An effective thermal conductivity model of nanofluids with a cubical arrangement of spherical particles

The theoretical investigation of the effective thermal conductivities of nanofluids, a new class of solid-liquid suspensions, is important in both predicting and designing nanofluids with effective thermal conductivities. We have developed a new thermal conductivity model for nanofluids that is based on the assumption that monosized spherical particles are uniformly dispersed in the liquid and are located at the vertexes of a simple cubic lattice, with each particle surrounded by a liquid layer having a thermal conductivity that differs from that of the bulk liquid. This model nanofluid with a cubical arrangement of nanoparticles gives a more practical upper limit of thermal conduction than a model nanofluid with a parallel arrangement of nanoparticles. The new model unexpectedly shows a nonlinear relationship of thermal conductivity with particle concentration, whereas the conductivity-concentration curve changes from convex upward to concave upward with increasing volume concentration. The effects of particle and layer parameters on the effective thermal conductivities are also analyzed. A comparison of predicted thermal conductivity values and experimental data shows that the predicted values are much higher than the experimental data, a finding that indicates that there is a potential to further improve the effective thermal conductivities of nanofluids with more uniformly dispersed particles.