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

• Autorzy: Koniorczyk, P. , Zmywaczyk, J.
• Języki publikacji: EN

Abstrakty

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].

Słowa kluczowe

PL

przepływ ciepła radiacyjno-przewodnościowego; środki anizotropowe; zmniejszanie przewodnictwa

EN

anisotropic scattering media; radiative-conductive heat transfer; reduction of thermal conductivity

• Czasopismo: Archives of Thermodynamics
• Rocznik: 2008
• Tom: Vol. 29, no. 2
• Strony: 47-60
• Opis fizyczny: Bibliogr. 9 poz.,tabl., wykr., wz.,

Twórcy

autor

Koniorczyk, P.

autor

Zmywaczyk, J.

• Military University of Technology, ul. Kaliskiego 2, 00-908 Warsaw, Poland,

Bibliografia

• [1] HOTTEL H.C., SAROFIM A.F.: Radiative transfer, McGraw-Hill Book Company, 1967, 427-437.
• [2] REISS H.: Radiative Transfer in Nontransparent, Dispersed Media, Springer-Verlag, 1988.
• [3] KONIORCZYK P., ZMYWACZYK J.: Approximate analysis of influence of surface emissivity on combined heat radiation and conduction in aspect of the fiat sample thickness effect on heat conduction of semitransparent media, Arch. of Thermodynamics, Vol. 26(2005), No. 4, 3-16.
• [4] KONIORCZYK P., ZMYWACZYK J.: Reduction of an effective thermal conductivity in the aspect of two flux model for absorbing, emitting and scattering media, Arch. of Thermodynamics, Vol. 25(2004), No. 4, 19-29.
• [5] KONIORCZYK P., ZMYWACZYK J.: Analysis of the thermal conductivity reduction in grey medium using a two-flux model for radiation heat transfer, Arch. of Thermodynamics, Vol. 28(2007), No. 3, 41-56.
• [6] ASLLANAJ F., MILANDRI A., JEANDEL G., ROCHE J.R.: A finite difference solution of nonlinear systems of radiative-conductive heat transfer equations, Int. J. for Numerical Methods in Engineering, No 54, 2002, 1649-1668.
• [7] MODEST M.F.: Radiative Heat Transfer, McGraw-Hill International Editions, 1993.
• [8] KONIORCZYK P., ZMYWACZYK J.: "Thickness effect curve" as a result of radiative -conductive heat transfer phenomenon, Military University of Technology, Warsaw, Poland 2008 (monograph in Polish - to be published in 2008).
• [9] SAAD Y.: Iterative methods for solving sparse linear systems, INTERNET (http://www-users.cs.umn.edu/~saad/books.html)