Calculations of absorption, transport scattering, and radiation diffusion coefficients for a highly porous material of quartz fibers are performed by use of rigorous scattering theory for arbitrarily oriented cylinders. New results concerning resonance absorption in the semitransparency region and intensive “scattering by absorption” at refractive index n ≈ 1 in the opacity region are obtained. Numerical results for the radiation diffusion coefficient from a theoretical model without taking into account both dependent scattering and interference effects are in a good agreement with the experimental data for isotropic fibrous material of density 144 kg/m3. Calculations allow us to give practical proposals to simplify the determination of optical properties of poly disperse material with randomly oriented fibers. Some results on the radiative–conductive heat transfer in the material considered are presented. The radiation transfer is described in the P1 approximation. A two-band spectral model with bands corresponding to semitransparency and opacity regions is proposed. Applicability of a modified radiative conduction approximation both to transient and to steady-state calculations is discussed.
Issue Section:
Radiative Transfer
Topics:
Heat transfer,
Porous materials,
Quartz fibers,
Radiation (Physics),
Thermal insulation,
Absorption,
Electromagnetic scattering,
Approximation,
Diffusion (Physics),
Cylinders,
Density,
Fibers,
Heat conduction,
Refractive index,
Resonance,
Scattering theory,
Steady state,
Transients (Dynamics)
1.
Alifanov
O. M.
Gerasimov
B. P.
Elizarova
T. G.
1985
, “Mathematical Simulation of Combined Heat Transfer in Disperse Materials
,” J. Engng Phys.
, Vol. 49
, No. 5
, pp. 781
–791
.2.
Arduini
M.
DePonte
F.
1987
, “Combined Radiation and Conduction Heat Transfer in Insulating Materials
,” High Temperatures—High Pressures
, Vol. 19
, No. 3
, pp. 237
–249
.3.
Bankvall
C.
1973
, “Heat Transfer in Fibrous Materials
,” J. Testing and Evaluation
, Vol. 1
, No. 3
, pp. 235
–243
.4.
Banner
D.
Klarsfeld
S.
Langlais
C.
1989
, “Temperature Dependence of the Optical Characteristics of Semitransparent Porous Media
,” High Temperatures—High Pressures
, Vol. 21
, No. 3
, pp. 347
–354
.5.
Bohren, C. F., and Huffman, D. R., 1983, Absorption and Scattering of Light by Small Particles, Wiley, New York.
6.
Case, K. M., and Zweifel, P. F., 1967, Linear Transport Theory, Univ. of Michigan, Addison-Wesley Publ. Co.
7.
Cooke
D. D.
Kerker
M.
1969
, “Light Scattering From Long Thin Glass Cylinders at Oblique Incidence
,” J. Opt. Soc. Amer.
, Vol. 59
, No. 1
, pp. 43
–48
.8.
Dombrovsky, L. A., 1974, “Radiative Equilibrium in Plane-Parallel Layer of Absorbing and Scattering Medium,” Trans. USSR Acad. Sci., Fluid and Gas Mech., No. 4, pp. 183–186 [in Russian].
9.
Dombrovsky, L. A., 1976, “Radiation of Isothermal Polydisperse Layer,” High Temperature, Vol. 14, No. 4.
10.
Dombrovsky
L. A.
1990
, “Approximate Expressions for Calculation of the Main Radiative Properties of Spherical Particles in the Mie Scattering Region
,” Teplofiz Vysok. Temp
, Vol. 28
, No. 6
, pp. 1242
–1245
[in Russian].11.
Dombrovsky, L. A., Kolpakov, A. V., and Yukina, E. P., 1991a, “Calculation of Radiative-Conductive Heat Transfer in Thermal Processing of Synthetic Fibers,” Applied Problems of Aeromechanics and Space Physics, Moscow, pp. 58–62 [in Russian].
12.
Dombrovsky
L. A.
Kolpakov
A. V.
Surzhikov
S. T.
1991
b, “On Applicability of the Transport Approximation for Directional Radiation Transfer Calculations in Anisotropically Scattering Erosion Plume
,” High Temperature
, Vol. 29
, No. 6
, pp. 954
–960
.13.
Dombrovsky
L. A.
Yukina
E. P.
Kolpakov
A. V.
Ivanov
V. A.
1993
, “A Method of Thermal Destruction Calculation for Phenolic Carbon by Action of Intensive Infrared Radiation
,” High Temperature
, Vol. 31
, No. 4
, pp. 619
–625
.14.
