The purpose of this paper is to obtain the temperature field inside a cylinder filled in with a dense nonscattering semitransparent medium from directional intensity data by solving the inverse radiative transfer equation. This equation is solved in a first approach with the help of a discrete scheme, and the solution is then exactly obtained by separating the physical set on two disjoint domains on which a Laplace transform is applied, followed by the resolution of a first kind Fredholm equation.
Issue Section:
Radiative Heat Transfer
1.
Milne
, A. E.
, 1966, “Thermodynamics of Stars
,” Selected Papers in Radiation Transfer
, D. H.
Menzil
, ed., Dover Publication
, New York
.2.
Chahine
, M. T.
, 1968, “Determination of the Temperature Profile in an Atmosphere From Its Outgoing Radiance
,” J. Opt. Soc. Am.
0030-3941, 58
, pp. 1634
–1637
.3.
Ben-Abdallah
, P.
, 1998, “A Variational Method to Inverse the Radiative Transfer Equation: Application to Thermal Sounding of Atmospheres of Giant Planets
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 60
(1
), pp. 9
–15
.4.
Siewert
, C. E.
, 1994, “A Radiative Inverse-Source Problem for a Sphere
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 52
(2
), pp. 157
–160
.5.
Li
, H. Y.
, 1994, “Estimation of the Temperature Profile in a Cylindrical Medium by Inverse Analysis
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 52
(6
), pp. 755
–764
.6.
Kocifaj
, M.
, 1994, “The Inversion Problem of Interaction of Shortwave Direct Solar Radiation With Small Dust Particles in the High Atmosphere
,” Contributions of the Astronomical Observatory Skalnate Pleso
, 24
, pp. 57
–64
.7.
Liu
, H. G.
, and Jiang
, J.
, 2001, “Inverse Radiation Problem for Reconstruction of Temperature Profile in Axisymmetric Free Flames
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 70
(2
), pp. 207
–215
.8.
Deiveegan
, M.
, Balaji
, C.
, and Venkateshan
, S. P.
, 2006, “Comparison of Various Methods for Simultaneous Retrieval of Surface Emissivities and Gas Properties in Gray Participating Media
,” ASME J. Heat Transfer
0022-1481, 128
(8
), pp. 829
–837
.9.
Park
, H. M.
, and Lee
, W. J.
, 2002, “The Solution of Inverse Radiation Problems Using an Efficient Computational Technique
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 73
(1
), pp. 41
–54
.10.
Kim
, K. W.
, and Baek
, S. W.
, 2007, “Inverse Radiation-Conduction Design Problem in a Participating Concentric Cylindrical Medium
,” Int. J. Heat Mass Transfer
0017-9310, 50
, pp. 2828
–2837
.11.
Ertürk
, H.
, Ezekoye
, O. A.
, and Howell
, J. R.
, 2002, “Comparison of Three Regularised Solution Techniques in a Three-Dimensional Inverse Radiation Problem
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 73
, pp. 307
–316
.12.
Viskanta
, R.
, Hommert
, P. J.
, and Groninger
, G. L.
, 1975, “Spectral Remote Sensing of Temperature Distribution in Semitransparent Solids Heated by an External Radiative Source
,” Appl. Opt.
0003-6935, 14
(2
), pp. 428
–437
.13.
Zhou
, H. C.
, Hou
, Y. B.
, Chen
, D. L.
, and Zheng
, C. G.
, 2002, “An Inverse Radiative Transfer Problem of Simultaneously Estimating Profiles of Temperature and Radiative Parameters From Boundary Intensity and Temperature Measurements
,” J. Quant. Spectrosc. Radiat. Transf.
0022-4073, 74
(5
), pp. 605
–620
.14.
Kudo
, K.
, Kuroda
, A.
, Eid
, A.
, Saito
, T.
, and Ogurna
, M.
, 1995, “Solution of the Inverse Radiative Load Problems by the Singular Value Decomposition
,” Proceedings of the First International Symposium on Radiative Transfer
, Kusadasi, Turkey.15.
Natterer
, F.
, 1983, “Exploiting the Ranges of Radon Transforms in Tomography in Numerical Treatment of Inverse Problems in Differential and Integral Equations
,” Progress in Scientific Computing
, Vol. 2
, P.
Deuflhard
and E.
Hairer
, eds., Birkhauser
, Stuttgart
, pp. 290
–303
.16.
Sakami
, M.
, Le Dez
, V.
, and Lallemand
, M.
, 1991, “Retrieval of Temperature Profiles in Cylinders of Semi-Transparent Media
,” Fourth Annual Inverse Problems in Engineering Seminar
, Michigan State University, Jun.17.
Le Dez
, V.
, Huclin
, J. C.
, and Lallemand
, M.
, 1993, “Directional Emissivities of Semi-Transparent Media. Cases of Dihedron, Infinite Cylinder and Cone
,” Glastech. Ber.
0017-1085, 66
(5
), pp. 127
–137
.18.
Press
, W. H.
, Teukolsky
, S. A.
, Vetterling
, W. T.
, and Flannery
, B. P.
, 2007, “Numerical Recipies in Fortran 77
,” The Art of Scientific Computing
, 2nd ed., Cambridge University Press
, New York
.19.
Abramowitz
, M.
, and Stegun
, I. A.
, eds., 1972, Handbook of Mathematical Functions
, National Bureau of Standards
, Washington, DC
.20.
Tricomi
, F. G.
, 1985, Integral Equations
, Dover
, New York
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.