Modeling the effective thermal conductivity of nanofluids using full factorial design analysis

In this paper, a full factorial design analysis is proposed for predicting nanofluid thermal conductivity ratio (TCR) as well as determining the effects of critical factors and their interactions. A statistical design of experiment approach with three variables (volume fraction, temperature, and nanoparticle diameter) at two levels is carried out. Three types of oxide-water nanofluids (Al2O3-water, CuO-water, and TiO2-water) are used to evaluate the effectiveness of the proposed mathematical model. The significance and adequacy of the regression model were evaluated by the analysis of variance. The predicted model has a root mean square error equals to 0.0074, R-2 = 0.99, and P < .0013, thus showing good results compared to a set of experimental data as well as other mathematical model results. The results illustrate that the TCR of metallic oxide nanofluids increases with temperature and nanoparticles volume fraction but decreases when nanoparticle size intensi?es. Furthermore, it is found that the nanoparticles volume fraction has a great impact on the nanofluids thermophysical properties. Finally, the obtained results confirm that the proposed model is considerably accurate and capable of predicting nanofluids thermal conductivity and that it can be used with ease as an alternative to many other models.