A Green function approach is used with the fluctuation-dissipation theorem to develop a qualitative theoretical model of radiation heat transfer across an evacuated microscale spherical geometry bounded by silicon carbide. The appropriate scalar Green function is presented by employing an impedance boundary condition to describe the electromagnetic spherical interface condition and thus capture the surface modes. This work shows that the spherical boundary can result in spectral conditions for surface mode excitation that depend not only on the dielectric function, but on the sphere radius as well. The surface modes are shown to enhance the radiation significantly and are attributed to surface phonon polariton modes excited at the interface, and surface modes excited by the mechanism of total internal reflection.

1.
Suwanmethanond
,
V.
,
Goo
,
E.
,
Liu
,
P.
,
Sahimi
,
G.
, and
Tsotsis
,
T.
, 2000, “
Porous Silicon Carbide Sintered Substrates for High-Temperature Membranes
,”
Ind. Eng. Chem. Res.
0888-5885,
39
, pp.
3264
3271
.
2.
Sung
,
I.-K.
,
Christian
,
Mitchell
,
M.
,
Kim
,
D.-P.
, and
Kenis
,
P.
, 2005, “
Tailored Macroporous SiCN and SiC Structures for High-Temperature Fuel Reforming
,”
Adv. Funct. Mater.
1616-301X,
15
, pp.
1336
1342
.
3.
Wang
,
H.
,
Zheng
,
S.-Y.
,
Li
,
X.-D.
, and
Kim
,
D.-P.
, 2005, “
Preparation of Three-Dimensional Ordered Macroporous SiCN Ceramic Using Sacrificing Template Method
,”
Microporous Mesoporous Mater.
1387-1811,
80
,
357
362
, and references therein.
4.
Siegel
,
R.
, and
Howell
,
J.
, 1992,
Thermal Radiation Heat Transfer
,
3rd ed.
,
Hemisphere
, Washington, DC.
5.
Cravalho
,
E.
,
Tien
,
C.
, and
Caren
,
R.
, 1967, “
Effect of Small Spacings on Radiative Transfer Between Two Dielectrics
,”
J. Heat Transfer
0022-1481,
89C
, pp.
351
357
.
6.
Hammonds
,
J.
, 2006, “
Thermal Transport via Surface Phonon Polaritons Across a Two-Dimensional Pore
,”
Appl. Phys. Lett.
0003-6951,
88
(
4
), p.
041912
.
7.
Raether
,
H.
, 1988,
Surface Plasmons
,
Springer-Verlag
, Berlin.
8.
Polder
,
D.
, and
Hove
,
M. V.
, 1971, “
Theory of Radiative Heat Transfer Between Closely Spaced Bodies
,”
Phys. Rev. B
0556-2805,
4
(
5
), pp.
3303
3314
.
9.
Felsen
,
L.
, and
Marcuvitz
,
N.
, 1973,
Radiation and Scattering of Waves
,
Prentice-Hall
, Englewood Cliffs, NJ.
10.
Wang
,
D.-S.
, 1987, “
Limits and Validity of the Impedance Boundary Condition on Penetrable Surfaces
,”
IEEE Trans. Antennas Propag.
0018-926X,
AP-35
(
4
), pp.
453
457
.
11.
Lax
,
M.
, and
Feshbach
,
H.
, 1948, “
Absorption and Scattering for Impedance Boundary Conditions of Spheres and Circular Cylinders
,”
J. Acoust. Soc. Am.
0001-4966,
20
(
2
), pp.
108
124
.
12.
Padture
,
N.
,
Gell
,
M.
, and
Jordan
,
E.
, 2002, “
Thermal Barrier Coatings for Gas-Turbine Engine Applications
,”
Science
0036-8075,
296
(
5566
), pp.
280
284
.
13.
Shchegrov
,
A.
,
Joulain
,
K.
,
Carminati
,
R.
, and
Greffet
,
J.-J.
, 2000, “
Near-Field Spectral Effects Due to Electromagnetic Surface Excitations
,”
Phys. Rev. Lett.
0031-9007,
85
(
7
), pp.
1548
1551
.
14.
Henkel
,
C.
,
Joulain
,
K.
,
Carminati
,
R.
, and
Greffet
,
J.-J.
, 2000, “
Spatial Coherence of Thermal Near Fields
,”
Opt. Commun.
0030-4018,
186
, pp.
57
67
.
15.
Caren
,
R.
, 1974, “
Thermal Radiation Between Closely Spaced Metal Surfaces at Low Temperature Due to Traveling and Quasi-Stationary Components of the Radiation Field
,”
Int. J. Heat Mass Transfer
0017-9310,
17
(
7
), pp.
755
765
.
16.
Xu
,
J.-B.
,
Läuger
,
K.
,
Möller
,
R.
,
Dransfeld
,
K.
, and
Wilson
,
I.
, 1994, “
Heat Transfer Between Two Metallic Surfaces at Small Distances
,”
J. Appl. Phys.
0021-8979,
76
(
11
), pp.
7209
7216
.
17.
Park
,
C.
,
Haus
,
H.
, and
Weinberg
,
M.
, 2002, “
Proximity-Enhanced Thermal Radiation
,”
J. Phys. D
0022-3727,
35
, pp.
2857
2863
.
18.
Pfeiffer
,
C.
,
Economou
,
E.
, and
Ngai
,
K.
, 1974, “
Surface Polaritons in a Circularly Cylindrical Interface: Surface Plasmons
,”
Phys. Rev. B
0556-2805,
10
(
8
), pp.
3038
3051
.
19.
Greffet
,
J.-J.
,
Carminati
,
R.
,
Joulain
,
K.
,
Mulet
,
J.-P.
,
Mainguy
,
S.
, and
Chen
,
Y.
, 2002, “
Coherent Emission of Light by Thermal Sources
,”
Nature (London)
0028-0836,
416
, pp.
61
64
.
20.
Marcuse
,
D.
, 1982,
Light Transmission Optics
,
2nd ed.
,
Van Nostrand Reinhold
, New York.
You do not currently have access to this content.