Transient, Sub-Continuum, Heat Conduction in Irregular Geometries

Phonon transfer in irregular shapes is important for assessing the influence of shape effect on thermal transport characteristics of low-scale films. It becomes critical for evaluating the contribution of the scattering phonons to the phonon intensity distribution inside the film. Hence, the sub-continuum ballistic-diffusive model is incorporated to formulate the phonon transport in an irregular geometry of low-size film adopting the transient, frequency-independent, equation of phonon radiative transfer. The discrete ordinate method is used in the numerical discretization of the governing transport equation. It is demonstrated that the geometric feature of the film influences the phonon intensity distribution within the film material. The transport characteristics obtained from the Fourier and the ballistic-diffusive models are markedly different in their spatial and temporal behavior. This is true when the device sizes are of the same order of magnitude as the mean-free path of the heat carriers.