Hydrodynamic Heat Transport in Compact and Holey Silicon Thin Films

The breakdown of Fourier's law in nanoscale thermal transport, which has become (ahem) a $h\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}t$ topic lately due to improvements in experimental precision, presents a serious problem for analysis of heat flow. The authors show that the observed discrepancies can be naturally explained by adopting a hydrodynamic extension to Fourier's law. With parameters calculated $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$, this equation shows remarkable agreement with experiments on films of ``holey'' Si. The simplicity of this multiscale model allows numerical solutions for arbitrary geometries using finite-element methods, providing a good tool for interpreting recent experiments with complex setups.