Radiation transfer within a cloud of magnetite (Fe3O4) particles contained in an infinite slab is considered. The particulate cloud is modeled as a pseudo-continuous, nongray, nonisothermal, absorbing, emitting, and anisotropically scattering medium. The energy source is concentrated solar irradiation, which is assumed to be diffusely and uniformly distributed over a circular opening and has a 5780 K blackbody spectrum. Mie-scattering theory is applied to calculate the spectrally and directionally dependent optical properties of the particles. The Monte Carlo ray-tracing method is used to calculate the attenuation characteristics of the cloud and the temperature distribution under radiative equilibrium. The Monte Carlo simulation is optimized by incorporating the appropriate cumulative probability density functions via Bezier surfaces. The effect of spectral and directional dependency is investigated by comparing the results with those obtained for a gray and isotropic-scattering medium under diffuse or perpendicular incident radiation. It is found that a cloud of Mie-scattering Fe3O4 particles under perpendicular incident radiation requires approximately twice as much optical thickness to obtain the same attenuation (of radiation at all wavelengths and directions) as a cloud of isotropic-scattering particles under diffuse incident radiation. It is demonstrated that the gray approximation using Planck mean values can lead to considerable error in the temperature solution because the spectral absorption coefficient is higher in the region of longer wavelengths where the peak emission by Fe3O4 particles occurs.

Issue Section:
Radiative Transfer
Keywords:
Numerical Methods, Radiation, Solar Energy
Topics:
Electromagnetic scattering, Irradiation (Radiation exposure), Particulate matter, Radiation (Physics), Solar energy
1.
Abdelrahman
M.
,
Fumeaux
P.
, and
Suter
P.
,
1979
, “
Study of Solid-Gas-Suspensions Used for Direct Absorption of Concentrated Solar Radiation
,”
Solar Energy
, Vol.
22
, pp.
45
–
48
.
2.
Bohren, F. C., and Huffman, D. R., 1983, Absorption and Scattering of Light by Small Particles, Wiley, New York, Appendix A: BHMIE subroutine, pp. 477–482.
3.
Canadas
L.
,
Salvador
L.
, and
Ollero
P.
,
1990
, “
Radiative Heat-Transfer Model in the Interior of a Pulverized Coal Furnace
,”
Ind. Eng. Chem. Res.
, Vol.
29
, pp.
669
–
675
.
4.
Edwards
D. K.
,
Glassen
L. K.
,
Hauser
W. C.
, and
Tuchscher
J. S.
,
1967
, “
Radiation Heat Transfer in Nonisothermal Nongray Gases
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
89
, pp.
219
–
229
.
5.
Engeln-Muellges, G., and Reutter, F., 1987, Numerische Mathematik fuer Ingenieure, B. I. Wissenschaftsverlag, Zurich, pp. 339–347.
6.
Evans
G.
,
Houf
W.
,
Greif
R.
, and
Crowe
C.
,
1987
, “
Gas-Particle Flow Within a High Temperature Solar Cavity Receiver Including Radiation Heat Transfer
,”
ASME Journal of Solar Energy Engineering
, Vol.
109
, pp.
134
–
142
.
7.
Grasse, W., Becker, M., and Finnstroem, B., 1987, “Solar Energy for High Temperature Technology and Applications,” DFVLR, Cologne, Germany.
8.
Gupta
R. P.
,
Wall
T. F.
, and
Truelove
J. S.
,
1983
, “
Radiative Scatter by Fly Ash in Pulverized-Coal-Fired Furnaces: Application of the Monte Carlo Method to Anisotropic Scatter
,”
Int. J. Heat Mass Transfer
, Vol.
26
, pp.
1649
–
1660
.
9.
Heaslet
M. A.
, and
Warming
R. F.
,
1965
, “
Radiative Transport and Wall Temperature Slip in an Planar Medium
,”
Int. J. Heat Mass Transfer
, Vol.
8
, pp.
979
–
994
.
10.
Hellwege, K. H., ed., 1982, Landolt-Boernstein Numerical Data and Functional Relationships in Science and Technology, New Series, Springer-Verlag, Berlin, Vol. 17g, p. 543.
11.
Houf
W. G.
, and
Greif
R.
,
1987
, “
Radiant Transfer in a Solar Absorbing Particle Laden Flow
,”
Chemical Engineering Communications
, Vol.
51
, pp.
153
–
165
.
12.
Howell
J. R.
, and
Perlmutter
M.
