This paper proposed radiative characteristics' expressions for media containing randomly oriented fibers in space. In deriving these simple radiative characteristics' expressions, the fibrous medium effective extinction coefficient is defined to match with the one of large particle obtained by combining geometric optics and Fraunhofer diffraction theory. Fibrous media radiative characteristics are then derived as an average over all incident radiation angles of single fiber radiative characteristics. Theoretical hemispherical reflectance and normal transmittance predictions using the proposed fibrous media radiative characteristics based on the Mie theory agreed well with literature experiments. Therefore, media containing fiber randomly oriented in space can be scaled to a suitable equivalent media such that scattering mechanisms behave similarly to that occurring in a participating media containing spherical particles. Numerical investigations show that a theoretical model which assumes Henyey–Greenstein (HG) scattering phase function can conveniently be used for the estimation of equivalent fibrous media radiative characteristics using hemispherical reflectance measurements. On the other hand, the estimated equivalent fibrous media radiative characteristics from hemispherical measurements and using a two-flux model with isotropic scaling radiative characteristics may be subjected to serious errors in the case of semitransparent media for which the absorption is significant.
Issue Section:
Research Papers
References
1.
Dombrovsky
, L. A.
, and Baillis
, D.
, 2010
, Thermal Radiation in Disperse Systems: An Engineering Approach
, Begell House
, Redding, CT
.2.
Sacadura
, J.-F.
, 2011
, “Thermal Radiative Properties of Complex Media: Theoretical Prediction Versus Experimental Identification
,” Heat Transfer Eng.
, 32
(9
), pp. 754
–770
.3.
Lumley
, N. P. G.
, Ford
, E.
, Minford
, E.
, and Porter
, J. M.
, 2015
, “A Simplified Model for Effective Thermal Conductivity of Highly Porous Ceramic Fiber Insulation
,” ASME J. Therm. Sci. Eng. Appl.
, 7
(4
), p. 041022
.4.
Viskanta
, R.
, and Menguc
, M. P.
, 1989
, “Radiative Transfer in Dispersed Media
,” ASME Appl. Mech. Rev.
, 42
(9
), pp. 241
–259
.5.
Baillis
, D.
, and Sacadura
, J.-F.
, 2000
, “Thermal Radiation Properties of Dispersed Media: Theoretical Prediction and Experimental Characterization
,” J. Quant. Spectrosc. Radiat. Transfer
, 67
(5
), pp. 327
–363
.6.
Randrianalisoa
, J.
, Baillis
, D.
, and Pilon
, L.
, 2006
, “Improved Inverse Method for Radiative Characteristics of Closed-Cell Absorbing Porous Media
,” AIAA J. Thermophys. Heat Transfer
, 20
(4
), pp. 871
–883
.7.
Zhang
, C.
, and Kribus
, A.
, 2002
, “Effective Radiative Properties of a Cylinder Array
,” ASME J. Heat Transfer
, 124
(1
), pp. 198
–200
.8.
Zhao
, J.-J.
, Duan
, Y.-Y.
, Wang
, X.-D.
, and Wang
, B.-X.
, 2012
, “Radiative Properties and Heat Transfer Characteristics of Fiber-Loaded Silica Aerogel Composites for Thermal Insulation
,” Int. J. Heat Mass Transfer
, 55
(19–20), pp. 5196
–5204
.9.
Nicolau
, V. P.
, Raynaud
, M.
, and Sacadura
, J. F.
, 1994
, “Spectral Radiative Properties Identification of Fiber Insulating Materials
,” Int. J. Heat Mass Transfer
, 37
(1
), pp. 311
–324
.10.
Nisipeanu
, E.
, and Jones
, P. D.
, 2003
, “Monte Carlo Simulation of Radiative Heat Transfer in Coarse Fibrous Media
,” ASME J. Heat Transfer
, 125
(4
), pp. 748
–752
.11.
Tahira
, M. A.
, Tafreshi
, H. V.
, Hosseini
, S. A.
, and Pourdeyhimi
, B.
, 2010
, “Modeling the Role of Microstructural Parameters in Radiative Heat Transfer Through Disordered Fibrous Media
,” Int. J. Heat Mass Transfer
, 53
(21–22), pp. 4629
–4637
.12.
Arambakam
, R.
, Tafreshi
, H. V.
, and Pourdeyhimi
, B.
