Flash Experiment on a Semitransparent Material : Interest of a Reduced Model

The subject deals with a reduced model of the conductiveradiative transient transfer in a participating medium. The accuracy of the analytical solution based on the well-known two-flux approximation and expressed with global radiative coefficients is tested in the case of sharp thermal excitation by a heat pulse on the front face of anisotropically scattering media. A very good agreement is achieved compared with numerical and analytical simulations involving high forward scattering, linear anisotropic scattering or Rayleigh scattering. This reduced model is then used in the inverse approach in order to determine the intrinsic diffusivity of semitransparent media. INTRODUCTION The increasing use of glasses, insulated foams, polymers in new technological products forced gradually the heat transfer community to take an interest in the study of combined radiative and conductive transfer in semitransparent media. Nevertheless only a limited amount of work is available on the inverse problem in this field [1, 2, 3]. Concerning the thermal diffusivity measurement, a lot of authors tried to extend the use of the flash method, first developped for opaque materials, to semitransparent media. In those participating media, the measured diffusivity is an apparent one. It takes both conductive and radiative transfers into account. In order to obtain the phonic diffusivity which is an intrinsic parameter, it is necessary to build a model including both radiative and conductive effects. As a consequence, the number of parameters increases. The aim of this study does not consist in evaluating all the parameters : it will be utopian with only one information namely the evolution of the rear face temperature. We rather try to show that a reduced model is able to reproduce the thermal behavior of absorbing, emitting and anisotropically scattering in a realistic way. More specifically, it allows to reach the phonic diffusivity which is a significant parameter for the engineering calculations. NOMENCLATURE a : phonic diffusivity (ms) p c ρ : volumetric heat capacity (J.m K) e : slab thickness (m) k : intrinsic thermal conductivity * L : intensity 4 0 2 4 T n L σ π ( M : global radiative parameter e M ) 2 ( σ χ + = N : global radiative parameter e N σ = pl N : Planck number 3 0 2 4 T n k σ β ( n : refractive index * p : dimensionless Laplace variable a p e * r q : dimensionless radiative heat flux 4 0 2 4 T n qr σ (