Backward Method of Characteristics in Radiative Heat Transfer

Katika, Kamal M.; Pilon, Laurent

doi:10.1615/ichmt.2004.rad-4.340

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…Extensive discussion of this method for both transient and steady-state radiation transfer has been previously reported [24,26] and need not be repeated here. Comparison between numerical integral solutions [9] and the modified method of characteristics were found to be in good agreement with a mean error of less than 5% for βL = 0.5 and ω = 0.05 and 0.95 [25].…”

Section: Methods Of Solutionmentioning

confidence: 99%

Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

Smith

Katika

Pilon

2007

Journal of Quantitative Spectroscopy and Radiative Transfer

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This paper presents a parametric study of the time-resolved hemispherical reflectance of a plane-parallel slab of homogeneous, cold, absorbing, and isotropically scattering medium exposed to a collimated Gaussian pulse. The front surface of the slab is transparent while the back surface is assumed to be cold and black. The onedimensional time-dependent radiation transfer equation is solved using the modified method of characteristics. The parameters explored include (1) the optical thickness, (2) the single scattering albedo of the medium, and (3) the incident pulse width. The study pays particular attention to the maximum transient hemispherical reflectance and identifies optically thin and thick regimes. It shows that the maximum reflectance is independent of the optical thickness in the optically thick regime. In the optically thin regime, however, the maximum hemispherical reflectance depends on all three parameters explored. The transition between the optically thick and thin regimes occurs when the optical thickness is approximately equal to the dimensionless pulse width. Finally, correlations relating the maximum of the hemispherical reflectance as a function of the optical thickness, the single scattering albedo of the materials and the incident pulse width have been developed. These correlations could be used to retrieve radiation characteristics or serve as initial guesses for more complex inversion schemes accounting for anisotropic scattering.

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Section: Methods Of Solutionmentioning

confidence: 99%

Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

Smith

Katika

Pilon

2007

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…A wide variety of computational methods have been developed in order to solve the TRTE, which describes the spatial and temporal variations of the radiation intensity into a participating medium along a particular direction. Among these methods: the traditional [16,17] and reverse [18] Monte Carlo formulations, the classical spherical harmonics [19], the modified MP 1/3 A [20], the two-flux approaches [19], the radiation element methods [21], the discrete ordinates approaches [22][23][24], the integral formulations [25,26], the backward method of characteristics [27,28], the discrete transfer method [29] and the Galerkin approach [30,31].…”

Section: Introductionmentioning

confidence: 99%

Short-pulsed laser transport in absorbing and scattering media: time-based versus frequency-based approaches

Francoeur

Rousse

2007

J. Phys. D: Appl. Phys.

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Optical tomography (OT) is a promising non-intrusive characterization technique of absorbing and scattering media that uses transmitted and/or reflected signals of samples irradiated with visible or near-infrared light. The quality of OT techniques is directly related to the accuracy of their forward models due to the use of inversion algorithms. In this paper, forward models for transient OT approaches are investigated. The system under study involves a one-dimensional absorbing and scattering medium illuminated by a short laser pulse; this problem is solved using a discrete ordinates–finite volume (DO–FV) method in both time and frequency domain. Previous works have shown that time-domain approaches coupled with first order spatial interpolation schemes cannot represent the physics of the problem adequately as transmitted fluxes emerge before the minimal physical time required to leave the medium. In this work, the Van Leer and Superbee flux limiters, combined with the second order Lax–Wendroff scheme, are used in an attempt to prevent this. Results show that despite significant improvement, flux limiters fail to completely eliminate the physically unrealistic behaviour. On the other hand, results for transmittance obtained from the frequency-based method are accurate, without physically unrealistic behaviours at early time periods. The frequency-dependent approach is however computationally expensive, since it requires approximately five times more computational time than its temporal counterpart when used as a forward model for transient OT. On the other hand, the great advantages of the frequency-based approach is that limited windows of temporal signals can be calculated efficiently (in transient OT), and it can also be used as a forward model for steady-state, frequency-based and transient OT techniques.

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“…Recently, the modified method of characteristics has been developed as an accurate technique to solve the equation for phonon radiative transfer (EPRT) [20]. The method was extended to solve the radiative transfer equation (RTE) for both steady and transient problems in homogeneous media with diffuse surfaces and incident intensities [21]. In this paper we extend the method further to solve the transient radiative transfer equation for a medium irradiated by a collimated ultra-short pulse laser beam.…”

Section: Introductionmentioning

confidence: 99%

Ultra-Short Pulsed Laser Transport in a Multilayered Turbid Media

Katika

Pilon

2004

Heat Transfer, Volume 2

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This paper presents the modified method of characteristics for simulating the transient transport of light in an absorbing and scattering medium exposed to collimated light. This method is based on the method of characteristics that follows photons along their pathlines. After showing the validity of the method it is used to solve for the transient transport of light in human skin. Skin has been modelled as a seven layer medium with different scattering and absorbing coefficients and scattering asymmetry factors. The angular distribution of reflected light from skin is presented. This technique could be used as a tool for designing various biomedical applications.

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Backward Method of Characteristics in Radiative Heat Transfer

Cited by 4 publications

References 19 publications

Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

Short-pulsed laser transport in absorbing and scattering media: time-based versus frequency-based approaches

Ultra-Short Pulsed Laser Transport in a Multilayered Turbid Media

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