Approximate One-Dimensional Models for Multigroup Neutral-Particle Transport in Ducts

Garcia, R. D. M.; Ono, Shizuca; Vieira, Wilson José

doi:10.1081/tt-120025064

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…This may be seen by setting R z = 0 in (65), (66) and (69). Of course, the internal reflection from the sides of the cylinder still remain via the term g(µ) as defined by equation (7).…”

Section: Problem (2): the Infinite Half-cylindermentioning

confidence: 99%

“…In the text, we have made use of a function g(µ), defined by equation (7). It is useful to note a few properties of that function.…”

Section: Infinite Half-cylindermentioning

confidence: 99%

“…To put it otherwise, the r-z problem was reduced to one in z only by averaging over the radial direction 1 All correspondence to 2a Lytchgate Close, South Croydon, Surrey, CR2 0DX, UK and azimuthal photon trajectory angle. Such a technique was already available from the work of Prinja and Pomraning [2] and Larsen [3], with further developments given by Prinja [4], Larsen et al [5] and also Garcia et al [6,7]. We have generalised the equations of Larsen to specular reflection governed by the Fresnel laws [8].…”

Section: Introductionmentioning

confidence: 99%

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Radiation transport in a light duct using a one-dimensional model

Williams

2007

Phys. Scr.

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A study is made of radiative transfer along a cylindrical duct using the one-dimensional approximation of Larsen. This method enables three-dimensional effects to be included in a one-dimensional equation. We have generalised Larsen's approach so that the internal reflection from the cylinder surface is governed by the Fresnel law. Two problems are considered. In the first, we assume an infinite cylinder with a plane source at the origin and, in the second, we have a semi-infinite cylinder with an incident beam on the surface. A Fourier transform is employed for the infinite cylinder and the Wiener-Hopf technique for the semi-infinite one. We are able to calculate the radiation intensity as a function of position along the cylinder and the mean square distance of travel of a photon. For the semi-infinite case, we obtain the albedo, the surface intensity and the mean distance of travel. Several features arise which demonstrate that the one-dimensional approximation preserves important features of the three-dimensional problem, thereby making the present approach a valuable tool in dealing with more complex problems.

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“…This may be seen by setting R z = 0 in (65), (66) and (69). Of course, the internal reflection from the sides of the cylinder still remain via the term g(µ) as defined by equation (7).…”

Section: Problem (2): the Infinite Half-cylindermentioning

confidence: 99%

“…In the text, we have made use of a function g(µ), defined by equation (7). It is useful to note a few properties of that function.…”

Section: Infinite Half-cylindermentioning

confidence: 99%