Response surface methodology-based new model to optimize heat transfer and shear stress for ferrites/motor oil hybrid nanofluid

Purpose This study aims to optimize heat transfer efficiency and minimize friction factor and entropy generation in hybrid nanofluid flows through porous media. By incorporating factors such as melting effect, buoyancy, viscous dissipation and no-slip velocity on a stretchable surface, the aim is to enhance overall performance. Additionally, sensitivity analysis using response surface methodology is used to evaluate the influence of key parameters on response functions. Design/methodology/approach After deriving suitable Lie-group transformations, the modeled equations are solved numerically using the “spectral local linearization method. ” This approach is validated through rigorous numerical comparisons and error estimations, demonstrating strong alignment with prior studies. Findings The findings reveal that higher Darcy numbers and melting parameters are associated with decreased entropy (35. 86% and 35. 93%, respectively) and shear stress, increased heat transmission (16. 4% and 30. 41%, respectively) in hybrid nanofluids. Moreover, response surface methodology uses key factors, concerning the Nusselt number and shear stress as response variables in a quadratic model. Notably, the model exhibits exceptional accuracy with R² values of 99. 99% for the Nusselt number and 100. 00% for skin friction. Additionally, optimization results demonstrate a notable sensitivity to the key parameters. Research limitations/implications Lubrication is a vital method to minimize friction and wear in the automobile sector, contributing significantly to energy efficiency, environmental conservation and carbon reduction. The incorporation of nickel and manganese zinc ferrites into SAE 20 W-40 motor oil lubricants, as defined by the Society of Automotive Engineers, significantly improves their performance, particularly in terms of tribological attributes. Originality/value This work stands out for its focus on applications such as hybrid electromagnetic fuel cells and nano-magnetic material processing. While these applications are gaining interest, there is still a research gap regarding the effects of melting on heat transfer in a NiZnFe₂O₄-MnZnFe₂O₄/20W40 motor oil hybrid nanofluid over a stretchable surface, necessitating a thorough investigation that includes both numerical simulations and statistical analysis.