Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt.
Department of Basic Science, Egyptian Academy for Engineering and Advanced Technology Affiliated to The Ministry of Military Production, Cairo, Egypt.
Sci Rep. 2023 Apr 21;13(1):6560. doi: 10.1038/s41598-023-33368-9.
The coupled equations of pollution and aeration for flow in a river were studied under generalized assumptions in terms of parameter dependency on space and time, as well as general boundary constraints. An analytical solution was obtained in the steady-state case. Also, the system was solved in its unsteady state numerically in a dimensionless form using the finite difference scheme. The effect of different parameters controlling the flow (such as the velocity, Peclet number, injected pollutants, and so on…) was studied. Investigations indicate that the special cases of the proposed model (i.e., uniform distribution of pollutant and Dissolved Oxygen concentrations, and zero injected pollutants along the river) give results that agree with the previous studies. This simple model helps in understanding the behavior of the pollution-aeration process and its relation to the injected pollution along a river and its effect on fish survival. A simple procedure was discussed in this study to help in regulating farming, industrial, and urban practices and impose restrictions if necessary. This study determines with accuracy the intervals of the river at which fish can survive at a given time, as well as the maximum amount of pollutants allowed to be injected along the river for fish survival.
在广义假设下，研究了河流中流动的污染和曝气的耦合方程，这些假设考虑了参数对空间和时间的依赖性以及一般边界约束。在稳态情况下得到了解析解。此外，还使用有限差分方案以无量纲形式对非稳态系统进行了数值求解。研究了控制流动的不同参数（例如速度、佩克莱数、注入污染物等）的影响。研究表明，所提出模型的特殊情况（即污染物和溶解氧浓度的均匀分布，以及沿河流零注入污染物）给出的结果与先前的研究一致。这个简单的模型有助于理解污染-曝气过程的行为及其与河流中注入污染的关系及其对鱼类生存的影响。本文讨论了一种简单的方法，以帮助管理农业、工业和城市实践，并在必要时施加限制。本研究准确确定了在给定时间内鱼类可以生存的河流区间，以及允许沿河流注入的最大污染物量，以确保鱼类的生存。
