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 current research explores the thermal transport and entropy generation phenomena in a three-dimensional magneto-bioconvective Casson nanofluid stagnation-point flow over a rotating Riga plate in the presence of thermal radiation, Joule heating, and an exponential heat source. The flow is considered within a rotating frame of reference, while gyrotactic microorganisms are incorporated to analyze bioconvection phenomena in the Casson nanofluid. The improved Buongiorno nanofluid model is employed to account for Brownian motion and thermophoretic diffusion effects. Convective boundary conditions are imposed to accurately describe the thermal transport mechanism at the surface. Suitable similarity transformations are utilized to convert the governing nonlinear partial differential equations into a system of dimensionless ODEs (ordinary differential equations). The consequential mathematical model is resolved analytically using the homotopy analysis method (HAM). The impacts of various physical parameters on velocity, temperature, nanoparticle concentration, microorganism density, and entropy generation are examined through graphical illustrations. The obtained results reveal that the velocity profiles decrease with increasing values of the magnetic parameter, Casson parameter, and mass Grashof number, whereas the Hartmann numbers in both axial directions enhance the fluid velocity. The temperature distribution significantly increases due to stronger thermal radiation, Joule heating, exponential heat generation, and larger Biot number values. Furthermore, the nanoparticle concentration profile intensifies with increasing thermophoresis parameter and activation energy, while Brownian motion enhances nanoparticle dispersion within the fluid. The density of motile microorganisms is found to increase with higher Peclet number values. Entropy generation is amplified by thermal radiation, magnetic effects, and Joule dissipation, indicating greater irreversibility within the system. The present investigation provides useful insights for advanced thermal engineering systems, bioconvective transport mechanisms, and industrial applications involving electromagnetic heating and nanofluid technologies.