, 2012
, “Analytical Monte Carlo Ray Tracing Simulation of Radiative Heat Transfer Through Bimodal Fibrous Insulations With Translucent Fibers
,” Int. J. Heat Mass Transfer
, 55
(23–24), pp. 7234
–7246
.13.
Tong
, T. W.
, and Tien
, C. L.
, 1980
, “Analytical Models for Thermal Radiation in Fibrous Insulations
,” J. Therm. Insul.
, 4
, pp. 27
–44
.14.
Houston
, R. L.
, and Korpela
, S. A.
, 1982
, “Heat Transfer Through Fiberglass Insulation
,” 7th International Heat Transfer Conference
, Munchen, Germany, Sept. 6–10, Vol. 2
, pp. 499
–504
.15.
Lee
, S. C.
, 1986
, “Radiative Transfer Through a Fibrous Medium: Allowance for Fiber Orientation
,” J. Quant. Spectrosc. Radiat. Transfer
, 36
(3
), pp. 253
–263
.16.
Coquard
, R.
, and Baillis
, D.
, 2006
, “Radiative Properties of Dense Fibrous Medium Containing Fibers in the Geometric Limit
,” ASME J. Heat Transfer
, 128
(10
), pp. 1022
–1030
.17.
Daryabeigi
, K.
, Cunnington
, G. R.
, Miller
, S. D.
, and Knutson
, J. R.
, 2010
, “Combined Heat Transfer in High-Porosity High Temperature Fibrous Insulations: Theory and Experimental Validation
,” AIAA
Paper No. 2010-4660.18.
Tong
, T. W.
, Yang
, Q. S.
, and Tien
, C. L.
, 1983
, “Radiative Heat Transfer in Fibrous Insulations—Part II: Experimental Study
,” ASME J. Heat Transfer
, 105
(1
), pp. 76
–81
.19.
Wang
, K. Y.
, and Tien
, C. L.
, 1983
, “Radiative Transfer Through Opacified Fibers and Powders
,” J. Quant. Spectrosc. Radiat. Transfer
, 30
(3
), pp. 213
–223
.20.
Guilbert
, G.
, Jeandel
, G.
, Morlot
, G.
, Langlais
, C.
, and Klarsfeld
, S.
, 1987
, “Optical Characteristics of Semi-Transparent Porous Media
,” High Temp. High Pressures
, 19
(3), pp. 251
–259
.21.
Tong
, T. W.
, Swathi
, P. S.
, and Cunnington
, G. R.
, Jr., 1989
, “Reduction of Radiative Heat Transfer in Thermal Insulations by Use of Dielectric Coated Fibers
,” Int. Commun. Heat Mass Transfer
, 16
(6
), pp. 851
–860
.22.
Wan
, X.
, and Fan
, J.
, 2012
, “Heat Transfer Through Fibrous Assemblies Incorporating Reflective Interlayers
,” Int. J. Heat Mass Transfer
, 55
(25–26), pp. 8032
–8037
.23.
Tong
, T. W.
, and Tien
, C. L.
, 1983
, “Radiative Heat Transfer in Fibrous Insulations—Part I: Analytical Study
,” ASME J. Heat Transfer
, 105
(1
), pp. 70
–75
.24.
Lee
, S. C.
, and Cunnington
, G. R.
, 2000
, “Conduction and Radiation Heat Transfer in High-Porosity Fiber Thermal Insulation
,” AIAA J. Thermophys. Heat Transfer
, 14
(2
), pp. 121
–136
.25.
Cunnington
, G. R.
, and Lee
, S. C.
, 1996
, “Radiative Properties of Fibrous Insulations: Theory Versus Experiment
,” AIAA J. Thermophys. Heat Transfer
, 10
(3
), pp. 460
–466
.26.
Cunnington
, G. R.
, and Lee
, S. C.
, 1997
, “Experimental Verification of a Theory for Radiative Properties of High-Porosity Fibrous Media
,” Experimental Heat Transfer, Fluid Mechanics and Thermodynamics
, Vol. 4, M. Giot, F. Mayinger, and G. P. Celata, eds., Edizioni ETS, Pisa, Italy, pp. 2035
–2041
.27.
Marschall
, J.
, and Milos
, S. F.
