Experimental study and mathematical modeling of dynamic viscosity of MgO–Y₂O₃–SiO₂/water ternary hybrid nanofluid

In recent years, nanofluid (NF) rheology and thermal behavior have attracted growing attention due to their promising industrial applications. This study experimentally examines how temperature (T) and solid volume fraction (SVF) affect the dynamic viscosity (µ) of a ternary hybrid nanofluid (THNF) based on MgO–Y₂O₃–SiO₂ dispersed in water. In addition, mono nanofluids (MNFs) and binary hybrids nanofluids (HNFs) containing different combinations of the three oxides were prepared and analyzed under identical conditions. All NF samples were synthesized via the conventional two-step method, with SVFs ranging from 0.06% to 0.10%, and T varying between 20 °C and 60 °C. Zeta potential analysis confirmed the stability of the THNF. The µ measurements were performed using a Brookfield viscometer. Results indicate a consistent decrease in µ with rising T, while an increase in nanoparticle (NP) concentration leads to higher µ at any given T. Among all samples, Y₂O₃-based MNF exhibited the highest µ, with a value of 2.886 at 20 °C and SVF of 0.10%, corresponding to an enhancement of 187% compared to the BF. The THNF also showed significant thickening due to synergistic interactions between its constituents. Lastly, a predictive mathematical correlation was developed to estimate µ as a function of T and SVF. The proposed model closely matched the experimental data, confirming its reliability for future implementations. Lastly, two distinct mathematical modeling approaches were employed to estimate µ as a function of T and SVF. A 7th-degree polynomial regression model was developed, achieving an exceptional R2 ≈ 0.9996, alongside a Response Surface Methodology (RSM) model rigorously validated via Leave-One-Out Cross-Validation (LOOCV), achieving an R2 ≈ 0.987. Both models closely matched the experimental data, confirming their reliability for practical engineering applications. Effects of T (20–60 °C) and concentration (0.06–0.10 %) were experimentally studied. Increase in concentration/or decrease in T consistently resulted in higher viscosity. Y₂O₃/water nanofluid has highest µ increase, followed by MgO–Y₂O₃ and MgO nanofluid. SiO₂/water nanofluid has lowest µ increase, confirming mild rheological influence. MgO–Y₂O₃–SiO₂/water nanofluid was found to behave as a Newtonian fluid.