A survey of practical equations for prediction of effective thermal conductivity of spherical-particle nanofluids

Abstract Over the last two decades a large number of compact and convenient analytical and empirical equations for predicting effective thermal conductivity of nanofluids have appeared in the literature. The equations themselves are expressions of the underlying physics thought responsible for the enhancement to thermal conductivity, including effects of base fluid and particle properties, particle diameter, morphology, concentration, temperature, interfacial phenomena, Brownian motion, nano-scale heat transport and particle clustering. It is found that while all correlations appear well supported with experimental data when originally published, the relative importance given to the various mechanisms is in conflict. Representative equations for nanofluid thermal conductivity are compared with a much larger, updated experimental data set. While classical analytical continuum models generally under-predict the enhancement, surprisingly, there are also a small number of nanofluid data with anomalously low thermal conductivity. Models which take into account nanoscale effects are generally found to over-predict the enhancement when compared with a larger number of data. The most successful predictions come from empirical equations where a regression analysis has fitted the correlation to a significant number of experimental data. In this paper, a review of the latest experimental work is given, theoretical, analytical and empirical investigations for predicting thermal conductivity of nanofluids are introduced and critical comparisons of equations with available data are presented.