Popular numerical techniques for solving the Boltzmann transport equation (BTE) for sub-micron thermal conduction include the discrete ordinates method and the finite volume method. However, the finite wave speed associated with the BTE can cause large errors in the prediction of the equivalent temperature unless fine angular discretizations are used, particularly at low acoustic thicknesses. In this paper, we combine a ray-tracing technique with the finite volume method to substantially improve the predictive accuracy of the finite volume method. The phonon intensity is decomposed into ballistic and in-scattering components. The former is solved using a ray tracing scheme, accounting for finite wave speed; the latter is solved using an unstructured finite volume method. Comparisons between this new technique and traditional finite volume formulations are presented for a range of acoustic thicknesses, and substantial improvement is demonstrated.
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An Improved Computational Procedure for Sub-Micron Heat Conduction
J. Y. Murthy,
e-mail: jmurthy@ecn.purdue.edu
J. Y. Murthy
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
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S. R. Mathur
S. R. Mathur
Search for other works by this author on:
J. Y. Murthy
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
e-mail: jmurthy@ecn.purdue.edu
S. R. Mathur
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division June 26, 2002; revision received June 4, 2003. Associate Editor: G. Chen.
J. Heat Transfer. Oct 2003, 125(5): 904-910 (7 pages)
Published Online: September 23, 2003
Article history
Received:
June 26, 2002
Revised:
June 4, 2003
Online:
September 23, 2003
Citation
Murthy, J. Y., and Mathur, S. R. (September 23, 2003). "An Improved Computational Procedure for Sub-Micron Heat Conduction ." ASME. J. Heat Transfer. October 2003; 125(5): 904–910. https://doi.org/10.1115/1.1603775
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