Collocation mesh-free method to solve the gray phonon Boltzmann transport equation

References

• T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. Dewitt, Fundamentals of Heat and Mass Transfer, 7th ed., John Wiley & Sons, New York, 2011.
   Google Scholar
• K. E. Yazdani, and M. Asheghi, Ballistic Phonon Transport in Strained Si/SiGe Nanostructures with an Application to Strained-silicon Transistors, The Ninth Intersoc. Conf., vol. 2, pp. 424–430, IEEE, In Thermal and Thermomechanical Phenomena in Electronic Systems, 2004.
   Google Scholar
• G. Chen, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons, Oxford University Press, Oxford, 2005.
   Google Scholar
• X. Wang and Z. M. Wang, Nanoscale Thermoelectrics, Springer, Cham, 2014.
   Google Scholar
• J. Y. Murthy, S. V. J. Narumanchi, J. A. Pascual-Gutierrez, T. Wang, C. Ni, and S. R. Mathur, Review of Multiscale Simulation in Submicron Heat Transfer, Int. J. Multiscale Comput. Eng., vol. 3, no. 1, pp. 5–32, 2005.
   Web of Science ®Google Scholar
• S. Hamian, T. Yamada, M. Faghri, and K. Park, Finite Element Analysis of Transient Ballistic–Diffusive Phonon Heat Transport in Two-dimensional Domains, Int J. Heat Mass Transfer, vol. 80, pp. 781–788, 2015.
   Web of Science ®Google Scholar
• A. J. Minnich, G. Chen, S. Mansoor, and B. S. Yilbas, Quasiballistic Heat Transfer Studied Using the Frequency-dependent Boltzmann Transport Equation. Phys. Rev. B, vol. 84, no. 23, p. 235207, 2011.
   Web of Science ®Google Scholar
• J. Y. Murthy and S. R. Mathur, Computation of Sub-micron Thermal Transport Using an Unstructured Finite Volume Method, J. Heat Transfer, vol. 124, no. 6, pp. 1176–1181, 2002.
   Web of Science ®Google Scholar
• A. Mittal and S. Mazumder, Hybrid Discrete Ordinates Spherical Harmonics Solution to the Boltzmann Transport Equation for Phonons for Non-equilibrium Heat Conduction, J. Comput. Phys., vol. 230, no. 18, pp. 6977–7001, 2011.
   Web of Science ®Google Scholar
• J. Y. Murthy and S. R. Mathur, Computational Heat Transfer in Complex Systems: A Review of Needs and Opportunities, J. Heat Transfer, vol. 134(3), p. 031016, 2012.
   Web of Science ®Google Scholar
• P. Lee, R. Yang, and K. Maute, An Extended Finite Element Method for the Analysis of Submicron Heat Transfer Phenomena, In Multiscale Methods in Computational Mechanics, Springer, Netherlands, pp. 195–212, 2011.
   Google Scholar
• A. Mittal, Prediction of Non-equilibrium Heat Conduction in Crystalline Materials Using the Boltzmann Transport Equation for Phonons, Ph.D. thesis, The Ohio State University, 2011.
   Google Scholar
• M. Y. Kim, S. W. Baek, and J. H. Park, Unstructured Finite-volume Method for Radiative Heat Transfer in a Complex Two-dimensional Geometry with Obstacles. Numer. Heat Transfer Part B Fundam., vol. 39, no. 6, pp. 617–635, 2001.
   Web of Science ®Google Scholar
• A. Mittal, Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films, Master’s thesis, The Ohio State University, 2009.
   Google Scholar
• A. Nabovati, D. P. Sellan, and C. H. Amon, On the Lattice Boltzmann Method for Phonon Transport, J. Comput. Phys., vol. 230, no. 15, pp. 5864–5876, 2011.
   Web of Science ®Google Scholar
• F. N. Donmezer, D. Singh, W. James, A. Christensen, S. Graham, and J. Y. Murthy, Lattice Boltzmann and Discrete Ordinates Methods for Phonon Transport Modeling: A Comparative Study, ASME 2011 International Mechanical Engineering Congress and Exposition, Volume 10: Heat and Mass Transport Processes, Parts A and B, pp. 333–343, Denver, CO, 2011.
   Google Scholar
• A. Mittal and S. Mazumder, Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons, J. Heat Transfer, vol. 132, no. 5, p. 052402, 2010.
   Web of Science ®Google Scholar
• G. R. Liu and Y. T. Gu, An Introduction to Meshfree Methods and their Programming, Springer, Dortrecht, 2005.
   Google Scholar
• K. Luo, H. L. Yi, and H. P. Tan, Coupled Radiation and Mixed Convection in an Eccentric Annulus using the Hybrid Strategy of Lattice Boltzmann Meshless Method, Numer. Heat Transfer Part B Fundam., vol. 66, no. 3, pp. 243–267, 2014.
   Web of Science ®Google Scholar
• P. Heino, Lattice-Boltzmann Finite-difference Model with Optical Phonons for Nanoscale Thermal Conduction, Comput. Math. Appl., vol. 59, no. 7, pp. 2351–2359, 2010.
   Web of Science ®Google Scholar
• B. S. Yilbas and S. Bin Mansoor, Transient Effects of Phonon Transport in Two-dimensional Silicon Film, Numer. Heat Transfer Part A Appl., vol. 62, no. 9, pp. 742–760, 2012.
   Web of Science ®Google Scholar
• A. Chattopadhyay and A. Pattamatta, A Comparative Study of Submicron Phonon Transport Using the Boltzmann Transport Equation and the Lattice Boltzmann Method, Numer. Heat Transfer Part B Fundam., vol. 66, no. 4, pp. 360–379, 2014.
   Web of Science ®Google Scholar
• S. Srinivasan, R. S. Miller, and E. Marotta, Parallel Computation of the Boltzmann Transport Equation for Microscale Heat Transfer in Multilayered Thin Films, Numer. Heat Transfer Part B Fundam., vol. 46, no. 1, pp. 31–58, 2004.
   Web of Science ®Google Scholar
• S. Chandrasekhar, Radiative Transfer, Dover Publications, New York, NY, 1960.
   Google Scholar
• S. Zahiri, F. Daneshmand, and M. H. Akbari, Using Meshfree Weak-Strong Form Method for a 2-D Heat Transfer Problem. In ASME 2009 International Mechanical Engineering Congress and Exposition, Volume 9: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B and C, pp. 643–651, Lake Buena Vista, FL, 2009.
   Google Scholar
• S. Zahiri, Meshfree Methods, in J. Awrejcewicz (Ed.), Numerical Analysis–Theory and Application, Chap. Meshfree Methods, pp. 231–250, InTech, Rijeka, Croatia, 2011.
   Google Scholar
• A. Majumdar, Microscale Heat Conduction in Dielectric Thin Films, ASME J. Heat Transfer, vol. 115, pp. 7–16, 1993.
   Web of Science ®Google Scholar
• S. V. J. Narumanchi, J. Y. Murthy, and C. H. Amon, Simulation of Unsteady Small Heat Source Effects in Sub-micron Heat Conduction, J. Heat Transfer, vol. 125, pp. 896–903, 2003.
   Web of Science ®Google Scholar
• A. Christensen and S. Graham, Multiscale Lattice Boltzmann Modeling of Phonon Transport in Crystalline Semiconductor Materials, Numer. Heat Transfer Part B Fundam., vol. 57, no. 2, pp. 89–109, 2010.
   Web of Science ®Google Scholar