This study is focused on modeling and simulations of hybrid nanofluid flow. Uranium dioxide $U{O}_2$ nanoparticles are hybrid with copper Cu, copper oxide CuO and aluminum oxide $A{l}_2{O}_3$ while considering blood as a base fluid. The blood flow is initially modeled considering magnetic effect, non-linear thermal radiation and chemical reactions along with convective boundaries. Then for finding solution of the obtained highly nonlinear coupled system we propose a methodology in which q-homotopy analysis method is hybrid with Galerkin and least square Optimizers. Residual errors are also computed in this study to confirm the validity of results. Analysis reveals that rate of heat transfer in arteries increases up to 13.52 Percent with an increase in volume fraction of Cu while keeping volume fraction of $U{O}_2$ fixed to 1% in a base fluid (blood). This observation is in excellent agreement with experimental result. Furthermore, comparative graphical study of $Cu,CuO$ and $A{l}_2{O}_3$ for increasing volume fraction is also performed keeping $U{O}_2$ volume fraction fixed. Investigation indicates that Cu has the highest rate of heat transfer in blood when compared with CuO and $A{l}_2{O}_3$. It is also observed that thermal radiation increases the heat transfer rate in the current study. Furthermore, chemical reaction decreases rate of mass transfer in hybrid blood nanoflow. This study will help medical practitioners to minimize the adverse effects of $U{O}_2$ by introducing hybrid nano particles in blood based fluids.

This paper investigates the magnetohydrodynamic (MHD) flow along with heat and mass transfer behavior of Casson-type hybrid nanofluid through aluminum oxide (\({\varvec{A}}{{\varvec{l}}}_{2}{{\varvec{O}}}_{3}\)) as well as titanium dioxide (\({\varvec{T}}{\varvec{i}}{{\varvec{O}}}_{2}\)) nanoparticles dispersed throughout engine oil, a thermally stable functioning fluid that is used in utmost industrialized thermal exchanger applications. The advanced model incorporates the collective influences of heat radiation, Darcy–Forchheimer permeable media resistance, magnetic field-heating, and activation energy under nonlinear chemical reaction circumstances. Employing similarity transformations, the intricate governing equations are streamlined to ordinary differential equations (ODEs) that are numerically solved by means of the Bvp4c solver. The numerical solutions attained via the Bvp4c algorithm are employed for training a Morlet Wavelet Neural Network with Particle Swarm Optimization as well as Neural Network Algorithm (MWNN–PSO–NNA), through improving prediction robustness as well as generality behavior. The results show that strengthening the magnetic field leads to a decrease in the velocity distribution whereas thermal radiation growth in temperature, via variations falling within the range of 15–25% across the flow domain. Raising activation energy nearly 30% is observed to regulate species concentration as well as promote a more controlled thermal response inside the porous structure. In comparison with the base fluid and single-nanoparticle suspensions, the hybrid nanofluid exhibits superior thermal performance. Moreover, the MWNN–PSO–NNA outcomes remain in close agreement with the numerical solutions, yielding error levels of the order 10⁻⁵–10⁻⁶, which confirms the reliability of the proposed framework for complex non-Newtonian hybrid nanofluid systems relevant to industrial thermal applications. The proposed neural network model demonstrates strong predictive capability, achieving an accuracy greater than 99% while reducing computational time by approximately 45% when compared with traditional numerical methods. An ANN is developed to rapidly predict flow, heat, and mass transfer. Trained on bvp4c data, it achieves comparable accuracy while reducing computational time by 45% compared to repeated numerical simulations. Additionally, the hybrid nanofluid formulation displays strong potential for industrial lubrication applications, thermal control of mechanical components, and energy-based cooling systems, where improved heat transfer productivity is a main performance requirement. The main motivation of this study is to address the growing demand for efficient thermal management in industrial lubrication systems involving non-Newtonian fluids. The goal is to apply a robust MWNN–PSO–NNA framework to accurately predict the flow, heat, and mass transfer characteristics of Casson hybrid nanofluid over a radially stretching surface under combined physical effects. This study is the first to integrate engine-oil-based Casson hybrid nanofluid modeling with Darcy–Forchheimer porous effects and an optimized MWNN–PSO–NNA framework, providing highly accurate thermal–fluid predictions relevant to advanced industrial heat transfer systems.

In this paper, a new numerical technique was developed to investigate magnetohydrodynamic (MHD) flow of Williamson nanofluid past a nonlinear stretching surface imbedded in a porous medium laden with Soret and Dufour effects. The control equations, which are highly nonlinear partial differential equations, are first converted into ordinary differential equation (ODEs) using similarity transformation and then are solved effectively by the hybrid computational method applying Morlet Wavelet Neural Networks (MWNNs) combined with a heuristic optimizers neural network and particle swarm as MWNNs-PSO-NNA. The proposed MWNNs-PSO-NNA shows a very low mean square error and Theil’s Inequality Coefficient indicating that the accuracy of the model. To check the convergence and validation of the proposed approach, computing the hundred independent runs for statistical metrics. The fitness function, MSE and TIC values ranging from 10^–07 to 10^–05, 10^–09 to 10^–07 and 10^–06 to 10^–04 respectively. It is found that increasing the effects of the Williamson number, magnetic parameter, porosity and stretching index inhibit the velocity field while Brownian motion as well as the Williamson number enhances the temperature profile. The concentration rises with Soret and Brownian motion parameters but diminishes with intensified thermophoresis and magnetic influences. These findings confirm that the proposed hybrid model is not only computationally robust but also highly effective for solving complex fluid flow problems in engineering and applied sciences.

This manuscript contains the modeling and analysis of an unsteady Carreau fluid with a magnetohydrodynamical effect over a stretching sheet. The governing momentum and energy equations admit a self-similarity solution. The system of ordinary differential equations has been solved analytically by the homotopy analysis method (HAM) and numerically by BVP4C (Matlab routine). An analysis of results shows that obtained analytical and numerical solutions are in excellent agreement with existing results in the literature. Furthermore, the effect of various fluid parameters on the velocity and temperature profiles are studied graphically. It is observed that velocity increases in the stretching sheet for power law index n and the Weissenberg number $We$, whereas it decreases for magnetic parameter $M^2$. Tabular analysis on skin friction and heat transfer rate is also presented against pertinent fluid parameters.