The present research explores linear as well as nonlinear radiation patterns based on the MHD non-Newtonian (Maxwell) nanofluid flow having Arrhenius activation energy. This study's core focus is MHD properties in non-Newtonian fluid dynamics and boundary layer phenomena analysis. It initiates with time-dependent equations, employing boundary layer approximations. Extensive numerical computations, executed with custom Compact Visual Fortran code and the EFD method, provide profound insights into non-Newtonian fluid behavior, revealing intricate force interactions and fluid patterns. To check the stability of the solution, a convergence and stability analysis is performed. With the values of Delta Y = 0.25, Delta tau = 0.0005, and Delta X = 0.20; it is found that the model convergence occurs to the Lewis number, Le > 0.016 as well as the Prandtl number, Pr > 0.08. In this context, investigating non-dimensional results that depend on multiple physical factors. Explanation and visual representations of the effects of different physical characteristics and their resultant temperatures, concentrations, and velocity profiles are provided. As a result of the illustrations, the skin friction coefficient and Sherwood number, which are calculated, as well as Nusselt values, have all come up in discussion. Additionally, detailed representations of isothermal lines and streamlines are implemented, and it is pointed out that the development of these features occurs at the same time as Brownian motion. Furthermore, the temperature field for Maxwell fluid is modified due to the impression of chemical reaction as well as the Dufour number (Kr and Du). Our research demonstrates the superior performance of non-Newtonian solutions, notably in cases involving activation energy and nonlinear radiation. This paradigm shift carries significant implications. In another context, the interplay between Maxwell fluid and nonlinear radiation is notably affected by activation energy, offering promising applications in fields like medicine and industry, particularly in groundbreaking cancer treatment approaches.

This study investigated cyclic magneto-hydrodynamic radiative effects in Casson and Maxwell fluids, including nonlinear radiation and Arrhenius activation energy. It promotes non-Newtonian fluid use in diverse fields like industry, manufacturing, sciences, medicine, and engineering. Using boundary layer approximations, non-dimensional equations are formulated. For numerical solutions, widely recognized explicit finite difference method (EFDM) has been utilized. To ensure the robustness of EFDM results, stability and convergence tests are performed. Exploration involve a detailed sensitivity analysis by using RSM, offering a thorough understanding of influential parameters. These analyses explore complex interactions among physical parameters, affecting Nusselt number, skin friction, and Sherwood number. Maxwell fluid's velocity is more affected by periodic magnetic force than Casson fluid, during the presence of nonlinear radiation. Additionally, nonlinear thermal radiation has a greater impact on temperature and concentration profiles compared to linear radiation for both fluids. Moreover, Casson fluid has a stronger influence on the average heat transfer rate compared to Maxwell fluid with nonlinear thermal radiation which is 8.6 % greater than the Maxwell fluid. On the other hand, at constant thermal radiation (Ra), due to decrease of Brownian motion (Nb), the rate of heat transfer is reduced by 1.2 % and 0.3 % respectively for Maxwell and Casson fluid. Also, for thermophoresis parameter (Nt), this rate is reduced by 2 % and 1.6 % respectively. The investigation also revealed that the Ra exhibits a positive sensitivity towards average Nusselt number, while Nb and Nt are displayed a negative sensitivity.

In the automotive, electronics, and energy sectors, heat exchangers and cooling systems can be improved by the flow dynamics of thermally enriched nanomaterials across enlarged surfaces. In biomicrosystems, bionanocooling units, and the petroleum sector, the fluid’s stabilizing properties derive from the presence of microorganisms. Using nonlinear radiation, Arrhenius catalysts, and thermal convection, this work focuses on the electrically induced nanobioconvective migration of Maxwell fluid‐containing organisms across an exponentially grown surface. Using suitable transformations, the governing equations are converted into dimensionless forms to create a mathematical framework for nanofluids based on the Buongiorno model. After a stability analysis, the reformulated flow problems are solved using a finite difference approach, and the computational outcomes are verified against previous research. The results show that larger buoyancy ratios and magnetic components decrease the velocity of the nanofluid, while increasing viscosity and radiation increase its thermal energy. Furthermore, unpredictable motion and enhanced thermophoresis reduce heat transmission. Compared to linear radiation, nonlinear thermal radiation has a far bigger effect on thermal fields. Additionally, fewer dispersed bacteria result in a lower motile microbe density when the Peclet number ( Pe ) is larger. When it comes to estimating microbe density ( Nd ), the model’s statistical validation yields a 99.95% R ² at a 95% confidence level, indicating its dependability. Pe and Ae show the highest and lowest sensitivity to the motile density function in Maxwell fluid, respectively. By improving the circumstances for microbial growth in nanofluid settings, the findings of this study aid in the optimization of biofuel production.

