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Unsteady Self-similar Flow over an Impulsively Started Shrinking Sheet: Flow Augmentation with No Separation
Journal of Nonlinear, Complex and Data Science ( IF 1.5 ) Pub Date : 2020-05-26 , DOI: 10.1515/ijnsns-2018-0350
Ahmer Mehmood 1 , Ghulam Dastgir Tabassum 1 , Muhammad Usman 2 , Aman-ullah Dar 3
Affiliation  

Abstract The unsteady self-similar flow due to a permeable shrinking sheet is analyzed in this investigation. The current theoretical study is enacted in the light of correct self-similar formulation proposed by (Mehmood. A. Viscous flows: Stretching and shrinking of surfaces, Springer, 2017). For the existence of a meaningful solution the retarded boundary-layer developed due to retarded shrinking wall velocity uwx=±xt \left( {{u_w}\left( x \right) = {{ \pm x} \over t}} \right) is supported by the sufficient mass suction introduced at the shrinking surface. Main theme of this paper is to utilize the correct mathematical formulation for the shrinking sheet flow in order to investigate the existence of dual solutions of the considered problem. By using suitable self-similar transformations, the nonlinear Navier–Stokes equations are converted to corresponding non-linear ordinary differential equations. A reliable numerical technique (shooting method) is applied to solve the resulting ODEs for the involved physical parameters. Particular to this problem, it is observed that a sufficient amount of wall suction is mandatory SSc \left( { \left| S \right| \gt \left| {{S_c}} \right| } \right).

中文翻译:

脉冲开始收缩片上的非定常自相似流:无分离的流动增强

摘要 本研究分析了渗透性收缩板引起的非定常自相似流动。当前的理论研究是根据 (Mehmood. A. 粘性流:表面的拉伸和收缩,Springer,2017 年) 提出的正确自相似公式制定的。对于有意义解的存在,由于延迟收缩壁速度 uwx=±xt \left( {{u_w}\left( x \right) = {{ \pm x} \over t}} \右)由在收缩表面引入的足够质量吸力支持。本文的主题是利用正确的数学公式来计算收缩板流,以研究所考虑问题的双重解的存在性。通过使用合适的自相似变换,非线性 Navier-Stokes 方程转换为相应的非线性常微分方程。应用可靠的数值技术(射击方法)来求解所涉及物理参数的所得 ODE。特别是这个问题,据观察,足够的壁吸力是强制性的。Sc \left( { \left| S \right| \gt \left| {{S_c}} \right| } \right)。
更新日期:2020-05-26
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