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Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

机译:弱渗透性缓慢扩张或收缩壁之间二维粘性流的李群方法解

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摘要

The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number R_e and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted.
机译:考虑了非线性运动方程,该运动方程描述了矩形区域中的层流,等温和不可压缩的流动,该区域由两个弱渗透的活动多孔壁界定,这些壁使流体能够在连续的膨胀或收缩过程中进入或流出。我们应用李群方法确定偏微分方程的对称约简。李群方法从一组一般的无穷小变换开始,在这种变换下给定的偏微分方程是不变的,然后推导确定方程。确定方程是一组线性微分方程,其解给出了因变量和自变量的无穷小。在确定了组之后,可以从不变表面条件中找到给定偏微分方程的解,使得其解导致相似变量,从而减少系统中自变量的数量。通过分析和数值研究了渗透雷诺数R_e和无因次壁膨胀率α对自轴速度的影响,并绘制了结果。

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