A time dependent model to determine the thermal conductivity of a nanofluid

Abstract

In this paper we analyse the time-dependent heat equations over a finite domain to determine expressions for the thermal diffusivity and conductivity of a nanofluid (where a nanofluid is a fluid containing nanoparticles with average size below 100nm). Due to the complexity of the standard mathematical analysis of this problem we employ a well-known approximate solution technique known as the Heat Balance Integral Method. This allows us to derive simple analytical expressions for the thermal properties, which appear to depend primarily on the volume fraction and liquid properties. The model is shown to compare well with experimental data taken from the literature even up to relatively high concentrations and predicts significantly higher values than the Maxwell model for volume fractions approximately greater than 1