Two-dimensional lattice Boltzmann modeling for effective thermal conductivity in carbon black filled composites

Polymer composites filled with thermally conductive particles are widely used in thermo-electronic industry, and the prediction of effective properties is still important for design and use of composites. Thus, we propose a lattice Boltzmann model to predict the effective thermal conductivity of composites filled with carbon black. First, a method for reconstructing numerical material having filler distribution characteristic similar to that of actual material is introduced, and the process for obtaining the phase function and the volume fraction of grain filler is described. The energy transport governing equation is then solved through the two-dimensional discrete structure by using a lattice Boltzmann model. The effective thermal conductivity of two-phase composite is expressed by the conductivity of each phase and the temperature distribution in discrete rectangle. The resultant prediction is compared with theoretical and experimental data and indicates good agreement with experimental data.