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1

Analysis of thermal conductivity reduction in grey medium using a discrete ordinate method and the Henyey-Greenstein phase function for absorbing, emitting and anisotropically scattering media

Koniorczyk P., Zmywaczyk J.

Archives of Thermodynamics

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2008

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Vol. 29, no. 2

47-60

EN

This paper is a continuation of considerations concerning the analytical and numerical analysis of the problem of 'thickness effect curve' in interactive optical media mentioned in papers [3-5]. A model of 1-D steady-state combined conductive-radiative heat transfer in the absorbing, emitting and anisotropically scattering grey medium confined between black surfaces has been considered in this paper. To find the radiative thermal conductivity thickness dependence k[r](l) (for a sample thickness l) and dependence of the radiative heat flux density q[r](l) upon the sample thickness l, a finite difference method together with the discrete ordinate method (DOM) and the Henyey-Greenstein phase function expanded into Legendre polynomials have been used iteratively [1, 2, 7]. Taking into account the radiation field in a more than one direction of propagation is necessary due to anisotropy of the directional intensity resulting from at least partially transparent medium and from anisotropic scattering. As in our earlier papers the initial data for performing numerical calculations represent a group of semitransparent material with extinction coefficient K = 1000 m[^-1] and with the conductive component of thermal conductivity k[c] = 0.1 W m[^-1]K[^-1] [3-5].

2

Analysis of the thermal conductivity reduction in grey medium using a two-flux model for radiation heat transfer

Kaniorczyk P., Zmywaczyk J.

Archives of Thermodynamics

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2007

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Vol. 28, no. 3

41-56

EN

This paper is a continuation of considerations concerning the analytical and numerical analysis of the problem of "thickness effect curve" in interactive optical media mentioned in papers [3,4]. A 1-D conduction-radiation heat transfer model in an absorbing, emitting and scattering grey medium has been considered in this paper. To find the thermal conductivity thickness dependence k(l) (for a sample thickness l) and dependence of the radiative heat flux density q[r](l) upon the sample thickness /, a finite difference method together with the two-flux method (TFM) based on the Schuster-Schwarzschild approximation has been used iteratively [1,2]. The modified two-flux approximation assumes anisotropic scattering. The scattering albedo [omega], extinction coefficient [kappa] and backscattering coefficient b are used in the modified TFM [1,2]. Likewise to our earlier papers the initial data for performing numerical calculations represent a group of semi-transparent material (e.g. cellular concretes) with extinction coefficient [kappa] = 1000 m[^-1] and with the conductive component of thermal conductivity k[c] = 0,1 Wm[^-1]K[^-1] [3,4].

3

On one method for constructing a dynamical mesh of nonlinear quasiperfect processes in deformable anisotropic media

Bomba A., Kashtan S.

Journal of Applied Computer Science

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2004

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Vol. 12, nr 2

7-21

EN

A new algorithm has been developed for numerical solving inverse nonlinear boundary value problems on quasiconformal mapping in anisotropic media, which are curvilinear tetragons limited by lines of a flow and equipotential lines under action of a potential gradient tensor. The dynamical mesh has been constructed and the velocity field of the domain has been calculated.