Optimization of heat transfer in Sutterby nanofluid flow driven by a flexible surface with gyrotactic microorganism and activation energy

Abstract The present study investigates the bio‐convective, electrically conductive flow of a Maxwell–Sutterby nanofluid through an exponentially stretching channel under the influence of viscous dissipation and an exponential heat source/sink. The primary novelty of this work lies in the analysis of activation energy and thermal characteristics of the system in the presence of thermophoretic diffusion and nonlinear radiation effects, incorporated within a revised mathematical framework based on boundary layer theory. The governing nonlinear partial differential equations are formulated using the boundary layer approximations. These equations are subsequently transformed into a dimensionless form through appropriate similarity transformations and solved employing the Runge–Kutta–Fehlberg (RKF45) method to ensure computational accuracy and reliability of the results. Graphical representations are presented to illustrate the influence of key parameters on the pertinent flow profiles, supplemented by numerical data. A convergence criterion is established to verify the precision of the proposed model parameters. The outcomes of this study provide valuable insights that may guide future experimental validation and contribute to the improved design of mechanical systems utilizing nanofluids for enhanced heat and mass transfer performance.