Developing a novel form of thermal conductivity of nanofluids with Brownian motion effect by means of fractal geometry

Considering the effect of Brownian motion of nanoparticles, an analytical model for effective thermal conductivity of nanofluids is obtained. The formula of calculating effective thermal conductivity of nanofluids is given by taking into account the fractal distribution of nanoparticles. In the present approach, the proposed model is explicitly related to the thermal conductivities of the base fluids and the nanoparticles, the average diameter of nanoparticles, the nanoparticle concentration, the fractal dimension of nanoparticles and physical properties of fluids. It is found that the effective thermal conductivity of nanofluids increases with increasing of the concentration of nanoparticles. And the effective thermal conductivity of nanofluids for the smaller size of nanoparticles is larger than the bigger size at given concentration. A good agreement between the proposed model predictions and experimental data is found. The validity of the fractal model for effective thermal conductivity of nanofluids is thus verified. The proposed fractal model can reveal the physical mechanisms of heat transfer for nanofluids.