as well as in the industrial applications for a number of reasons like drag reduction, modification of effective heat flux, etc, and essentially get a serious attention in advanced and
modern fluid dynamics research. There are various models (constitutive equations) available in the open literature to explain the non-Newtonian behaviors of the fluids. Among all the non-Newtonian fluid models, the Ostwald-de-Waele power-law model (Bird et al. [1]) is well accepted since the boundary layer hypotheses can successfully be imposed on this model. Most importantly, this model also describes the behavior of a huge number of real non-Newtonian fluids. The theoretical research of the steady boundary layer flows for non-Newtonian power-law fluids was fi
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