This work applies fractal percolation theory to examine the impact of anomalous diffusion in short time-scale applications of random media. It is shown that there exist three regimes of heat transport corresponding to transport over the basic percolation unit (particle), the fractal cluster, and the homogeneous medium. Scaling is performed to determine the characteristic time scales of anomalous diffusion. The dependence of these time scales on both material properties and structure is examined to assess the impact of the anomalous diffusion regime on short time-scale energy transport. Additional criteria that determine the importance of anomalous diffusion relative to other transport phenomena and properties, such as radiation and thermal boundary resistance, are established.
Issue Section:
Heat Transfer in Manufacturing
1.
Alexander
S.
Orbach
R.
1982
, “Density of States on Fractals: Fractons
,” J. Phys. Lett.
, Vol. 43
, pp. 625
–631
.2.
Bunde, A., and Havlin, S., 1991, “Percolation I,” Fractals and Disordered Systems, A. Bunde and S. Havlin, eds., Springer-Verlag, New York, pp. 51–96.
3.
de Gennes
P. G.
1976
, “La Percolation: un Concept Unificateur
,” La Recherche´
, Vol. 7
, pp. 919
–927
.4.
Fournier
D.
Boccara
A. C.
1989
, “Heterogeneous Media and Rough Surfaces: A Fractal Approach for Heat Diffusion Studies
,” Physica A
, Vol. 157
, pp. 587
–592
.5.
Gefen
Y.
Aharony
A.
Alexander
S.
1983
, “Anomalous Diffusion on Percolating Clusters
,” Phys. Rev. Lett.
, Vol. 50
, pp. 77
–80
.6.
Goldman, C. H., Norris, P. M., and Tien, C. L., 1995, “Picosecond Energy Transport in Amorphous Materials,” Proc. 1995 ASME/JSME Thermal Engineering Joint Conference, Vol. 1, pp. 467–473.
7.
Havlin, S., and Bunde, A., 1991, “Percolation II,” Fractals and Disordered Systems, A. Bunde and S. Havlin, eds., Springer-Verlag, New York, pp. 97–150.
8.
Jagannathan
A.
Orbach
R.
Entin-Wohlman
O.
1989
, “Thermal Conductivity of Amorphous Materials Above the Plateau
,” Phys. Rev. B
, Vol. 39
, pp. 13465
–13477
.9.
Ka¨ding
O. W.
Skurk
H.
Goodson
K. E.
1994
, “Thermal Conduction in Metallized Silicon-Dioxide Layers on Silicon
,” Appl. Phys. Lett.
, Vol. 65
, pp. 1629
–1631
.10.
Kittel, C., 1986, Introduction to Solid State Physics, 6th ed., Wiley, New York, pp. 495–511.
11.
Little
W. A.
1959
, “The Transport of Heat Between Dissimilar Solids at Low Temperature
,” Can. J. Phys.
, Vol. 37
, pp. 334
–349
.12.
Lu
X.
Nilsson
O.
Fricke
J.
Pekala
R. W.
1993
, “Thermal and Electrical Conductivity of Monolithic Carbon Aerogels
,” J. Appl. Phys.
, Vol. 73
, pp. 581
–584
.13.
Mandelbrot, B. B., 1977, Fractals: Form, Chance, and Dimension, Freeman, San Francisco.
14.
Qiu
T. Q.
Tien
C. L.
1993
, “Heat Transfer Mechanisms During Short-Pulse Laser Heating of Metals
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 115
, pp. 835
–841
.15.
Richter
K.
Norris
P. M.
Tien
C. L.
1995
, “Aerogels: Applications, Structure, and Heat Transfer Phenomena
,” Annual Review of Heat Transfer
; Vol. VI
, pp. 61
–114
.16.
Stoner
R. J.
Marls
H. J.
1993
, “Kapitza Conductance and Heat Flow Between Solids at Temperatures From 50 to 300 K
,” Phys. Rev. B
, Vol. 48
, pp. 16373
–16387
.17.
Swartz
E. T.
Pohl
R. O.
1987
, “Thermal Resistance at Interfaces
,” Appl. Phys. Lett.
, Vol. 51
, pp. 2200
–2202
.18.
Vedavarz
A.
Kumar
S.
Moallemi
M. K.
1994
, “Significance of Non-Fourier Heat Waves in Conduction
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 116
, pp. 221
–224
.19.
von der Linde, D., 1993, “Ultrashort Interactions in Solids,” Ultrashort Laser Pulses: Generation and Applications, 2nd ed., W. Kaiser, ed., Springer-Verlag, New York, pp. 113–182.
20.
Weil, R., Deutscher, G., Zallen, R., and Adler, J., eds., 1983, Percolation Structures and Processes (Annals of the Israel Physical Society: Vol. 5), Adam Hilger, Bristol, United Kingdom.
21.
Young, D. A., Thomsen, C., Grahn, H. T., Maris, H. J., and Tauc, J., 1986, “Heat Flow in Glasses on a Picosecond Timescale,” Phonon Scattering in Condensed Matter V, A. C. Anderson, and J. P. Wolfe, eds., Springer-Verlag, Berlin, pp. 49–51.
22.
Zallen, R., 1983, The Physics of Amorphous Solids, Wiley, New York.
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