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.

The study of heat transfer deals with the determination of the rate of heat energy transfer from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often the fundamental principle behind several engineering systems. Heat transfer analysis is necessary while designing any product. The most common numerical method used to analyze heat transfer is the finite element method. This paper uses the finite element method to demonstrate steady and transient heat conduction in a three-dimensional bracket. The goal here was to determine the temperature distribution and rate of heat flow in the solid. This is crucial in designing machine elements as they are subjected to various thermal loads during operation and also due to fluctuations in the surrounding environmental conditions. The temperature significantly affects stress, displacements, and volumetric strains. Thus, to analyze thermal stresses induced in a machine element, it is necessary to find the temperature field first. The thermal analysis was performed using the open-source package FEniCSx on Python. The program was run using a preconditioned Krylov subspace method for higher-order function spaces. The Krylov subspace solver drastically reduces computational time. The time taken for the execution of each order was recorded and presented.