Directional spectral emittance of an absorbing and scattering isothermal system of packed spheres is predicted by a radiative model based on the discrete ordinates method. Radiative properties for the bed of packed opaque spheres are obtained using geometric optics laws corrected with a scaling factor to take into account the dependent scattering. This model requires the knowledge of several parameters. Particle diameter and porosity can be easily obtained, but particle hemispherical spectral reflectivity is very difficult to obtain a priori. This particle reflectivity is determined by an identification method (Gauss method of linearization) applied to bidirectional spectral reflectance data obtained from an experimental device using a Fourier transform infrared spectrometer. Directional spectral emittance is measured using a direct radiometric technique that has been recently proposed. For a system of packed opaque spheres at high temperature, good agreement is observed between experimental results of directional spectral and computed theoretical data.

1.
Viskanta
,
R.
, and
Mengu¨c¸
,
M. P.
,
1989
, “
Radiative Transfer in Dispersed Media
,”
Appl. Mech. Rev.
,
42
, No.
9
, pp.
241
259
.
2.
Baillis-Doermann, D., and Sacadura, J. F., 1998, “Thermal Radiation Properties of Dispersed Media: Theoretical Prediction and Experimental Characterization,” 2nd ICHMT Int. Symp. On Radiative Transfer, Kusadasi, Turquie, Radiative Transfer II, P. Mengu¨c¸, ed., Begell House Inc, NY, pp. 1–38.
3.
Drolen
,
B. L.
, and
Tien
,
C. L.
,
1987
, “
Independent and Dependent Scattering in Packed-Sphere Systems
,”
Journal of Thermophysics
,
1
, No.
1
, pp.
63
68
.
4.
Tien
,
C. L.
,
1988
, “
Thermal Radiation in Packed and Fluidized Beds
,”
ASME J. Heat Transfer
,
110
, pp.
1230
1242
.
5.
Brewster
,
M. Q.
, and
Tien
,
C. L.
,
1982
, “
Radiative Transfer in Packed Fluidized Beds: Dependent Versus Independent Scattering
,”
ASME J. Heat Transfer
,
104
, pp.
573
579
.
6.
Yang
,
Y. S.
,
Howell
,
J. R.
, and
Klein
,
D. E.
,
1983
, “
Radiative Heat Transfer Through a Randomly Packed Bed of Spheres by the Monte Carlo Method
,”
ASME J. Heat Transfer
,
105
, pp.
325
332
.
7.
Kamiuto
,
K.
,
1990
, “
Correlated Radiative Transfer in Packed-Sphere Systems
,”
J. Quant. Spectrosc. Radiat. Transf.
,
43
, No.
1
, pp.
39
43
.
8.
Chen
,
J. C.
, and
Churchill
,
S. W.
,
1963
, “
Radiant Heat Transfer in Packed Beds
,”
AIChE J.
,
9
, pp.
35
41
.
9.
Singh
,
B. P.
, and
Kaviany
,
M.
,
1992
, “
Modelling Radiative Heat Transfer in Packed Beds
,”
Int. J. Heat Mass Transf.
,
35
, No.
6
, pp.
1397
1405
.
10.
Jones
,
P. D.
,
McLeod
,
D. G.
, and
Dorai-Raj
,
D. E.
,
1996
, “
Correlation of Measured and Computed Radiation Intensity Exiting a Packed Bed
,”
ASME J. Heat Transfer
,
118
, pp.
94
102
.
11.
Lopes, R., Moura, L. M., Delmas, A., and Sacadura, J.-F., 1998, “Directional Spectral Emittance of Ceramic Material: Theoretical Prediction Compared to Experimental Data,” 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, Albuquerque, New Mexico.
12.
Moura, L. M, Baillis, D., and Sacadura, J. F., 1997, “Analysis of the Discrete Ordinate Method: Angular Discretization,” 14th Brazilian Congress of Mechanical Engineering, December 8–12, COB1425, Bauru, Brazil (in portuguese).
13.
Brewster, M. Q., 1992, Thermal Radiative Transfer and Properties, Wiley, New York, pp. 301–336.
14.
Touloukian, Y. S., and DeWitt, D. P., 1972, Thermophysical Properties of Matter; Thermal Radiative Properties: Nonmetalic Solids, IFI/Plenum, New York.
15.
Beck, J. V., and Arnold, K. J., 1977, Parameter Estimation in Engineering and Science, Wiley, New York.
16.
Nicolau
,
V. P.
,
Raynaud
,
M.
, and
Sacadura
,
J. F.
,
1994
, “
Spectral Radiative Properties Identification of Fiber Insulating Materials
,”
Int. J. Heat Mass Transf.
,
37
, pp.
321
324
.
17.
Baillis
,
D.
,
Raynaud
,
M.
, and
Sacadura
,
J. F.
,
1999
, “
Spectral Radiative Properties of Open-Cell Foam Insulation
,”
J. Thermophys. Heat Transfer
,
13
, No.
3
, pp.
292
298
.
18.
Griffiths, P. R., 1975, Chemical Infrared Fourier Transform Spectroscopy, Wiley, New York, p. 337.
19.
Nicolau, V. P., 1994, “Identification des proprie´te´s radiatives des mate´riaux semi-transparents diffusants,” Ph.D. thesis n∘ 94 ISAL. 0001, INSA de Lyon, France.
20.
Doermann, D., 1995, “Mode´lisation des transferts thermiques dans des mate´riaux semi-transparents de type mousse a` pores ouverts et pre´diction des proprie´te´s radiatives,” Ph.D. thesis n∘ 95 ISAL. 0010, INSA de Lyon, France.
21.
Li, J. C., Lopes, R., Vialle, C., and Sacadura, J. F., 1999, “Study of an Optical Device for Energy Homogenization of a High Power Laser Beam,” J. Laser Appl., 11, No. 6.
22.
Jones
,
P. D.
,
Dorai-Raj
,
D. E.
, and
McLeod
,
D. G.
,
1996
, “
Spectral-Directional Emittance of Oxidized Copper
,”
J. Thermophys. Heat Transfer
,
10
, No.
2
, pp.
343
349
.
You do not currently have access to this content.