Dombrovsky
L. A.
1994
a, “Quartz-Fiber Thermal Insulation: Calculation of Spectral Radiative Characteristics in the Infrared Region
,” High Temperature
, Vol. 32
, No. 2
, pp. 197
–203
.15.
Dombrovsky, L. A., 1994b, “Calculation of Spectral Radiative Properties of Quartz Fibrous Insulation in the Infrared,” Proc. 10th Int. Heat Transfer Conf., Vol. 2, pp. 25–30.
16.
Dombrovsky, L. A., 1994c, “Determination of Spectral Radiative Properties of Fiberglass Thermal Insulation From Steady-State Heat Flux Measurements,” Proc. 2nd Int. Conf. Identif. Dynam. Syst. and Inverse Problems, St. Petersburg, Aug. 22-25, Vol. 2, pp. D-10-1–D-10-11 [in Russian].
17.
Dombrovsky, L. A., 1994d, “Calculation of Radiative-Conductive Heat Transfer in Quartz Fibrous Insulation,” Proc. First Russ. Nat. Conf. on Heat and Mass Transfer, Moscow, Nov. 21–25, pp. 91–96 [in Russian].
18.
Dombrosky, L. A., 1995a, “The Mie Theory Analysis of Comparably Dense Disperse Systems,” Proc. Intern. Symp. on Radiat. Heat Transfer, Kus¸adasi, Turkey, Aug. 13–18, pp. 156–158.
19.
Dombrovsky
L. A.
1996
, “Calculation of Infrared Radiative Properties of Isotropic Fiberglass Materials in the Semitransparency Region
,” High Temperature
, Vol. 34
, No. 1
, pp. 156
–158
.20.
Houston, R. L., and Korpela, S. A., 1982, “Heat Transfer Through Fiberglass Insulation,” Proc. 7th Int. Heat Transfer Conf., Vol. 2, pp. 499–504.
21.
Howell
J. R.
1988
, “Thermal Radiation in Participating Media: The Past, the Present, and Some Possible Futures
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 110
, No. 4(B)
, pp. 1220
–1229
.22.
Jeandel
G.
Boulet
P.
Morlot
G.
1993
, “Radiative Transfer Through a Medium of Silica Fibers Oriented in Parallel Planes
,” Int. J. Heat Mass Transfer
, Vol. 36
, pp. 531
–536
.23.
Kolpakov, A. V., Dombrovsky, L. A., and Yukina, E. P., 1990, “Numerical Investigation of Light Scattering by Disperse Systems of Cylindrical Filaments,” Trans. XV Conf. Young Scient., Mosc. Inst. Phys. Engng, Moscow, Part 2 (Depon. VINITI, N 6175-B90, in Russian).
24.
Kondratenko
A. V.
Moiseyev
S. S.
Petrov
V. A.
Stepanov
S. V.
1991
, “Experimental Determination of Optical Properties of Fibrous Quartz Heat-Shielding Material
,” High Temperature
, Vol. 29
, No. 1
, pp. 126
–130
.25.
Kuo-Nan
Liou
1972
, “Electromagnetic Scattering by Arbitrarily Oriented Ice Cylinders
,” Applied Optics
, Vol. 11
, No. 3
, pp. 667
–674
.26.
Lee
S. C.
1986
, “Radiative Transfer Through a Fibrous Medium: Allowance for Fiber Orientation
,” J. Quant. Spectr. Radiat. Transfer
, Vol. 36
, No. 3
, pp. 253
–263
.27.
Lee
S. C.
1988
, “Radiation Heat-Transfer Model for Fibers Oriented Parallel to Diffuse Boundaries
,” J. Thermophys. and Heat Transfer
, Vol. 2
, No. 4
, pp. 303
–308
.28.
Lee
S. C.
1990
a, “Scattering Phase Function for Fibrous Media
,” Int. J. Heat Mass Transfer
, Vol. 33
, No. 10
, pp. 2183
–2190
.29.
Lee
S. C.
1990
b, “Dependent Scattering by Parallel Fibers: Effects of Multiple Scattering and Wave Interference
,” J. Thermophys. and Heat Transfer
, Vol. 6
, No. 4
, p. 589
589
.30.
Lind
A. C.
Greenberg
J. M.
1966
, “Electromagnetic Scattering by Obliquely Oriented Cylinder
,” J. Appl. Phys.
