The current study demonstrates the intricate thermo-solutal transportation features of a nanofluid experiencing non-linear kinematics as it flows across a rough porous stretched interface. Previous work has typically been limited to smooth geometries, narrow parameter ranges, and few physical intuitions. However, this paper extends the analysis to include surface roughness, porosity effect, nonlinear stretching and essential physical phenomena like effect of magnetic field, Brownian motion special case thermophoresis effect and variable suction/injection. The resulting extension does not only reproduce realistic flow cases, but reveals extremely sensitive solution behaviors that have been completely untouched in the literature. Using scaling transformation approach, the governing non-linear partial differential equations (PDEs) for the transport of momentum, energy, and solutal in the transformed independent variables are translated into a set of coupled ordinary differential equations (ODEs). Numerical simulation of the above transport equations with ten dimensionless parameters is done using the MATLAB BVP4C (built in solver) approach, which ensures computational stability and high precision across broad parametric domains. Additionally, using an expanded parameter domain revealed previously unknown solution properties. For instance, as the thermophoretic limitation raised, the species concentration rose by 5% and fell by 12%. Additionally, sensitivity was demonstrated by the velocity profiles shifting by 20% in response to a small variation in the slip parameter. Finding the limits at which qualitatively reactions to system modifications and other non-physical solutions arise from the qualitative responses is notably innovative. Such findings will propel the development of more efficient coatings and temperature control techniques, offering helpful advice to greatly improve transportation effectiveness in actual nanofluid applications.

The study presents a computational framework based on machine learning for the study of blood nanofluid flow and heat transmission via stenotic arteries. Calculation of the velocity and temperature fields that couple together for the system of blood nanofluid is done using a new form of a hyperbolic tangent sigmoid transfer function (HTSTF). This new HTSTF is applied in combination with the Navier–Stokes equations to solve the nonlinear model using a deep neural network (DNN) made up of two hidden layers with 30 neuron count for those layers, respectively. DNN is trained using Bayesian regularization and the Levenberg–Marquardt back propagation method. A valid set of data is created using bvp4c (two-point boundary value problem), which is broken down into a training (15%), testing (13%) and validation (72%) data set. The new approach has both very good convergence and very good accuracy; the sample's generated mean square error (MSE) values are 10^–12 to 10^–9 and absolute error values are as small as 10^–7. The sample also shows that there is good correspondence between predicted and reference solutions (for both velocity and temperature) based on statistical regression results. Nanoparticles' volume fraction greatly affects blood's rheological behaviour as well as heat transfer through the stenosed portion of a vessel. This new method is far more efficient and accurate than standard numerical methods and has potential applications within cardiovascular (CV) diagnostics, targeted drug delivery (TDL), and thermal therapies using nanoparticles.