Thermal conductivity in spherical nanocolloids

•Description of Brownian motion of nanoparticles using Hamiltonian.•Evaluating the mean velocity of the particles parallel to the temperature gradient.•Using Laplace equation to modeling the temperature outside the nanospheres.•Experiment thermal conductivity and temperature distribution in silver nanofluid.

In the present work, a proper description of Brownian motion of nanoparticles is offered and the mean velocity in a preferred direction and the mean free path of the nanoparticles are evaluated statistically. Based on this study, a proper model for thermal conductivity of nanocolloids is obtained. This modified model considers two main mechanisms that contribute in thermal conductivity; thermal carriers inside the particles and the Brownian motion of the particles. New models for both the mechanisms are proposed that have some virtues in comparison with the previous models. Evaluations show that in the thermal conductivity, the portion of Brownian motion is negligible in comparison with the other one. This model has been tested by silver nanoparticles dispersed in water. Using this model, simulation of the energy flux and the temperature distribution is offered.