Wastewater discharge plays a vital role in environmental management and various industries. Water pollution control and tracking are critical for conserving water resources and maintaining adherence to environmental standards. Therefore, the present analysis examines the impact of pollutant discharge concentration considering the non-Newtonian nanoliquids over a permeable Riga surface with thermal radiation. The analysis is made using two distinct kinds of non-Newtonian nanoliquids: second-grade and Walter’s liquid B. The governing equations are made using the applications of boundary layer techniques. Utilizing the suitable similarity variable reduces the formulated governing equations into an ordinary differential set of equations. The solutions will be obtained using an efficient numerical technique and the significance of various dimensionless constraints on their individual profiles will be presented using graphical illustrations. A comparative analysis is reported for second-grade and Walter’s liquid B fluids. The results show that the porous factor declines the velocity profile for both fluids. Radiation and external pollutant source variation constraints will improve thermal and concentration profiles. The rate of thermal distribution improved with the rise in radiation and solid volume factors. Further, essential engineering factors are analyzed. The outcomes of the present study will help in making decisions and putting efficient plans in place to reduce pollution and safeguard the environment.

The impact of convection and radiation on the thermal distribution of the wavy porous fin is examined in the present study. A hybrid model that combines the differential evolution (DE) algorithm with an artificial neural network (ANN) is proposed for predicting the heat transfer of the wavy porous fin. The equation representing the thermal variation in the wavy porous fin is reduced to its dimensionless arrangement and is numerically solved using Rung, e-Kutta-Fehlberg’s fourth-fifth order method (RKF-45). The study demonstrates the effectiveness of this hybrid model, and the results indicate that the proposed approach outperforms the ANN model with parameters obtained through grid search (GS), showcasing the superiority of the hybrid DE-ANN model in terms of accuracy and performance. This research highlights the potential of utilizing DE with ANN for improved predictive modeling in the heat transfer sector. The originality of this study is that it addresses the heat transfer problem by optimizing the selection of parameters for the ANN model using the DE algorithm.

Evolutionary algorithms are a large class of optimization techniques inspired by the ideas of natural selection, and can be employed to address challenging problems. These algorithms iteratively evolve populations using crossover, which combines genetic information from two parent solutions, and mutation, which adds random changes. This iterative process tends to produce effective solutions. Inspired by this, the current study presents the results of thermal variation on the surface of a wetted wavy fin using a genetic algorithm in the context of parameter estimation for artificial neural network models. The physical features of convective and radiative heat transfer during wet surface conditions are also considered to develop the model. The highly nonlinear governing ordinary differential equation of the proposed fin problem is transmuted into a dimensionless equation. The graphical outcomes of the aspects of the thermal profile are demonstrated for specific non-dimensional variables. The primary observation of the current study is a decrease in temperature profile with a rise in wet parameters and convective-conductive parameters. The implemented genetic algorithm offers a powerful optimization technique that can effectively tune the parameters of the artificial neural network, leading to an enhanced predictive accuracy and convergence with the numerically obtained solution.

The Soret and Dufour effects have significant importance in several practical scenarios, especially in the domain of fluidic mass and temperature transfer. Nanofluidics, biological systems, and combustion processes are all areas where these consequences are crucial. Because of its distinct geometry, a wedge-shaped structure has aerodynamics, production, and engineering applications. Wedge shapes are used in aerodynamics for analyzing and improving airflow across various objects. Nanofluids increase thermal conductivity over traditional fluids making them ideal for cooling high-power electronics, boosting temperature transfer efficiencies, and boosting the solar energy system output. This work is of critical importance since it examines the consequences of a heat source/sink, the Soret impact and the Dufour impact, on the movement of a ternary nanofluid over a wedge. This work uses appropriate similarity constraints to reduce the complexity of the underlying governing equations, allowing for fast computational solutions with the Runge–Kutta–Fehlberg 4–5^th order method (RKF-45). Analysis of these phenomena helps determine their possible real-world applications across various engineering fields, by presenting numerical results through plots. The results reveal that adjusting the moving wedge factor lessens the temperature profile, improving the magnetic constraint increases the velocity, and modifying the heat source/sink, Dufour, and Soret factors increases the temperature and concentration profiles. Dufour and heat source/sink constraints speed-up the heat transmission rate. In all cases, ternary nano liquids show significant performance over hybrid nano liquids.