Ballistic-Diffusive Equations for Transient Heat Conduction From Nano to Macroscales

[+] Author and Article Information
Gang Chen

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139-4307

J. Heat Transfer 124(2), 320-328 (Aug 06, 2001) (9 pages) doi:10.1115/1.1447938 History: Received August 31, 2000; Revised August 06, 2001
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Majumdar,  A., 1993, “Microscale Heat Conduction in Dielectric Thin Films,” Journal of Heat Transfer, , 115, pp. 7–16.
Goodson,  K. E., and Ju,  Y. S., 1999, “Heat Conduction in Novel Electronic Films,” Annu. Rev. Mater. Sci., 29, pp. 261–293.
Chen,  G., 2001, “Phonon Heat Conduction in Superlattices and Nanostructures,” Semiconductors and Semimetals, 71, pp. 203–259.
Chen,  G., 2001, “Ballistic-Diffusive Heat Conduction Equations,” Phys. Rev. Lett., 86, pp. 2297–2230.
Olfe,  D. B., 1967, “A Modification of the Differential Approximation for Radiative Transfer,” AIAA J., 5, pp. 638–643.
Modest, M. F., 1993, Radiative Heat Transfer, McGraw-Hill, New York.
Pomraning, G. C., 1973, The Equation of Radiation Hydrodynamics, Pergamon, New York.
Yang, R. G., Chen, G., and Taur, Y., 2002, “Ballistic-Diffusive Equations for Multidimensional Nanoscale Heat Conduction,” to be presented at 12 Int. Heat Transfer Conf., Grenoble, France, Aug. 18–23, 2002.
Joseph,  D. D., and Preziosi,  L., 1990, “Heat Waves,” Rev. Mod. Phys., 62, pp. 375–391.
Wu,  C. Y., 1987, “Successive Improvement of the Modified Differential Approximation in Radiative Heat Transfer,” J. Thermophys. Heat Transfer, 1, pp. 296–300.
Modest,  M. F., 1989, “Modified Differential Approximation for Radiative Transfer in General Three-Dimensional Media,” J. Thermophys. Heat Transfer, 3, pp. 283–288.
Joshi,  A. A., and Majumdar,  A., 1993, “Transient Ballistic and Diffusive Phonon Heat Transport in Thin Films,” J. Appl. Phys., 74, pp. 31–39.
Swartz,  E. T., and Pohl,  R. O., 1989, “Thermal Boundary Resistance,” Rev. Mod. Phys., 61, pp. 605–668.
Klitsner,  T., VanCleve,  J. E., Fischer,  H. E., and Pohl,  R. O., 1988, “Phonon Radiative Heat Transfer and Surface Scattering,” Phys. Rev. B, 38, pp. 7576–7594.
Chen,  G., 1996, “Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles,” J. Heat Transf., , 118, pp. 539–545.
Chen,  G., 1998, “Thermal Conductivity and Ballistic Phonon Transport in Cross-Plane Direction of Superlattices,” Phys. Rev. B, 57, pp. 14958–14973.
Little,  W. A., 1959, “The Transport of Heat Between Dissimilar Solids at Low Temperatures,” Can. J. Phys., 37, pp. 334–349.
Chen,  G., and Zeng,  T., 2001, “Nonequilibrium Phonon and Electron Transport in Heterostructures and Superlattices,” Microscale Thermophys. Eng., 5, pp. 71–88.
Simons,  S., 1974, “On the Thermal Boundary Resistance between Insulators,” J. Phys. C, 7, pp. 4048–4052.
Katerberg,  J. A., Reynolds,  C. L., and Anderson,  A. C., 1977, “Calculations of Thermal Boundary Resistance,” Phys. Rev. B, 16, pp. 673–679.


Grahic Jump Location
Nondimensional temperature and heat flux distributions calculated from the Boltzmann equation and the ballistic-diffusive equations for different carrier Knudsen number (Kn) and differential nondimensional time (t*)
Grahic Jump Location
Contribution of the ballistic and the diffusive components to the nondimensional total internal energy (temperature) and heat flux. The weak wave front in the diffusive component is artificially caused by the diffusion approximation.
Grahic Jump Location
Comparison of temperature and heat flux distributions obtained from the Boltzmann equation, the ballistic-diffusive equations, the Cattaneo equation, and the Fourier law for different time and Knudsen number
Grahic Jump Location
Comparison of surface heat flux obtained from the Boltzmann equation, the ballistic-diffusive equations, the Cattaneo equation, and the Fourier law as a function of time for different Knudsen numbers
Grahic Jump Location
Schematic drawing for discussing the consistency of temperature used in the equations and the boundary conditions
Grahic Jump Location
Normalized temperature and heat flux distributions rescaled to the difference of the instantaneous medium temperatures at the two boundaries



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In