In this article, we report the results of a robust model developed for estimating the thermal conductivity of a copper oxide-water nano-suspensions using Response Surface Methodology (RSM) at different temperatures and various mass fractions of nanoparticles. To increase the reliability, an ANOVA statistical approach was utilised to further identify the F-value and P-value of the model. To rank the operating parameters, a normal probability assessment was applied to the data to calculate the value of the noise and potential error distribution of the model. Results revealed that the developed model is robust, reliable and the achieved outcome is in a reasonable agreement with those data obtained by the experiments for the thermal conductivity of CuO (II)/water NF within 25 °C to 40 °C and mass concentrations of 1000 ppm to 4000 ppm. The values of R-squared (R2) and average absolute deviation (AAD%) were 0.9939 and 0.615%, respectively showing the accuracy and robustness of the established model. We also validated the RSM model by conducting further experiments. It was shown that the model can predict the thermal conductivity of the NF with less than 2% error. •A model was developed for prediction of thermal conductivity of CuO-water.•Temperature and mass fraction were considered as input variables.•ANOVA technique was used to identify F-value and P-value of the model.•The obtained values of R2 and AAD% were 0.9939 and 0.615% for proposed model.