<p>The current research focuses on optimizing heat transfer in the electro-osmotic bioconvective flow of a blood-based Casson hybrid nanofluid, which comprises multi-walled carbon nanotubes and copper (Cu) nanoparticles within a squeezing channel. The study considers significant aspects, including quadratic thermal radiation, Joule heating, a porous media in the electro-magnetized flow, and applying velocity slip and convective temperature boundary conditions at the top plate. An extensive entropy study is conducted to examine the system-generated thermodynamic irreversibilities. The dimensional equations that govern the system under consideration are non-dimensionalized, implementing relevant dimensionless similarity variables. A semi-analytical series solution is acquired from the dimensional governing equations following the semi-analytical homotopy analysis method. An innovative feature of this research is heat transfer optimization, which is achieved by applying the response surface methodology technique and a comprehensive quadratic central composite design architecture. Additionally, sensitivity analysis was carried out to identify the most influential parameter. The findings reveal that the heat transfer rate positively correlates with the electroosmotic effect, zeta potential, and nanoparticle inclusion in the fluid. The system produces higher entropy for enhanced magnetic effect, Eckert number, and nanoparticle concentration. Electroosmosis induces higher entropy near the upper plate than in its absence. This research can be applied to microfluidic biomedical devices, optimizing heat transfer for better drug delivery and diagnostics temperature control.</p>