Abstract The study of fluid flow in non-Darcy porous medium subjected to Hall current is very important in scientific and engineering applications such as water filters, groundwater discharge in aquifers, petroleum engineering, MHD generators and chemical engineering. Forchheimer model is needed at high flow rate, where, flow will exhibit non-linearity with respect to velocity which make Darcy law inapplicable at these conditions. In this case, the momentum equations become non-linear. The classical differential transformation method transforms the non-linear differential equations to a non-linear algebraic system which gives more than one solution and may be unstable that leads to divergence of the required solution. The novelty of present method that it is a power series solution avoiding solution multiplicity and divergence by a linearization technique that is applied on non-linear governing equations to obtain the unique and convergent solution. The uniqueness, convergence and stability of the new technique are tested by comparisons with previously available works and it is also verified by a fourth order accurate finite difference (FOFDM) solution. The effects flow parameters on the velocity and friction factor are illustrated. The values of parameters in the present work are chosen according to: the available previous results, the power of the persent method to compute over a lagre range of parameters and the distinctiveness between curves in figures.

中文翻译：

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考虑霍尔电流的多孔平行板间非达西介质中MHD流动的微分变换新方法

摘要 霍尔电流作用下非达西多孔介质中流体流动的研究在水过滤器、含水层地下水排放、石油工程、MHD发生器和化学工程等科学和工程应用中具有重要意义。在高流速下需要 Forchheimer 模型，其中，流动将表现出相对于速度的非线性，这使得达西定律在这些条件下不适用。在这种情况下，动量方程变为非线性。经典的微分变换方法将非线性微分方程变换为非线性代数系统，该系统给出不止一个解并且可能不稳定，导致所需解发散。本方法的新颖之处在于它是一种幂级数解，通过将线性化技术应用于非线性控制方程以获得唯一且收敛的解，从而避免解的多重性和发散性。新技术的唯一性、收敛性和稳定性通过与先前可用作品的比较进行测试，并通过四阶精确有限差分（FOFDM）解决方案进行验证。说明了流动参数对速度和摩擦系数的影响。当前工作中的参数值是根据以下因素选择的：可用的先前结果、持续方法计算大范围参数的能力以及图形中曲线之间的独特性。新技术的唯一性、收敛性和稳定性通过与先前可用作品的比较进行测试，并通过四阶精确有限差分（FOFDM）解决方案进行验证。说明了流动参数对速度和摩擦系数的影响。当前工作中的参数值是根据以下因素选择的：可用的先前结果、持续方法计算大范围参数的能力以及图形中曲线之间的独特性。新技术的唯一性、收敛性和稳定性通过与先前可用作品的比较进行测试，并通过四阶精确有限差分（FOFDM）解决方案进行验证。说明了流动参数对速度和摩擦系数的影响。当前工作中的参数值是根据以下因素选择的：可用的先前结果、持续方法计算大范围参数的能力以及图形中曲线之间的独特性。