This research article explores the influence of the magnetic field and Joule heating on the 2D stagnation point flow of a Cross-nanofluid. Viscous dissipation, multiple slips, thermophoresis and Brownian motion are embedded in the current model. The artificial neural network (ANN) is one of the notable alternative approaches to solve fluid flow problems since it effectively reduces the processing time. The ANN model is best suited for predicting the data after training, validation and testing with existing data. ANN results are verified via feed-forward neural networks with the Levenberg-Marquard Scheme-based Backpropagation Technique (NN-BLMS). Data was collected for training, certification, and testing in the ANN model. To obtain this data, we solved the nonlinear coupled ordinary differential equations using the MATLAB software bvp4c. ANN model is used to select data, create and train a network, and evaluate its performance using mean square error and regression analysis. ANN data got a good agreement with the numerical data. Velocity, temperature, concentration, entropy generation rate and Bejan number outlines are revealed and deliberated for innumerable cases, namely outer convex, uniform thickness, and inner convex stretching sheet.

This current investigation aims to explore the significance of induced magnetic fields and double-diffusive convection in the radiative flow of Carreau nanofluid through three distinct geometries. To simplify the fluid transport equations, appropriate self-similarity variables were employed, converting them into ordinary differential equations. These equations were subsequently solved using the Runge–Kutta–Fehlberg (RKF) method. Through graphical representations like graphs and tables, the study demonstrates how various dynamic factors influence the fluid’s transport characteristics. Additionally, the artificial neural network (ANN) approach is considered an alternative method to handle fluid flow issues, significantly reducing processing time. In this study, a novel intelligent numerical computing approach was adopted, implementing a Levenberg–Marquardt algorithm-based MLP feed-forward back-propagation ANN. Data collection was conducted to evaluate, validate, and guide the artificial neural network model. Throughout all the investigated geometries, both velocity and induced magnetic profiles exhibit a declining trend for higher values of the magnetic parameter. An increase in the Dufour number corresponds to a rise in the nanofluid temperature. The concentration of nanofluid increases with higher values of the Soret number. Similarly, the nanofluid velocity increases with higher velocity slip parameter values, while the fluid temperature exhibits opposite behavior, decreasing with increasing velocity slip parameter values.

The physiological system loses thermal energy to nearby cells via the bloodstream. Such energy loss can result in sudden death, severe hypothermia, anemia, high or low blood pressure, and heart surgery. Gold and iron oxide nanoparticles are significant in cancer treatment. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. The present study provides a novel implementation of an intelligent numerical computing solver based on an MLP feed-forward backpropagation ANN with the Levenberg–Marquard algorithm to interpret the Cattaneo–Christov heat flux model and demonstrate the effect of entropy production and melting heat transfer on the ferrohydrodynamic flow of the Fe₃O₄-Au/blood Powell–Eyring hybrid nanofluid. Similarity transformation studies symmetry and simplifies PDEs to ODEs. The MATLAB program bvp4c is used to solve the nonlinear coupled ordinary differential equations. Graphs illustrate the impact of a wide range of physical factors on variables, including velocity, temperature, entropy generation, local skin friction coefficient, and heat transfer rate. The artificial neural network model engages in a process of data selection, network construction, training, and evaluation through the use of mean square error. The ferromagnetic parameter, porosity parameter, distance from origin to magnetic dipole, inertia coefficient, dimensionless Curie temperature ratio, fluid parameters, Eckert number, thermal radiation, heat source, thermal relaxation parameter, and latent heat of the fluid parameter are taken as input data, and the skin friction coefficient and heat transfer rate are taken as output data. A total of sixty data collections were used for the purpose of testing, certifying, and training the ANN model. From the results, it is found that the fluid temperature declines when the thermal relaxation parameter is improved. The latent heat of the fluid parameter impacts the entropy generation and Bejan number. There is a less significant impact on the heat transfer rate of the hybrid nanofluid over the sheet on the melting heat transfer parameter.