Optimization of an Al₂O₃–Water Nanofluid Loop: Response Surface Modeling, ANOVA and Desirability Analysis for Thermoelectric Cooling

Victor Chimdike Obinani (Department of Mechanical Engineering, College of Engineering and Technology, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria)
Chinedum Ogonna Mgbemena (Department of Mechanical Engineering, College of Engineering and Technology, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria)
Olusegun David Samuel (Department of Mechanical Engineering, College of Engineering and Technology, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria)

International Journal of Quantitative Research and Modeling
Vol. 7 No. 3 (2026): International Journal of Quantitative Research and Modeling (IJQRM)

A closed Al₂O₃–water nanofluid loop was built to reject heat from the hot junctions of a dual-thermoelectric household water dispenser, and its operating window was mapped experimentally and then optimized statistically. A full factorial design of 48 runs was executed on an instrumented rig, combining four nanoparticle sizes (10, 20, 30 and 50 nm), four volume concentrations (0.5, 2.0, 4.0 and 5.0 vol%) and three volumetric flow rates (0.5, 1.2 and 2.4 L min⁻¹) at a fixed module current of 4.0 A and an ambient temperature of 27 ± 1 °C, with a deionized-water baseline recorded separately. Six responses were measured or derived for every run: hot-junction temperature, pressure gradient, Darcy friction factor, Nusselt number, performance evaluation criterion (PEC) and system coefficient of performance (COP). Five responses were fitted with quadratic response surfaces and PEC with a linear model; each model was reduced by backward elimination at α = 0.05 under the hierarchy principle, tested by Type-III analysis of variance, and checked against externally studentized residual diagnostics and leave-one-out PRESS statistics. The COP model was highly significant (F = 46.15, p < 0.0001) with R² = 0.916, adjusted R² = 0.896 and predicted R² = 0.874. Volume concentration was the dominant term (F = 85.36, p < 0.0001) and its negative quadratic partner (F = 49.59, p < 0.0001) located an interior maximum at 4.28 vol%, a reversal that is also present at 5.0 vol% in every raw series and in the directly measured hot-junction temperature. The linear PEC model was significant overall (F = 4.30, p = 0.0096) but was governed by flow rate (F = 8.35, p = 0.0060) rather than by concentration, and accounted for only 22.7% of the observed variance, so the factor that controls loop efficiency is not the factor that controls device efficiency. Derringer–Suich desirability optimization over all six responses under equal weighting converged on a particle size of 11.4 nm, a concentration of 4.30 vol% and a flow rate of 2.4 L min⁻¹, with a composite desirability of 0.649, a predicted COP of 0.667 against 0.42 for the deionized-water baseline and a predicted hot-junction temperature of 32.7 °C. At the nearest tested condition, five of the six responses were predicted to within 8% and COP to within 4.7%.