Moisture/air-flow over the aircraft wing and bonnet of a moving car in aerodynamical systems exhibit dynamic behavior characterized by accelerating and decelerating flows. These analysis is essential and applicable in various fields, including physics, engineering, and fluid mechanics. The present investigation aim to explore the dynamics of accelerating and decelerating flows within the framework of boundary layer examination. To achieve these objectives, a non-similar group of transformations is employed to convert the governing dimensional two-variable dynamical system into a dimensionless differential form, with and as the independent variables. To gain physical understanding of the mathematical equations governing the flow, an efficient bivariate spectral collocation method (BSCM) is employed for analyzing the flow dynamics. This method allows for a thorough investigation of the behavior and characteristics of the accelerating and decelerating Casson flows. Subject to the convergence and residual error analysis of the numerical results, the effects of pertinent parameters on the flow variables were investigated. The findings of this study show that the effects of flow parameters on decelerating and accelerating flows are not completely opposite. Additionally, the Biot parameter positively impacts the velocity and temperature profiles of the two dynamical flows. However, an increase in the Casson fluid parameter has an opposing effect on the temperature and concentration profiles of both flows.

中文翻译：

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加速和减速流的动力学：采用非相似方法和对流边界条件的边界层检查

空气动力学系统中飞机机翼和移动汽车发动机盖上的湿气/气流表现出以加速和减速流动为特征的动态行为。这些分析在物理、工程和流体力学等各个领域都是必不可少的和适用的。本研究旨在探索边界层检查框架内加速和减速流动的动力学。为了实现这些目标，采用非相似变换组将控制维二变量动力系统转换为无量纲微分形式，以 和 作为自变量。为了获得对控制流动的数学方程的物理理解，采用有效的双变量谱配置方法（BSCM）来分析流动动力学。该方法可以对加速和减速卡森流的行为和特征进行彻底研究。通过对数值结果的收敛和残差分析，研究了相关参数对流动变量的影响。这项研究的结果表明，流动参数对减速和加速流动的影响并不完全相反。此外，Biot 参数对两个动态流的速度和温度曲线有积极影响。然而，卡森流体参数的增加对两种流的温度和浓度分布具有相反的影响。