Free-molecular heat transfer of vibrating cantilever and bridges

Vibrating cantilever and bridge structures for micro- and nanodevices are characterized by high frequencies and length scales below the continuum limit. Free-molecular heat transfer equations are used to estimate the heat transfer from structures vibrating at high frequencies. The heat transfer is computed for a cantilever cross section as a function of a frequency and amplitude of vibration. These results are then integrated across the mode shape of cantilever and bridge structures to give a net heat transfer for the system. In micro- and nanodevices, the effect of frequency on the heat transfer is strongest for devices operating at cryogenic temperatures and extremely high frequencies. In mesoscale devices, the effect of frequency can be seen for devices with amplitudes on the order of microns and frequencies in the kilohertz region.