The effective thermal conductivity of micro/nanofilm under different heating conditions using nongray Boltzmann transport equation

It is known that Fourier's law breaks down at micro/nanoscale and that the classical definition of thermal conductivity from this law becomes invalid. Therefore, adopting a size-dependent effective thermal conductivity for micro and nanofilm is a prevalent strategy to describe the heat transfer at micro/nanoscale. Most of the existing discussion focuses on the size effect of effective thermal conductivity, while the dependence of thermal conductivity on heating conditions is less explored. In this work, we employed the nongray phonon Boltzmann transport equation to obtain the effective thermal conductivity of micro/nanofilm under three typical heating conditions, including temperature difference, internal heat source, and transient thermal grating. It is found that for all three heating conditions, the effective thermal conductivity increases with characteristic length and converges to the bulk value. Nevertheless, the effective thermal conductivities in the three heating conditions are different. For the same characteristic length, the effective thermal conductivity extracted with the temperature difference is larger than transient thermal grating, and both are larger than that with the internal heat source. Such a conclusion is further consolidated by the calculation results for a few different semiconductor materials with diverse mean free path distributions. Furthermore, we proposed a convenient semi-analytical approach to accurately predict effective thermal conductivity under different heating conditions for micro/nanofilms.