Three-Dimensional MHD Flow and Heat Transfer Analysis of an Upper-Convected Maxwell Nanofluid with Bioconvection Over a Bidirectional Stretching Surface

This paper examined magnetohydrodynamic flow and heat transfer of an upper-convected Maxwell nanofluid with bioconvection over a bidirectional stretchable surface. The overall objective was to develop a comprehensive model capable of simultaneously capturing viscoelastic effects, nanoparticle transport, heat absorption, nonlinear thermal radiation, and motile microorganism dynamics under the sway of a magnetic field. The originality of this work lay in combining Maxwell fluid elasticity with bioconvection and nonlinear radiation in a complete three-dimensional stretching configuration, which had rarely been investigated collectively. The governing nonlinear PDEs were transformed into a set of coupled ODEs using suitable similarity functions and were solved numerically using the MATLAB bvp4c solver. The sway of key dimensionless parameters, including Brownian motion parameter, magnetic parameter, radiation parameter, Deborah number, thermophoresis parameter, and bioconvection parameters, on velocity, temperature, nanoparticle concentration, and microorganism density were analyzed. The findings indicated that magnetic and elastic effects suppressed velocity while enhancing thermal and concentration boundary layers. Motile microorganisms expressively altered heat and mass transfer characteristics. These results were found to be valuable for applications in thermal management, polymer processing, and bioengineering systems.