Optimization and sensitivity analysis in time‐dependent magneto‐hydrodynamic squeezing flow of radiative Eyring–Powell hybrid nanofluid with gyrotactic microorganisms: Entropy analysis

Abstract This article explores the heat transfer and entropy generation in a time‐dependent squeezing flow of Eyring–Powell hybrid nanofluid with gyrotactic microorganisms through a horizontal channel. Combining the response surface methodology (RSM) method with a comprehensive quadratic central composite designs (CCDs) design to optimize heat transmission and evaluate parameter sensitivity is a novel feature of this study. The flow incorporates the impact of a magnetic field, heat absorption/generation, thermal radiation, and chemical reaction. The hybrid nanofluid is created by suspending gold and silver nanoparticles in the base fluid of blood, a non‐Newtonian fluid. The research holds relevance in pharmaceutical technology and healthcare industries. Appropriate similarity transformations are applied to the governing partial differential equations (PDEs) to obtain a system of nonlinear ordinary differential equations (ODEs). The semi‐analytical solution is derived using the Homotopy Analysis Method (HAM). The numerical solutions are validated by comparing them with those available for a specific case of the problem, showcasing a favorable agreement. The influence of governing parameters on the modeled system is examined through graphical analysis. Results indicate that significant increases in heat transmission rate are linked to higher levels of thermal radiation and a stronger magnetic impact. The rate of heat transmission is highly sensitive to thermal radiation but it exhibits minimal sensitivity to changes in the volume fraction of gold nanoparticles. Minimizing the magnetic parameter and Eckert number, entropy production in the system can be reduced.