Hydrodynamic Heat Transport in Compact and Holey Silicon Thin Films

Amultiscale hydrodynamic-heat-transportmodel applicable to arbitrary geometries using finite-element methods is compared with the experimental effective thermal conductivity of silicon thin films and periodic holey membranes for different sizes and temperatures. The range of system length scales and temperatures in which the model predictions agree with experimental data is discussed and quantitatively determined. The model agrees with experimental results when the smallest system size is larger than twice the nonlocal length, an intrinsic property of the material that depends only on temperature. These results open the door to the use of the hydrodynamic equation instead of an effective Fourier model to interpret current heat-transport experimental data.