Modeling of time-resolved coupled radiative and conductive heat transfer in multilayer semitransparent materials up to very high temperatures
Résumé
This paper presents an original modeling approach that enables the calculation of the temperature field within multilayer materials submitted to the flash method. The model takes into account the time-resolved coupled conducto-radiative heat transfer and the temperature of experiments. The compound can be subdivided into as many layers as desired, and their thicknesses and relevant physical properties can be chosen arbitrarily. Unconventional experimental thermograms can be reproduced faithfully by the calculations. This model, thus, makes it possible to correctly estimate the effective thermal diffusivity of semitransparent materials, thereby providing a deeper insight into the analysis of the physical phenomena involved. V C 2011 American Institute of Physics. [doi:10.1063/1.3664408] This study is part of a larger research project and its objective is to model the heat transfer in textured materials, such as foams and porous ceramics. 1,2 Modeling of the flash method, 3,4 in order to characterize the effective thermal dif-fusivity of specific materials, has been devoted a particular interest. The experimental thermograms (i.e., temperature versus time curves) that have been obtained for certain samples clearly demonstrated that conduction is not the only mode of heat transfer that occurs in these materials. Indeed, the phenomena that appear at very short times, e.g., a non-zero slope, a sharp temperature increase, a temperature step, point to the existence of radiative heat transfer as a result of the semitransparent nature of the materials. This semitrans-parent behavior can be explained by the texture of the materials as well as by their chemical composition from the local (i.e., the mean free path of the phonons) to the macroscopic scale. Moreover, our characterization studies have been conducted at several temperature levels including high temperatures where radiation becomes dominant. A model coupling both transfer modes (conduction and radiation) and taking into account the temperature level of the experiment was developed. This paper presents the validation of the model for a few cases, and it will be shown that unconventional thermograms collected on various samples can be quite satisfactorily reproduced by our model under the assumption of a one-dimensional heat transfer. Our model solves the heat transfer problem associated to the flash experiment applied to a 1D semitransparent cylindrical sample. In the case of a porous medium, no convec-tion transfer is assumed to take place according to Rayleigh's criteria. The front surface of the sample is submitted to a pulsed energy deposition of short duration, which is assumed to be uniform over the surface. The lateral surface is presumed to be adiabatic, whereas the front face and its opposite side (the back face) are submitted to boundary conditions of emission, diffuse reflection, and heat dissipa-tion through a coupled convective-radiative exchange coefficient. All these assumptions render it possible to develop a one-dimensional heat transfer model coupling conduction and radiation, where the latter is assumed to present an azi-muthal symmetry. Four more assumptions were made: (i) the intensity field was supposed to be isotropic in each half-space, (ii) the material under study was presumed to be grey (i.e., of radiative properties independent of the wavelength),