A semi-Analytical model for the thermal conductivity of nanofluids and determination of the nanolayer thickness

Nanofluid shows a huge potential to be the next-generation heat transfer fluid since the nanoparticles can suspend in the base fluids for a long time and the thermal conductivity of the nanofluid can be far above those of convectional solid-liquid suspension. It has long been known that liquid molecules close to a solid surface can form a layer which is solid-like in structure, but little is known about the connection between this layer and the thermal properties of the suspension. In this study, a semi-analytical model for calculating the enhanced thermal conductivity of nanofluids is derived from the steady heat conduction equation in spherical coordinates. The effects of nanolayer thickness, nanoparticle size, volume fraction, thermal conductivity of nanoparticles and base fluid are discussed. A linear thermal conductivity profile inside the nanolayer is considered in the present model. The proposed model, while investigating the impact of the interfacial nanolayer on the effective thermal conductivity of nanofluids, provides an equation to determine its nanolayer thickness for different types of nanofluids. Hence, different relationships between the nanolayer thickness and the nanoparticle size are found for each type of nanofluid. Moreover, based on the present model's prediction, it is found that the effective thermal conductivities of nanofluids show the same result as the Maxwell model when the nanolayer thickness value approaches to zero. Lastly, the effective thermal conductivities of different types of nanofluids calculated by the present model is in good agreement with the experimental results and the prediction is much better than the Maxwell model and Bruggeman model.