Optimizing a modified Buongiorno model of ternary nanofluid flow with radiation and gyrotactic microorganisms using RSM-Taguchi approaches

Purpose This study aims to investigate the behavior of a ternary nanofluid composed of alumina (Al2O3), copper (Cu) and titania (TiO2) nanoparticles dispersed in water (H2O) flowing over a permeable shrinking surface. Thi study applies the modified Buongiorno model, which accounts for Brownian motion, thermophoresis, gyrotactic microorganisms and radiation. The main aim is to analyze the thermal characteristics of current flow and to determine the optimal nanoparticle composition for maximizing heat transfer rates. Design/methodology/approach Two types of analysis are conducted. The numerical analysis is first involved by formulating the governing differential equations using a similarity transformation technique. The equations are then solved using the bvp4c solver in MATLAB, where detailed graphical results of velocity and temperature profiles are presented. At the same time, a statistical analysis is performed to optimize the heat transfer rate using response surface methodology (RSM) and the Taguchi method in Minitab software. Findings The numerical results reveal that the shrinking parameter produces dual solutions (first and second branches), where the first branch of the solution is proven to be stable by a temporal stability analysis. Notably, ternary nanofluid flow achieves the highest temperature distribution compared to single and hybrid nanofluids. The presence of radiation and thermophoresis parameters is also demonstrated to significantly increase the temperature profiles. From the optimization, the RSM suggests that the highest number of Al2O3, Cu and TiO2 nanoparticles predicts the maximum heat transfer rate at 33.6%, while the Taguchi method estimates it at 32.3%. Practical implications The current mathematical model and statistical approach used in this study can be applied in areas such as biomedical fluids or drug delivery systems, where improved heat transfer and fluid stability are important in achieving optimal outputs. The ability to control and enhance thermal properties through nanoparticle composition and surface conditions can benefit various engineering and medical applications. Originality/value The originality of this work lies in applying both RSM and the Taguchi method to a ternary nanofluid system modeled by the modified Buongiorno model. While the Buongiorno model has been widely used in nanofluid studies, its combination with statistical optimization techniques for a ternary nanoparticle mixture provides a new understanding of thermal performance concepts. This is especially true with gyrotactic microorganisms and radiation. The dual approach of optimization techniques allows for both theoretical and practical optimization of nanofluid-based systems.