, 1997
, “The Calculation of Anisotropic Extinction Coefficients for Radiation Diffusion in Rigid Fibrous Ceramic Insulations
,” Int. J. Heat Mass Transfer
, 40
(3
), pp. 627
–634
.28.
Yuen
, W. W.
, and Cunnington
, G.
, 2007
, “Radiative Heat Transfer Analysis of Fibrous Insulation Materials Using the Zonal-GEF Method
,” AIAA J. Thermophys. Heat Transfer
, 21
(1
), pp. 105
–113
.29.
Zhao
, S.-Y.
, Zhang
, B.-M.
, and Du
, S.-Y.
, 2009
, “An Inverse Analysis to Determine Conductive and Radiative Properties of a Fibrous Medium
,” J. Quant. Spectrosc. Radiat. Transfer
, 110
(13
), pp. 1111
–1123
.30.
Yamada
, J.
, and Kurosaki
, Y.
, 2000
, “Radiative Characteristics of Fibers With a Large Size Parameter
,” Int. J. Heat Mass Transfer
, 43
(6
), pp. 981
–991
.31.
Lind
, A. C.
, and Greenberg
, J. M.
, 1966
, “Electromagnetic Scattering by Obliquely Cylinders
,” J. Appl. Phys.
, 37
(8
), pp. 3195
–3303
.32.
Kerker
, M.
, 1969
, The Scattering of Light and Other Electromagnetic Radiation
, Academic Press
, New York
.33.
Bohren
, C. F.
, and Huffman
, D. R.
, 1983
, Absorption and Scattering of Light by Small Particles
, Wiley
, New York
.34.
Cohen
, A.
, and Alpert
, P.
, 1979
, “Extinction Efficiency of Obliquely and Randomly Oriented Infinite Cylinders
,” J. Appl. Phys.
, 50
(12
), pp. 8262
–8264
.35.
Kokhanovsky
, A. A.
, 2008
, Aerosol Optics: Light Absorption and Scattering by Particles in the Atmosphere
, Praxis Publishing
, Chichester, UK
.36.
Jeandel
, G.
, Boulet
, P.
, and Morlot
, G.
, 1993
, “Radiative Transfer Through a Medium of Silica Fibres Oriented in Parallel Planes
,” Int. J. Heat Mass Transfer
, 36
(2
), pp. 531
–536
.37.
Modest
, F. M.
, 2013
, Radiative Heat Transfer
, 3rd ed., McGraw-Hill
, New York
.38.
Howell
, J. R.
, Siegel
, R.
, and Mengüç
, M. P.
, 2011
, Thermal Radiation Heat Transfer
, 5th ed., CRC Press
, Boca Raton, FL
.39.
Matthews
, L. K.
, Viskanta
, R.
, and Incropera
, F. P.
, 1984
, “Development of Inverse Methods for Determining Thermophysical and Radiative Properties of High-Temperature Fibrous Materials
,” Int. J. Heat Mass Transfer
, 27
(4
), pp. 487
–495
.40.
Lee
, H.
, and Buckius
, R. O.
, 1982
, “Scaling Anisotropic Scattering in Radiation Heat Transfer for a Planar Medium
,” ASME J. Heat Transfer
, 104
(1
), pp. 68
–75
.41.
Dombrovsky
, L. A.
, 2012
, “The Use of Transport Approximation and Diffusion-Based Models in Radiative Transfer Calculations
,” Comput. Therm. Sci.
, 4
(4
), pp. 297
–315
.42.
Dombrovskii
, L. A.
, 1994
, “Quartz-Fiber Thermal Insulation: Calculation of Spectral Radiation Characteristics in the Infrared Region
,” High Temp.
, 32
(2
), pp. 197
–203
.43.
Palik
, E. D.
, 1998
, Handbook of Optical Constant of Solids
, Academic Press
, San Diego, CA.44.
Kitamura
, R.
, Pilon
, L.
, and Jonasz
, M.
, 2007
, “Optical Constants of Silica Glass From Extreme Ultraviolet to Far Infrared at Near Room Temperature
,” Appl. Opt.
, 46
(33
), pp. 8118
–8133
.45.
Singh
, B. P.
, and Kaviany
, M.
, 1991
, “Independent Theory Versus Direct Simulation of Radiation Heat Transfer in Packed Beds
,” Int. J. Heat Mass Transfer
, 34
(11
), pp. 2869
–2882
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