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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

2007

Vol. 28, no. 3

41-56

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].