A new correlation for predicting the thermal conductivity of nanofluids; using dimensional analysis

Thermal conductivity of nanofluids is a key thermophysical property, which depends on concentration and size of nanoparticles, temperature and thermophysical properties of the base fluid. Over last decades, several works have been done on the thermal conductivity of nanofluids while a number of numerical and theoretical models have been proposed. However, most of these models were not able to predict appropriately the thermal conductivity for a variety of nanofluids. In the present paper, using the Vaschy-Buckingham theorem, new correlations for predicting the thermal conductivity of nanofluids were developed based on the existing experimental data. The new correlation proposed took into account the Brownian motion, the variation of volume fraction, the temperature and the size distribution of nanoparticles. The expression developed successfully predicts the thermal conductivity of a variety of nanofluids, TiO2, Al2O3, Al, Cu, Fe, MWCNTs/EG, Al2O3, SiO2/methanol, TiO2, Al2O3, CuO, MWCNTs/water, Al2O3/radiator coolant, Al2O3/R141b, Al, CNTs/Engine Oil, and Cu/Therminol 66, and suits the data with a mean and standard deviation of 2.74%, 3.63%, respectively. The correlation was derived from 196 values of nanofluids thermal conductivity, 86% of them are correlated within a mean deviation of ±5%, while 98% of them belong to an interval of ±10%. Moreover, the proposed correlation has been tested on 284 values of thermal conductivity of different nanofluids, and the predicted values have been found in excellent agreement with the experimental ones with a mean deviation of 3%. The mean deviation between the correlated and the tested point found to be 2.94%. The present correlation will be a good tool for engineers in preparing the nanofluid for different applications in heat exchangers and thermal solar collectors.