Analyzing the impact of non-Newtonian nanofluid flow on pollutant discharge concentration in wastewater management using an artificial computing approach

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.