It is well known that Fourier law breaks down for the prediction of heat conduction in nano-scale, where the length scale is comparable to the mean free path of energy carriers. Over the past decade, Boltzmann transport equation (BTE) has been used to predict thermal transport in dielectrics and semiconductors at micro-scale and nano-scale. In this work, a new modified gray model is obtained from BTE. The implicit lattice Boltzmann method (LBM) is developed to simulate the thermal transport process. Based on the new model, we can derive Guyer-Krumhansl equation. Transient heat conduction through a thin nano-film and hotspot self-heating in sub-micron transistors are examined. The numerical results are compared with those provided by Fourier, Cattaneo, and Guyer-Krumhansl equation.
A Novel Approach for Lattice Boltzmann Modeling of Energy Transport
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Wang, D, & Ma, Y. "A Novel Approach for Lattice Boltzmann Modeling of Energy Transport." Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition. Volume 7: Fluids and Heat Transfer, Parts A, B, C, and D. Houston, Texas, USA. November 9–15, 2012. pp. 2961-2964. ASME. https://doi.org/10.1115/IMECE2012-89661
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