Purpose: A parabolic trough solar collector is an advanced concentrated solar power technology that significantly captures radiant energy. Solar power will help different sectors reach their energy needs in areas where traditional fuels are in use. This study aims to examine the sensitivity analysis for optimizing the heat transfer and entropy generation in the Jeffrey magnetohydrodynamic hybrid nanofluid flow under the influence of motile gyrotactic microorganisms with solar radiation in the parabolic trough solar collectors. The influences of viscous dissipation and Ohmic heating are also considered in this investigation. Design/methodology/approach: Governing partial differential equations are derived via boundary layer assumptions and nondimensionalized with the help of suitable similarity transformations. The resulting higher-order coupled ordinary differential equations are numerically investigated using the Runga-Kutta fourth-order numerical approach with the shooting technique in the computational MATLAB tool. Findings: The numerical outcomes of influential parameters are presented graphically for velocity, temperature, entropy generation, Bejan number, drag coefficient and Nusselt number. It is observed that escalating the values of melting heat parameter and the Prandl number enhances the Nusselt number, while reverse effect is observed with an enhancement in the magnetic field parameter and bioconvection Lewis number. Increasing the magnetic field and bioconvection diffusion parameter improves the entropy and Bejan number. Originality/value: Nanotechnology has captured the interest of researchers due to its engrossing performance and wide range of applications in heat transfer and solar energy storage. There are numerous advantages of hybrid nanofluids over traditional heat transfer fluids. In addition, the upswing suspension of the motile gyrotactic microorganisms improves the hybrid nanofluid stability, enhancing the performance of the solar collector. The use of solar energy reduces the industry’s dependency on fossil fuels.

Purpose: The purpose of this paper is to assess the flow of a nanofluid over a porous moving wedge. The passive control model along with the magnetohydrodynamic (MHD) effects is used to formulate the problem. Furthermore, in energy equation, the non-linear thermal radiation has also been incorporated. The equations governing the flow are transformed into a set of ordinary differential equations by using suitable similarity transforms. The reduced system of equations is then solved numerically using a well-known Runge–Kutta–Fehlberg method coupled with a shooting technique. The influence of parameters involved on velocity, temperature and concentration profiles is highlighted with the help of a graphical aid. Expressions for skin-friction coefficient, local Nusselt number and Sherwood number are obtained and presented graphically. Design/methodology/approach: Numerical solution of the problem is obtained using the well-known Runge–Kutta–Fehlberg method. Findings: The analysis provided gives a clear description that the increase in m and magnetic parameter M results in an increased velocity profile. Both these parameters normalize the velocity field. Radiation parameter, Rd, increases the temperature and concentration of the system so does the temperature ratio θ_ω reduces the heat transfer rate at the wall for both stretching and shrinking wedge. Originality/value: In the study presented, the flow of nanofluid over a moving permeable wedge is considered. The solution of the equations governing the flow is presented numerically. For the validity of results obtained, a comparison is also presented with already existing results. To the best of the authors’ knowledge, this investigation is the first of its kind on the said topic.

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.

Quantum calculus provides a significant generalization of classical concepts and overcomes the limitations of classical calculus in tackling non-differentiable functions. Implementing the q-concepts to obtain fresh variants of classical outcomes is a very intriguing aspect of research in mathematical analysis. The objective of this article is to establish novel Milne-type integral inequalities through the utilization of the Mercer inequality for q-differentiable convex mappings. In order to accomplish this task, we begin by demonstrating a new quantum identity of the Milne type linked to left and right q derivatives. This serves as a supporting result for our primary findings. Our approach involves using the q-equality, well-known inequalities, and convex mappings to obtain new error bounds of the Milne–Mercer type. We also provide some special cases, numerical examples, and graphical analysis to evaluate the efficacy of our results. To the best of our knowledge, this is the first article to focus on quantum Milne–Mercer-type inequalities and we hope that our methods and findings inspire readers to conduct further investigation into this problem.

In tackling the intricate challenge of selecting optimal cities for sports events, our innovative approach, the stepwise weight assessment ratio analysis (SWARA)-alternative ranking order method accounting for two-step normalization (AROMAN) method, merges the SWARA and the AROMAN under the intuitionistic fuzzy set (IFS)-based framework. Noteworthy for its integration of linear and vector normalization techniques, the AROMAN method ensures precise data structures, enhancing the reliability of subsequent calculations. A critical facet of our methodology is its practical application, exemplified in a comprehensive case study evaluating and ranking five alternative cities for hosting sports events. Criteria such as accessibility, facilities, community engagement, weather conditions, economic viability, safety, cultural fit, and environmental impact are considered. This real-world scenario demonstrates the SWARA-AROMAN method’s efficacy in navigating the complexities of city selection, providing decision-makers with a robust tool for informed choices in sports event management. The methodology not only acknowledges the nuanced dynamics of the selection process but also contributes to the creation of impactful and well-rounded sports experiences, aligning seamlessly with the evolving landscape of sports management.