Statistical analysis (SA) stands as an indispensable tool in materials science and engineering, aiding in the understanding and optimization of heat and mass transport processes. This study delves into the interplay between periodic magneto-hydrodynamics (MHD) and chemical reactions concerning entropy generation over an inclined porous cylinder (IPC). We employ a statistical approach, amalgamating the robust 6th order Runge-Kutta (R-K) integration algorithm with the Nachtsheim-Swigert (N-S) shooting iteration method, subsequent to converting the governing equations into Ordinary Differential Equation (ODE) form. The primary objective of this study is to analyze the behavior of entropy generation, unveiling the intricate relationship between entropy dynamics, radiative periodic MHD on IPC, and chemical processes. The numerical findings encapsulate the dynamics of temperature, velocity, and entropy generation, visually portrayed across various dimensionless parameters. The primary findings of this investigation indicate that Casson fluid flow generates 18.99 % more entropy in comparison to Newtonian fluid flow. Furthermore, entropy is 9.87 % larger in an inclined cylinder than in a level cylinder. In contrast, entropy production falls by 3.34 % in the presence of periodic MHD as opposed to non-periodic MHD. Regression study reveals a genuine and significant interaction between variables inside the entropy-generating systems, as well, with a correlation value (R²) of 99.82 % at a 95 % confidence level. The correlation study shows that there is a significant 98.13 % relationship between entropy generation and chemical processes. Understanding the heightened entropy associated with Casson fluid flow benefits tissue engineering, drug delivery systems, and renewable energy. Increased entropy in inclined cylinders aids in optimizing drainage systems, pipeline design, and aerodynamic efficiency in aerospace engineering.

In this study, an integrated finite-difference and deep neural network analysis of the simultaneous multiphysics of coupled momentum, heat, nanoparticle, and pollutant transport in a Sutterby tri-hybrid nanofluid over a quadratically radiative Riga surface is developed. The Fe₃O₄, Al₂O₃, and TiO₂ nanoparticles are considered, and a mixture of propylene glycol and water is used, along with electroosmotic forcing, electromagnetic actuation, nonlinear thermal radiation, viscous dissipation, Brownian motion, thermophoresis, and pollutant transport. The key novelty is the ability to formally connect these strongly coupled nonlinear transport processes with a deep neural network (DNN) surrogate model to allow for the rapid and accurate prediction of complex thermo-fluid and mass-transfer responses. The governing equations are then transformed into nonlinear equations and solved numerically using a finite difference method (FDM) coded in FORTRAN to produce high fidelity numerical data sets that are used to train a feed-forward back-propagation deep neural network (DNN) implemented in Python with PyTorch. The optimized DNN successfully predicted the velocity, temperature, field of nanoparticles, and pollutant concentration, with the RMSE less than (3.2 × 10⁻²) and (R² > 0.987), which indicates that the optimized DNN possesses high predictive accuracy and reliability. The fluid motion is improved by the increased electroosmotic and electromagnetic parameters due to increased electrokinetic and Lorentz forces, and the increased Brinkman number increases the fluid viscous dissipation heating and raises the temperature field. The enhanced Brownian motion facilitates the migration of nanoparticles and greatly affects coupled heat and mass transport while pollutant-related parameters control concentration distributions. The proposed DNN framework has the potential of being an efficient surrogate for fast simulations, parametric evaluation, and optimization for nonlinear multiphysics systems, and has direct applications to thermal management systems in industry, microfluidic processing, electrochemical technologies, electromagnetic flow-control devices, industrial wastewater treatment systems, and pollutant removal systems.