Predicting the effective thermal conductivity of foam-polymer materials


Аuthors

*, Bardushkin V. V.**, Yakovlev V. B.***, Bardushkin A. V.****

Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia

*e-mail: iglavr@mail.ru
**e-mail: bardushkin@mail.ru
***e-mail: yakvb@mail.ru
****e-mail: i170k@yandex.ru

Abstract

The problem of calculating the effective thermal conductivity of a sample of inhomogeneous material in the case of dependence of the thermal conductivity of material components on temperature and the presence of a large temperature difference at the boundaries of this sample is considered. A two-stage scheme for finding the effective thermal conductivity of a sample for such a case is proposed. This two-stage scheme is used to calculate the effective thermal conductivity of a foam-polymer sample in the form of a disk, the thickness of which is small compared to its radius. The opposite bases of the disk are maintained at constant significantly different temperatures. The first step is to calculate the effective thermal conductivity of the thin layer of the sample, the temperature at all points of which can be considered approximately the same. At the second stage, the effective thermal conductivity of the sample of the homogeneous reference medium of the same shape as the sample of the initial foam-polymer is calculated, with the same dependence of the thermal conductivity on the temperature as of the effective thermal conductivities of the ordered thin layers of the foam sample. The size of the pores is considered small enough to neglect convective heat exchange in them, the transfer of heat by radiation in the pores is taken into account by an effective coefficient of thermal conductivity in the pores. Model calculations of the effective thermal conductivity of the thin layer and the entire sample of foam-epoxy material based on a binder ED-20 with spherical pores filled with Freon-21, depending on the apparent density of the foam-epoxy material, were carried out. Calculations were carried out on the basis of a generalized singular approximation in two options for choosing a comparison medium parameter, as well as using the asymmetric Bruggeman formula. It has been shown that the effective thermal conductivity of the foam layer depends significantly on its temperature, as well as on the size of the pores. It has been established that both for the thin layer and for the entire sample of foam-epoxy material, all the studied dependences of the effective thermal conductivity on the apparent density of the material are nonlinear and monotonously increasing.

Keywords:

effective thermal conductivity, foam-polymer material, composite, matrix, inclusion, Maxwell – Garnett approximation, generalized singular approximation

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