A comparative study of RSM regression models to achieve the most optimal rheological behavior of MWCNT/SiO2(50−50)-SAE40 hybrid nanofluid and provide optimal lubrication conditions during the start of movement

In this statistical study, the performance of MWCNT-SiO2(50−50)/SAE40 hybrid nanofluid (HNF) was investigated and compared with different regression models. The purpose of this study is to determine and present the best function of the modeler in predicting the objective function in accordance with the quality indicators of RSM for the cold environmental conditions of lubrication (or the equivalent of starting). The study was carried out in laboratory conditions with temperature range T = 25–55 °C, solid volume fraction SVF= 0.0625–1% and shear rate γ̇=SR= 666.5–9331 s−1. By comparing the performance of the model maker based on statistical quality indicators, it was found that the Quartic model is the most suitable model for analyzing the rheological behavior of the present HNF. To select the most optimal model, the statistical criteria of coefficient of determination, coefficient of variation (C.V), probability value and correlation deviation (C.D) were used. The values of each statistical index for the quartic model are respectively 0.9995, 1.11, 2.9956003e-246 and − 3.38%