PDF(Pubmed)
Abstract：
This article provides a comparison among the generalized Second Grade fluid flow described by three recently proposed fractional derivatives i.e. Atangana Baleanu fractional derivative in Caputo sense (ABC), Caputo Fabrizio (CF) and Constant Proportional-Caputo hybrid (CPC) fractional derivative. The heat mass transfer is observed during the flow past a vertical porous plate that is accelerated exponentially under the effects of the Magneto hydro dynamics. The effects of the heat generation and exponential heating in the temperature boundary layer and chemical reaction at the concentration boundary layer are also analyzed in this article. The flow model is described by three partial differential equations and the set of non-dimensional PDE\'s is transformed into ODE\'s by utilization of the integral transform technique (Laplace transform). For the better understanding of the rheological properties of the Second Grade fluid we used the CF, ABC and CPC operators to describe the memory effects. The analytical exact solution of the problem is obtained in the form of G-functions and Mittag Leffler functions. For the physical significance of flow parameters, different parameters are graphed. From this analysis it is concluded that the CPC is the most suitable operator to describe the memory effects.
摘要：
本文提供了三个最近提出的分数导数，即Caputo意义上的AtanganaBaleanu分数导数（ABC）描述的广义二级流体流之间的比较，卡普托·法布里齐奥(CF)和常数比例-卡普托混合(CPC)分数导数。在流过垂直多孔板的过程中观察到传热传质，该垂直多孔板在磁流体动力学的作用下呈指数加速。本文还分析了温度边界层的热产生和指数加热以及浓度边界层的化学反应的影响。流动模型由三个偏微分方程描述，并利用积分变换技术（拉普拉斯变换）将无量纲PDE集转换为ODE。为了更好地理解二级流体的流变特性，我们使用了CF，ABC和CPC运算符来描述记忆效应。问题的解析精确解以G函数和MittagLeffler函数的形式获得。对于流动参数的物理意义，不同的参数被绘制出来。从该分析可以得出结论，CPC是描述记忆效应的最合适的运算符。
