Numerical simulation for thermal conductivity of nanograin within three dimensions

In order to improve the accuracy of simulation, the lattice Boltzmann method was adopted to get the thermal conductivities of 3-D nanograins. For the wide application, the length of nanograins axis is between 1 nm to 9 nm, and the diameter ratio of gap to spherical segment is 0.2 to 0.9, 30 sets of results of numerical simulation were taken. Correlations were fitted from the results of numerical simulation by multiple linear regression analysis. Then, in the range of temperature between 294 K to 700 K, the temperature value was taken every 50 K. Then final fitted formula of thermal conductivity for nanograins was got by the binomial fitting method. The results of fitted formula agree well with the numerical results. The results show that the thermal conductivities decrease with the diameter of nanograins reducing within the 3-D spherical segment when the diameter ratio, δ, of the gap to spherical segment is fixed. The effective thermal conductivities would increase with the ratio, δ, increasing when the spherical segment diameter is fixed and the ratio is lower than 0.6. The thermal conductivities would remarkably decrease when the ratio is larger 0.6.