This manuscript delineates a thorough study on the heat and mass transfer phenomenon of the Williamson fluid flow embedded with a tetra-hybrid nanofluid evaluating a wide range of considered and physical effects such as magnetohydrodynamics (MHD), porous medium, radiative heat flux, Joule heating, Soret and Dufour effects, and a Stefan blowing parameter at the boundary, and the rest. A tetra-hybrid nanofluid containing nanofluid gold (Au), silver (Ag), titanium dioxide (TiO₂), and aluminium oxide (Al₂O₃) is used for the improvement of significant thermal and mass transport characteristics. In the back, the demand for efficient thermal systems relates to sets with multiple, integrated transport mechanisms; however, the synergistic transport mechanisms have been largely unexplored, and the coupled hybrid advanced dimensions nanofluids have been unexplored in terms of their combined influences on these parameters. The core target was to examine the active relationships within the physical dynamics parameters while also evaluating the relative increases in the velocity, temperature, and concentration. This paper employs a robust computational approach to the study by solving the governing systems of non-linear ordinary differential equations using an appropriate method of similarity transformation and subsequent numerical techniques. The integration of artificial neural network (ANN) models within this spectrum for the first time, with predictions and optimization set for the outputs, adds a new dimension to this work. The data show that incorporating Soret and Dufour effects, along with the tetra-hybrid nanoparticles, markedly increases the Nusselt and Sherwood numbers, indicating improved heat and mass transfer rates. Furthermore, streamline plots are created to illustrate alterations in the flow structure induced by the Soret and Dufour parameters. This research makes valuable contributions to the development of refined cooling technologies, particularly in energy, chemical, and other process-oriented industries, highlighting the practical utility and innovation potential of the synergistic application of artificial neural networks alongside sophisticated nanofluid models.

The purpose of this investigation is to explore in depth a duct flow that incorporates the Al2O3/H2O nanofluid while it is subjected to an external field impact. The duct is made up of two opposing fins that are joined to the walls that are opposite each other. The temperature may be considered to be uniform at the cross-sectional plane of the duct. Additionally, the heat flow at the border is not variable. The finite volume approach was chosen because it offers a satisfactory balance between computing efficiency and the accuracy of its solutions. Importantly, our results indicate that the slowness of flow that is caused by increased Rayleigh numbers may be efficiently regulated by introducing an external magnetic field that has been carefully measured. The significance of this study demonstrates how magnetic-field modulation can be strategically employed to control thermal-hydraulic behavior in internally finned duct systems. The results provide valuable guidance for designing advanced cooling channels, energy devices, and thermal management systems where enhanced heat transfer and flow stability are required under magnetic field environments. The installation of an external magnetic field of moderate strength resulted in a drop of about 75 % in both the maximum velocity and temperature across the duct. Further, a jump of approximately 66 % in the average Nusselt number has been brought about by 25 % increase in the fin height. Through the use of this study framework, a link between thermal-hydraulic behavior and the application of magnetic force is established. The involvement of the Lorentz force, which offers resistance to the motion of the fluid by operating in a direction that is perpendicular to the direction in which the fluid is flowing, and the magnetic force, is brought about as a consequence of the magnetic forces. Consequently, it is possible to draw the conclusion that a larger Nusselt number is the result of both a higher Rayleigh number and a higher magnetic parameter.

Purpose: After being motivated by the diverse applications of blood rheology, nanotechnology, magnetic field, chemical reaction, solar radiation, and non-Darcy porous media in nano-industrial, medical, and chemical engineering domains. The current computational study aims to numerically examine the influences of velocity slip, internal thermal generation or absorption, chemical reactions, and thermal radiation on magneto-hydrodynamic blood-based nanofluid flow with thermo-Brownian motion through an extending interface within a high-permeability medium. Furthermore, the sensitive analysis of flow features with respect to the independent flow parameters is considered. Design/methodology/approach: Suitable similarity equations are employed to convert the partial differential equations into ordinary differential equations together with their boundary constraints. The NDSolve method in Mathematica 11.0 is employed to numerically analyze the flow model, yielding data for the stream function, velocity profile, frictional force coefficient, temperature profile, concentration profile, local Nusselt number, and Sherwood number across several rheological parameters. Main findings: A boundary slip diminishes momentum transmission from the fluid to the surface; when velocity slip escalates, the velocity profile declines. The intensity of the thermal boundary layer escalates with the thermal Grashof number. The temperature distribution is exacerbated by the influence of radiation. As the Brownian parameter grows, the nanofluid temperature intensifies. The chemical reaction parameter substantially affects the enhancement of both skin friction and the Sherwood number. The Nusselt number is enhanced by increasing the thermal Grashof number. The sensitivity analysis indicates that the chemical reaction and concentration Grashof number significantly influence the improvement of rheological properties. Applications: The results of this work are relevant for regulating film thickness, chemical vapour deposition, drug delivery systems, and process optimization.

The analytical results presented here not only deepen the understanding of coupled magneto-bioconvective transport phenomena but also highlight the possibility of various applications including microelectronic cooling, renewable energy systems, electromagnetic flow control, biomedical transport, microbial fuel cells, and advanced nanofluid-based thermal technologies. The present study investigates a three-dimensional Casson nanofluid flow over a Riga surface at stagnation point under the influence of an applied magnetic field, an exponential heat source, and a rotating frame. This study explores how these combined physical mechanisms influence velocity, temperature, nanoparticle concentration, and microorganism distributions. Also, it assesses whether the Homotopy analysis method (HAM) is capable of yielding precise analytical solutions for such a highly nonlinear transport model. The original nonlinear partial differential equations representing magneto-bioconvective Casson nanofluid flow are first converted to a dimensionless system of ordinary differential equations by using appropriate similarity transformations. The coupled system thus obtained is then solved analytically by the HAM. The solutions achieved through this method are checked against results from the literature to ensure their validity. The finding shows that enhancement in the Casson fluid parameter, magnetic parameter, and mass Grashof number leads to a notable decrease in velocity field as a result of increased flow resistance. In contrast, the higher Hartmann numbers produced by the Riga surface aid fluid motion via electromagnetic forcing. A stronger heat source and larger Biot number cause temperature distribution to rise, whereas thermophoresis lowers nanoparticle concentration. Also, higher activation energy affects concentration transport, but an increase in Peclet number boosts microorganism distribution and bioconvection strength.