,
1964
, “
Monte Carlo Solution of Thermal Transfer Through Radiant Media Between Gray Walls
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
86C
, pp.
116
–
122
.
13.
Hsia
H. M.
, and
Love
T. J.
,
1967
, “
Radiative Heat Transfer Between Parallel Plates Separated by a Nonisothermal Medium With Anisotropic Scattering
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
89C
, pp.
197
–
204
.
14.
Hunt, A. J., and Brown, C. T., 1983, “Solar Test Results of an Advanced Direct Absorption High Temperature Gas Receiver (SPHER),” Proc. ISES Solar World Congress, Perth, Australia, Aug. 15–19, Vol. 2, pp. 959–962.
15.
Hunt, A. J., Ayer, J., Hull, P., Miller, F., Noring, J. E., and Worth, D., 1986, “Solar Radiant Heating of Gas-Particle Mixtures,” Lawrence Berkeley Laboratory, University of California LBL-22743, Berkeley, CA 94720.
16.
Kim
T. K.
,
Menart
J. A.
, and
Lee
H. S.
,
1991
, “
Nongray Radiative Gas Analysis Using the S-N Discrete Ordinates Method
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
113
, pp.
946
–
952
.
17.
Kumar
S.
, and
Tien
C. L.
,
1990
, “
Analysis of Combined Radiation and Convection in a Particulate-Laden Liquid Film
,”
ASME Journal Solar Energy Engineering
, Vol.
112
, pp.
293
–
300
.
18.
Mengu¨c, M. P., and Viskanta, R., 1986, “An Assessment of Spectral Radiative Heat Transfer Predictions for a Pulverized Coal-Fired Furnace,” Heat Transfer—1986, Vol. 2, pp. 815–820.
19.
Miller
F.
, and
Koenigsdorff
R.
,
1991
, “
Theoretical Analysis of a High-Temperature Small-Particle Solar Receiver
,”
Solar Energy Materials
, Vol.
24
, pp.
210
–
221
.
20.
Modest
M.
, and
Azad
F.
,
1980
, “
The Influence and Treatment of Mie-Anisotropic Scattering in Radiative Heat Transfer
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
102
, pp.
92
–
98
.
21.
Nakamura
T.
,
1977
, “
Hydrogen Production From Water Utilizing Solar Heat at High Temperatures
,”
Solar Energy
, Vol.
19
, pp.
467
–
475
.
22.
Rightley
M. J.
,
Matthews
L.
, and
Mulholland
G. P.
,
1992
, “
Experimental Characterization of the Heat Transfer in a Free-Falling-Particle Receiver
,”
Solar Energy
, Vol.
48
, pp.
363
–
374
.
23.
Sasse, C., 1992, Ph.D. Thesis, University of Karlsruhe, Germany.
24.
Siegel, R., and Howell, J. R., 1992, Thermal Radiation Heat Transfer, 3rd ed., Hemisphere Publishing Corp., Washington DC.
25.
Sparrow, E. M., and Cess, R. D., 1966, Radiation Heat Transfer, Wadsworth Publishing Company, Belmont, CA.
26.
Tien
C. L.
, and
Drolen
B. L.
,
1987
, “
Thermal Radiation in Particulate Media With Dependent and Independent Scattering
,”
A. Rev. Numer. Fluid Mech. Heat Transfer
, Vol.
1
, pp.
1
–
32
.
27.
Usiskin
C. M.
, and
Sparrow
E. M.
,
1960
, “
Thermal Radiation Between Parallel Plates Separated by an Absorbing-Emitting Nonisothermal Gas
,”
Int. J. Heat Mass Transfer
, Vol.
1
, pp.
28
–
36
.
28.
Wang
K. Y.
, and
Yuen
W. W.
,
1987
, “
Rapid Heating of Gas/Small Particle Mixture
,”
ASME Journal Solar Energy Engineering
, Vol.
109
, pp.
143
–
149
.
29.
Welford, W. T., and Winston, R., 1989, High Collection Nonimaging Optics, Academic Press, Inc., San Diego, CA.
30.
Yamada
Y.
,
Cartigny
J. D.
, and
Tien
C. L.
,
1986
, “
Radiative Transfer With Dependent Scattering by Particles: Part 2—Experimental Investigation
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
108
, pp.
614
–
618
.
31.
Yuen
W. W.
, and
Ma
A.
,
1992
, “
Evaluation of Total Emittance of an Isothermal Nongray Absorbing, Scattering Gas-Particle Mixture Based on the Concept of Absorption Mean Beam Length
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
114
, pp.
653
–
658
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.