Wastewater discharge is important in numerous areas of industries and in governance of the environmental sectors. Controlling and monitoring water pollution are essential for protecting the availability of water and upholding standards of sustainability. Thus, in the current study, the effects of pollutant discharge concentration (PDC) are considered while analyzing the flow of non-Newtonian nanofluids (NNNF) through the permeable Riga surface subject to heat radiation. Walter’s B fluid (WBF) and second-grade fluids (SGFs), two distinct types of NNNF, have been investigated. The fluid flow is expressed as a system of PDEs, which are simplified into lower order by employing similarity approach. These equations (ODEs) are solved using the Levenberg Marquardt back-propagation optimization algorithm (LMBOA) of the artificial neural network (ANN). The Matlab package “bvp4c” is used for generating the dataset in order to validate the results of the ANN-LMBOA. The dataset was developed for various flow scenarios, as well as ANN evaluation and validation. The accuracy of the ANN-LMBOA model is estimated though numerous statistical tools, i.e., histogram, regression measures, curve fitting, performance plots, and validation tables. The numerical outcomes of bvp4c package are also compared to the published literature. Which show best accuracy and resemblance with each other for the limiting case. The targeted date absolute error is accomplished within the range of 10^–4-10^–5 which confirms the outstanding accuracy of ANN-LMBOA. It is concluded form error histograms (EHs) that the EHs values for case 1–4 is lie about \(3 \cdot 6 \times 10^{{ - 7}}\), \(7 \cdot 83 \times 10^{{ - 9}}\), \(- 4.7 \times 10^{{ - 8}}\) and \(- 2 \cdot 9 \times 10^{{ - 6}}\) respectively.

废水排放在许多工业领域和环境部门的治理中都很重要。控制和监测水污染对于保护水资源供应和维护可持续性标准至关重要。因此，在目前的研究中，在分析非牛顿纳米流体 （NNNF） 在热辐射经可渗透里加表面的流动时，考虑了污染物排放浓度 （PDC） 的影响。已经研究了 Walter B 液 （WBF） 和二级液 （SGF），这是 NNNF 的两种不同类型。流体流动表示为偏微分方程系统，通过采用相似性方法将其简化为低阶。这些方程 （ODE） 使用人工神经网络 （ANN） 的 Levenberg Marquardt 反向传播优化算法 （LMBOA） 进行求解。Matlab 包 “bvp4c” 用于生成数据集，以验证 ANN-LMBOA 的结果。该数据集是为各种流场景以及 ANN 评估和验证而开发的。ANN-LMBOA 模型的准确性是通过许多统计工具估计的，即直方图、回归测量、曲线拟合、性能图和验证表。bvp4c 包的数值结果也与已发表的文献进行了比较。对于极限情况，它们显示出最佳的准确性和彼此的相似性。目标日期绝对误差在 10-4-10-5 的范围内完成，这证实了 ANN-LMBOA 的出色准确性。从误差直方图 （EHs） 中得出结论，情况 1-4 的 EHs 值约为 \（3 \cdot 6 \times 10^{{ - 7}}\）、\（7 \cdot 83 \times 10^{{ - 9}}\）、\（- 4。7 \times 10^{{ - 8}}\） 和 \（- 2 \cdot 9 \times 10^{{ - 6}}\）。