Powder Technology, Volume 239, May 2013, Pages 409-414.
Boqi Xiao, Yi Yang, Lingxia Chen.
School of Mechanical and Electrical Engineering, Sanming University, Sanming 365004, PR China and
Institute of Textiles and Clothing, Hong Kong Polytechnic University, Kowloon, Hong Kong and
Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong.
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.
This work was supported by the National Natural Science Foundation of China (Grant No. 11102100), the Natural Science Foundation of Fujian Province of China (Grant No. 2012J01017), and the Scientific Research Special Foundation for Provincial University of Education Department of Fujian Province of China (Grant No. JK2011056).
In this work, the famous Maxwell’s Equation is corrected. We construct Maxwell-Xiao Equation which can effectively predict thermal conductivity of nanofluids based on fractal geometry theory.
Fig.1 compares the effective thermal conductivity of nanofluids from the present model calculated using Eq. (26) and that from reported experiments [6,8,57]for different nanoparticle-water suspensions. It is seen from Fig. 1 that the predicted thermal conductivities by fractal technique are in good agreement with the experimental data. It can be found that the effective thermal conductivity of the nanofluids increases with increasing of the concentration of nanoparticles from Fig. 1. It may also be noted in Fig. 1 that the effective thermal conductivity of the nanofluids for the smaller size of nanoparticles is larger than the bigger size at given concentration. This can be explained that the small size the nanoparticles at lower concentration causes the increase of nanoparticles moving in fluids, leading to the increase of the effective thermal conductivity from convection.
Figure 2 depicts the average size of nanoparticles dependence of the effective thermal conductivity of the nanofluids. It can be seen from Fig. 2 that the effective thermal conductivity () decreases with the increase of the average size of nanoparticles for CuO–water nanofluid. It is also interestingly seen from figure 2 that when the average size of nanoparticles is less than about 16 nm, the effective thermal conductivity increases drastically. This reveals that the convection due to the Brownian motion of nanoparticles has the significant influence on the thermal conductivity of nanofluids when the average size of nanoparticles is less than about 16 nm. This phenomenon can be interpreted that the small the size of nanoparticles causes the increase of Brownian motion of the nanoparticles in the fluids. However, the Maxwell model is not relevant to the average size of nanoparticles.
Fig. 1. Comparison of the proposed model (Eq. (26)) and current experimental data
for different nanofluids.
Fig. 2. Dependence of the thermal conductivity enhancement on nanoparticles diameter for the CuO–Water suspension at .