, Vol. 37
, No. 8
, pp. 3195
–3203
.31.
Mathes
R.
Blumenberg
J.
Keller
K.
1990
, “Radiative Heat Transfer in Insulations With Random Fibre Orientation
,” Int. J. Heat Mass Transfer
, Vol. 33
, No. 4
, pp. 767
–770
.32.
Mengu¨c¸
M. P.
Viskanta
R.
1983
, “Comparison of the Radiative Transfer Approximations for a Highly Forward Scattering Planar Medium
,” J. Quant. Spectr. Radiat. Transfer
, Vol. 29
, No. 5
, pp. 381
–392
.33.
Malitson
I. H.
1965
, “Interspecimen Comparison of the Refractive Index of Fused Silica
,” J. Opt. Soc. Amer.
, Vol. 55
, No. 10
, pp. 1205
–1209
.34.
Moiseyev
S. S.
Petrov
V. A.
Stepanov
S. V.
1990
, “Measurement of the Optical Properties of Highly Scattering Ceramic Materials
,” Int. J. Thermophysics
, Vol. 11
, No. 3
, pp. 587
–596
.35.
Moiseyev
S. S.
Petrov
V. A.
Stepanov
S. V.
1992
, “Optical Properties of High-Temperature Fibrous Silica Thermal Insulation
,” High Temperature—High Pressure
, Vol. 24
, No. 8
, pp. 391
–402
.36.
Nicolau
V. P.
Raynaud
M.
Sacadura
J. F.
1994
, “Spectral Radiative Properties Identification of Fiber Insulating Materials
,” Int. J. Heat Mass Transfer
, Vol. 37
, Suppl. 1. pp. 311
–324
.37.
O¨zis¸ik, M. H., 1973, Radiative Transfer and Interactions With Conduction and Convection, Wiley, New York.
38.
Petrov, V. A., 1979, “Optical Properties of Silica Glasses at High Temperatures in the Semi transparent Region,” Rev. on Thermophys. Propert. of Subst., No. 3(17), pp. 30–72 [in Russian].
39.
Petrov, V. A., 1993, “Optical and Thermophysical Properties of Semitransparent Materials in the Calculation of Combined Radiation-Conduction Heat Transfer,” Thermal Physics Reviews, Harwood Acad. Publ., New York, Vol. 4, Pt. 5.
40.
Reiss
H.
1990
, “Radiative Transfer in Nontransparent Dispersed Media
,” High Temperatures—High Pressures
, Vol. 22
, No. 5
, pp. 481
–522
.41.
Swathi
P. S.
Tong
T. W.
1988
, “A New Algorithm for Computing the Scattering Coefficients of Highly Absorbing Cylinders
,” J. Quant. Spectr. Radiat. Transfer
, Vol. 40
, No. 4
, pp. 525
–530
.42.
Tien
C. L.
1988
, “Thermal Radiation in Packed and Fluidized Beds
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 110
, No. 4(B)
, pp. 1230
–1242
.43.
Tong
T. W.
Tien
C. L.
1980
, “Analytical Model for Thermal Radiation in Fibrous Insulation
,” J. Thermal Insulation
, Vol. 4
, No. 7
, pp. 27
–44
.44.
Tong
T. W.
Tien
C. L.
1983
, “Radiative Heat Transfer in Fibrous Insulations. Part I: Analytical Study
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 105
, No. 1
, pp. 70
–75
.45.
Viskanta, R., 1982, “Radiation Heat Transfer: Interaction With Conduction and Convection and Approximate Methods in Radiation,” Proc. 7th Heat Transfer Conf., Vol. 1, pp. 103–121.
46.
Wait
J. R.
1955
, “Scattering of a Plane Wave From a Circular Dielectric Cylinder at Oblique Incidence
,” Canadian J. Phys.
, Vol. 33
, No. 5
, pp. 189
–195
.47.
Wang
K. Y.
Tien
C. L.
1983
, “Radiative Heat Transfer Through Opacified Fibers and Powders
,” J. Quant. Spectr. Radiat. Transfer
, Vol. 30
, No. 3
, pp. 213
–223
.48.
Yeh
H. Y.
Roux
J. A.
1988
, “Spectral Radiative Properties of Fiberglass Insulation
,” J. Thermophys. and Heat Transfer
, Vol. 2
, No. 1
, pp. 75
–81
.
This content is only available via PDF.
Copyright © 1996
by The American Society of Mechanical Engineers
You do not currently have access to this content.
