Thermodynamic irreversibility and heat transfer characteristics of MHD Eyring–Powell tri-hybrid nanofluid flow over a rotating disk

Advanced applications involving rotating machinery, thermal management systems, and bio-microfluidic technologies require working fluids capable of providing enhanced heat transport while maintaining controlled thermodynamic losses. In this context, tri-hybrid nanofluids offer improved thermal performance; however, the influence of non-Newtonian rheology on entropy generation in rotating-disk configurations, particularly in the presence of motile microorganisms, remains insufficiently explored. The present study investigates the individual effects of the two Eyring–Powell fluid parameters together with magnetic-field, porous-medium, and thermal-radiation effects on the hydrodynamic, thermal, bioconvective, and entropy-generation characteristics. A single-phase mathematical model is formulated for a tri-hybrid nanofluid containing [ZrO 2 , MWCNT, Fe 3 O 4 ] nanoparticles dispersed in an ethylene glycol–water mixture. The formulation incorporates nonlinear thermal radiation, viscous dissipation, and Joule heating to account for important thermal and irreversible effects. Through an appropriate similarity transformation, the coupled governing partial differential equations are converted into a system of nonlinear ordinary differential equations and solved numerically using the fourth-order Runge–Kutta shooting technique. The results demonstrate that the two Eyring–Powell parameters exhibit contrasting effects on the thermodynamic response: an increase in \(\lambda _{1}^{ * }\) , promotes shear-thinning behavior and decreases entropy generation, whereas \(\lambda _{2}^{ * }\) enhances resistance to deformation and increases entropy generation. Furthermore, increasing the Brinkman number from 1.0 to 3.0 intensifies irreversibility and decreases the Bejan numbe, indicating a greater contribution from viscous dissipation relative to heat-transfer irreversibility. A threefold increase in the bioconvection Lewis number reduces the microorganism density number. The surface skin-friction coefficient changes, while the heat and microorganism transfer rates vary by less. These findings indicate that the rheological characteristics exert a considerably stronger influence on the entropy-generation mechanism than on the corresponding surface transport rates.