Fractal analysis of the effect of particle aggregation distribution on thermal conductivity of nanofluids

• A thermal conductivity model is derived based on fractal aggregation distribution.
• The relationship between aggregation shape and fractal dimension is analyzed.
• Predictions of the proposed model show good agreement with experimental data.

A theoretical effective thermal conductivity model for nanofluids is derived based on fractal distribution characteristics of nanoparticle aggregation. Considering two different mechanisms of heat conduction including particle aggregation and convention, the model is expressed as a function of the fractal dimension and concentration. In the model, the change of fractal dimension is related to the variation of aggregation shape. The theoretical computations of the developed model provide a good agreement with the experimental results, which may serve as an effective approach for quantitatively estimating the effective thermal conductivity of nanofluids.