Thermal circuits based model for predicting the thermal conductivity of nanofluids

Abstract

A cell model based on thermal circuits is presented in this paper. The effective nanofluid thermal conductivity is rooted in heat transfer principles and scaling analysis. A combined series-parallel thermal circuits model has been presented for the static component of effective thermal conductivity and the heat transfer by micromixing due to Brownian motion of the particles have been taken in parallel to the static circuit. The effect of stationary, well-dispersed solids suspension as well as that of the convection due to Brownian motion has been considered. While the entire model is phenomenological, the coefficient for the Brownian motion component was empirical. The model was validated using data from nine studies that included oxide-water, oxide-ethylene glycol (EG), metal-water and metal-EG systems. Amongst the oxides, Al2O3, TiO2, CuO, and ZnO were considered. The coefficient was found to be of the order of one which validated the expectation that hdpkL∼PrRe1/2π1/2. The model was further refined by empirically determining the form of the coefficient for the convective term due to Brownian motion. It was found that the convective term is a function of temperature, solids volume fraction and particle size. A key aspect of the model is that it identifies a critical diameter at which the thermal conductivity is the maximum.