It is well known that continuum-based thermal transport models, such as the Fourier law, fail when the characteristic size of a system becomes comparable to the mean free path of carriers that transport thermal energy. The current work uses the lattice Boltzmann method to develop two modifications to the Fourier heat equation so that it can capture sub-continuum effects. The two modifications are: (i) a size-dependent thermal conductivity and (ii) a size-dependent temperature jump at the system boundaries.
Ballistic Heat Transfer Modelling in Semiconductor Electronic Devices: A Modified Fourier-Based Approach
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Nabovati, A, Sellan, DP, & Amon, CH. "Ballistic Heat Transfer Modelling in Semiconductor Electronic Devices: A Modified Fourier-Based Approach." Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition. Volume 4: Electronics and Photonics. Vancouver, British Columbia, Canada. November 12–18, 2010. pp. 203-207. ASME. https://doi.org/10.1115/IMECE2010-38810
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