Adding a small volume fraction of carbon nanotubes (CNTs) to a liquid enhances the thermal conductivity significantly. Recent experimental findings report an anomalously wide range of enhancement values that continue to perplex the research community and remain unexplained. In this paper we present a theoretical model based on three-dimensional CNT chain formation (percolation) in the base liquid and the corresponding thermal resistance network. The model considers random CNT orientation and CNT-CNT interaction forming the percolating chain. Predictions are in good agreement with almost all available experimental data. Results show that the enhancement critically depends on the CNT geometry (length), volume fraction, thermal conductivity of the base liquid and the nanofluid (CNT-liquid suspension) preparation technique. Based on the physical mechanism of heat conduction in the nanofluid, we introduce a new dimensionless parameter that alone characterizes the nanofluid thermal conductivity with reasonable accuracy (∼±5%). © IOP Publishing Ltd.