An analysis of upper-convected Maxwell nanofluid flow with motile organisms over a stretching surface

Abstract This study investigates the magnetohydrodynamic bioconvective flow of an upper-convected Maxwell (UCM) nanofluid containing gyrotactic microorganisms over a bidirectionally stretching surface under convective thermal boundary conditions. The developed mathematical model incorporates Brownian motion, thermophoresis, and nonlinear thermal radiation within a unified viscoelastic bioconvective framework. This coupled physical configuration has received relatively limited attention in previous studies. By employing suitable similarity transformations, the governing nonlinear partial differential equations are transformed into a coupled system of ordinary differential equations and solved numerically using the MATLAB BVP5C solver. The numerical results are further validated through comparisons with ODE45 and the classical fourth-order Runge–Kutta (RK4) method, showing excellent agreement among the different approaches. The results indicate that increasing the Weissenberg number and magnetic parameter suppresses both axial and radial velocity profiles because of enhanced viscoelastic and Lorentz force effects, respectively, while simultaneously increasing the temperature, nanoparticle concentration, and microorganism density near the wall. In contrast, higher values of the stretching ratio parameter enhance radial transport and reduce the thermal, solutal, and bioconvective boundary layer thicknesses. Furthermore, Brownian motion, thermophoresis and thermal radiation, whereas higher Prandtl, Lewis, and bioconvective Péclet numbers reduce the thermal and microorganism distributions. The present findings provide a comprehensive theoretical framework for optimizing heat and mass transport in magnetic nanofluid cooling systems, porous-media heat exchangers, and bio-microfluidic technologies.