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Solution of the Fractional Form of Unsteady Squeezing Flow through Porous Medium

机译：多孔介质中非恒定挤压流动的分数形式解

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摘要

We propose two friendly analytical techniques called Adomian decomposition and Picard methods to analyze an unsteady axisymmetric flow of nonconducting, Newtonian fluid. This fluid is assumed to be squeezed between two circular plates passing through porous medium channel with slip and no-slip boundary conditions. A single fractional order nonlinear ordinary differential equation is obtained by means of similarity transformation with the help of the fractional calculus definitions. The resulting fractional boundary value problems are solved by the proposed methods. Convergence of the two methods' solutions is confirmed by obtaining various approximate solutions and various absolute residuals for different values of the fractional order. Comparison of the results of the two methods for different values of the fractional order confirms that the proposed methods are in a well agreement and therefore they can be used in a simple manner for solving this kind of problems. Finally, graphical study for the longitudinal and normal velocity profiles is obtained for various values of some dimensionless parameters and fractional orders.
机译：我们提出两种友好的分析技术，分别称为Adomian分解和Picard方法，以分析非导电牛顿流体的非稳态轴对称流。假定该流体在两个带有滑动和无滑动边界条件的多孔介质通道的圆形板之间被挤压。在分数阶微积分定义的帮助下，通过相似变换获得一个分数阶非线性常微分方程。所提出的方法解决了分数分数边值问题。对于分数阶的不同值，通过获得各种近似解和各种绝对残差，可以确认这两种方法的解的收敛性。两种方法对于分数阶值不同的结果的比较证实，所提出的方法具有很好的一致性，因此可以以简单的方式使用它们来解决此类问题。最后，获得了一些无量纲参数和分数阶的各种值的纵向和法向速度分布图的图形研究。

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