The paper describes the longitudinal dispersion of passive tracer materials released into an incompressible viscous fluid, flowing through a channel with walls having first-order reaction. Its model is based on a steady advection–diffusion equation with Dirichlet’s and mixed boundary conditions, and whose solution represents the concentration of the tracers in different downstream stations. For imposing the boundary conditions properly, artanh transformation is used to convert the infinite solution space to a finite one. A finite difference implicit scheme is used to solve the advection–diffusion equation in the computational region, and an inverse transformation is employed for the solution in the physical region. It is shown how the mixing of the tracer molecule influenced by the shear flow and due to the action of the absorption parameter at both the walls of the channel. For convection-dominated flow, uniform mesh is failed to capture the layer phenomena along the different downstream stations and a piecewise uniform mesh; namely, Shishkin mesh is used. The results are compared with existing experimental and numerical data available in the literature, and we have achieved an excellent agreement with them. The study plays a significant role to understand the basic mechanisms of sewage dispersion.

中文翻译：

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稳定流中溶质通过具有吸收边界的通道的分散：在污水分散中的应用

该论文描述了释放到不可压缩粘性流体中的被动示踪材料的纵向分散，该流体流经具有一级反应壁的通道。其模型基于具有狄利克雷边界条件和混合边界条件的稳定对流-扩散方程，其解代表不同下游站点中示踪剂的浓度。为了适当地施加边界条件，使用artanh变换将无限解空间转换为有限解空间。计算区域采用有限差分隐式求解对流扩散方程，物理区域采用逆变换求解。它显示了示踪分子的混合如何受到剪切流的影响以及由于通道两壁吸收参数的作用。对于以对流为主的流动，均匀网格未能捕捉到沿不同下游站点的层现象和分段均匀网格；即使用 Shishkin 网格。结果与文献中现有的实验和数值数据进行了比较，我们与它们取得了很好的一致。该研究对于了解污水分散的基本机制具有重要意义。结果与文献中现有的实验和数值数据进行了比较，我们与它们取得了很好的一致。该研究对于了解污水分散的基本机制具有重要意义。结果与文献中现有的实验和数值数据进行了比较，我们与它们取得了很好的一致。该研究对于了解污水分散的基本机制具有重要意义。