Sensitivity analysis of heat transfer optimization in a buoyancy driven slip flow of Williamson-tri-hybrid nanofluid over thin needle using RSM

This study investigates the optimum heat transfer in a buoyancy-driven Williamson tri-hybrid nanofluid (HNF) flow over a thin needle, incorporating Cattaneo-Christov heat flux (CCHFM), slip effects, and nanoparticle-enhanced thermal efficiency utilizing response surface methodology (RSM). The flow over a thin needle has various applications in advanced cooling systems, biomedical devices, and energy-efficient thermal management. The CCHFM, Thompson and Thorian slip effects and heat transfer efficiency as a result of the dispersed three nanoparticles is mainly focused in this communication. The Runge-Kutta (RK-4) method is used to numerically solve the governing problem. Regression analysis is implemented to estimate the regression coefficients, and the RSM is utilized to establish a correlation between the nanomaterials load and the Nusselt number. The experimental sensitivity analysis is carried out to determine the sensitivity of three dispersed nanoparticle volumetric friction on Nusselt number. The results indicate that the Richardson number lowers the temperature profile. An increasing trend for velocity is seen because of positive thermal buoyancy. The tri-HNF increases the efficiency of heat transmission. Uplifting Weissenberg number result in reduced velocity because of elastic effects. Velocity and temperature show similar behavior against velocity slip and velocity ratio parameter. Both temperature and velocity show a declining trend under CCHFM due to thermal relaxation parameter. In comparison to Cu and A l 2 O 3 , the MnZnF e 2 O 3 display increasing effect on heat transfer rate. The Nusselt number is more sensitive to higher volume fraction of 5%.