NDLI: Hybrid Ballistic-Diffusive Solution of the Frequency-Dependent Phonon Boltzmann Transport Equation

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Allu, Pareekshith Mazumder, Sandip
Copyright Year	2016
Abstract	The phonon Boltzmann Transport Equation (BTE) is difficult to solve on account of the directional and spectral nature of the phonon intensity, which necessitates angular and spectral discretization, and ultimately results in a large number (typically few hundreds) of four-dimensional partial differential equations. In the ballistic (large Knudsen number) regime, the phonon intensity is highly anisotropic, and therefore, angular resolution is desirable. However, in the diffusive (small Knudsen number) regime, the intensity is fairly isotropic, and hence, angular discretization is wasteful. In such scenarios, the method of spherical harmonics may be effectively used to reduce the large number of directional BTEs to a few partial differential equations. Since the Knudsen number is frequency dependent, the decision to preserve or eliminate angular discretization may be made frequency by frequency based on whether the spectral Knudsen number is large or small. In this article, a hybrid method is proposed in which for some frequency intervals (bands), full angular discretization is used, while for others, the first order spherical harmonics (P1) is invoked to reduce the number of directional BTEs. The accuracy and efficiency of the hybrid method is tested by solving several steady state and transient nanoscale heat conduction problems in two and three-dimensional geometries. Silicon is used as the candidate material. It is found that hybridization is effective in significantly improving the efficiency of solution of the BTE — sometimes by a factor of three — without significant penalty on the accuracy.
Sponsorship	Heat Transfer Division
File Format	PDF
ISBN	9780791850336
DOI	10.1115/HT2016-7079
Volume Number	Volume 2: Heat Transfer in Multiphase Systems; Gas Turbine Heat Transfer; Manufacturing and Materials Processing; Heat Transfer in Electronic Equipment; Heat and Mass Transfer in Biotechnology; Heat Transfer Under Extreme Conditions; Computational Heat Transfer; Heat Transfer Visualization Gallery; General Papers on Heat Transfer; Multiphase Flow and Heat Transfer; Transport Phenomena in Manufacturing and Materials Processing
Conference Proceedings	ASME 2016 Heat Transfer Summer Conference collocated with the ASME 2016 Fluids Engineering Division Summer Meeting and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels
Language	English
Publisher Date	2016-07-10
Publisher Place	Washington, DC, USA
Access Restriction	Subscribed
Subject Keyword	Heat conduction Knudsen number Partial differential equations Anisotropy Phonons Nanoscale phenomena Silicon Resolution (optics) Steady state Transients (dynamics)
Content Type	Text
Resource Type	Article

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