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The utilization of Riverbank Filtration Systems (RBF) presents a promising approach for obtaining potable water from rivers or streams. However, the effectiveness of this technique relies significantly on two key factors: the width of the river and the presence of a clogging layer beneath the streambed, both of which influence the degree of contamination in the extracted water. Prior studies have predominantly relied on numerical models or simplistic one-dimensional flow assumptions to address these variables. In contrast, this research introduces a 3D analytical model utilizing the Green's function approach to analyze the movement of contaminants from the river towards the extraction well within RBF systems. By accounting for the dynamic interaction between river width and the clogging layer, this model offers a more accurate depiction of contaminant transport in three-dimensional water flow scenarios. The accompanying MATLAB code facilitates numerical integration of model equations, producing graphical representations for various hydrological inputs. Validation against MODFLOW software demonstrates a remarkable agreement, with outcomes aligning at 98–99%. Key findings underscore the exacerbation of pollutant concentrations with heightened clogging, increased river width, and optimal well placement. Moreover, the analysis underscores better predictive accuracy achieved by incorporating actual river width values compared to simple linear approximations. Notably, the research reveals minimal impact on contaminant concentrations when the distance between the river and the well exceeds twice the river's width, offering valuable insights for system design and management. [ABSTRACT FROM AUTHOR]

This study consider the development of three dimensional analytical solutions for contaminant transport induced by a pumping well near a stream. The solutions were derived for both line-width and finite-width streams based on Green's function approach. These solutions were implemented in an aquifer that was partially penetrated by the stream and were general enough to be applied to both unconfined and confined aquifers. The analytical solutions were checked to show the effect of stream width, leakance coefficient, distance from the river edge to pumping well and pumping rate on contaminant concentration. Generally, it was found that higher values of these parameters increased the contamination in the well area for both line and finite width stream. The graphical representation of the analytical solution shows that the contaminants attenuated vertically along z axis as well as horizontally along × axis. The finite width model produced more realistic estimate for the distribution of contaminants due to the effect of river width. In particular, the results shows higher contamination near the stream for finite width model. However, this impact of river width on contaminant concentration appear to be neglected if the distance between river and pumping well was more than twice the stream width. [ABSTRACT FROM AUTHOR]

• Unsteady mixed convection in EMHD nanofluid flow over a vertical plate is deliberated. • Concurrent Navier slips and double stratification are presented in the model. • Thermal radiation, Ohmic heating, and viscous dissipation impingement have been addressed. • Numerical solution are obtained viz implicit finite routine. The present study explores the two-dimensional linear permeable stretched flow of nanofluid in the presence of double stratification and slip impacts. The mathematical model is developed in the presence of Joule heating, viscous dissipation and chemical reaction impacts. Nanofluid is electrically conducting in the presence of applied electric and magnetic fields. Suitable transformations yield the couple of nonlinear set of ordinary differential systems. The resulting system of equations has been solved numerically via implicit finite difference scheme. Graphs are plotted to examine the effects of physical emerging parameters on the velocity, temperature and concentration profiles. Also, the skin friction coefficients, local Nusselt and Sherwood numbers are computed and analyzed. [ABSTRACT FROM AUTHOR]

The LQR (linear quadratic regulator) control problem subject to singular system constitutes a optimization problem in which one must be find an optimal control that satisfy the singular system and simultaneously to optimize the quadratic objective functional. In this paper we establish a sufficient condition to obtain the optimal control of discounted LQR optimization problem subject to disturbanced singular system where the disturbance is time varying. The considered problem is solved by transforming the discounted LQR control problem subject to disturbanced singular system into the normal LQR control problem. Some available results in literatures of the normal LQR control problem be used to find the sufficient conditions for the existence of the optimal control for discounted LQR control problem subject to disturbanced singular system. The final result of this paper is in the form a method to find the optimal control of discounted LQR optimization problem subject to disturbanced singular system. The result shows that the disturbance is vanish with the passage of time. [ABSTRACT FROM AUTHOR]