Optimization of heat transfer characteristics of Casson hybrid nanofluid flow over a porous exponentially elongating surface using RSM approach

Research on non-Newtonian fluids has received significant attention in recent years due to its wide-ranging applications in a few engineering fields and applied sciences. Casson fluid, a non-Newtonian fluid characterized by a finite yield stress, finds application in biomedical engineering such as the drug delivery systems, tissue engineering processes, medical devices, etc. Motivated by its applications, the current research work extensively examines the flow behavior of a blood-based Casson hybrid nanofluid with silver and gold nanoparticles over an exponentially elongating sheet. Heat transmission in the Casson hybrid nanofluid is driven by convective, joule, and viscous dissipation, with significant influence from the presence of multiple slips, the porous medium, and magnetic forces. A dimensionless form of the governing equations is obtained through the implementation of a similarity approach and are solved numerically by the utilization of bvp4c package in MATLAB. The current research introduces a novel aspect by optimizing the thermal transport rate employing the Response Surface Methodology (RSM) based Box-Behnken Design (BBD). The outcomes elucidate that the phenomena of viscous dissipation and thermal radiation effectively contribute to enhancing the temperature profile, while the presence of a chemical reaction minimizes the concentration profile. The strengthening of the porous medium and the velocity slip substantially boosts the skin friction and the heat transfer rate. Stronger thermal radiation in the absence of velocity slip tends to enlarge the heat transfer rate of Ag-Au/blood. Additionally, Ag-Au/blood achieves an improvement of approximately 3.25–5.73% in thermal transfer rate surpassing Au/blood across a wide range of porosity parameter. Also, the proposed model demonstrates a remarkable precision with an \(R^{2}\) value of 99.73% for the Nusselt number suggesting the exceptional fit of the model.