One-dimensional stochastic model of radiative heat transfer in dielectric medium

Abstract

One-dimensional stochastic model that describes radiative heat transfer in dielectric medium is built. It is done on the basis of representation that heat transfer in a solid is realized both by means of its heat conductivity and by means of the heat electromagnetic radiation which is generated by thermal fluctuations in the medium. It is supposed that electromagnetic fluctuations are caused by thermal vibrations of solid skeleton connected with irradiation and absorption processes of photons. In the difference with previous works, it permits to formulate the stochastic model without using the supposition of susceptibility fluctuations and not to use the additional mathematical averaging on temporally slow process of thermal conductivity. It leads to the model in the form of the infinite dimensional Ornstein-Uhlenbeck process using the classic fluctuation-dissipative theorem. The energy flux of fluctuating electromagnetic field is calculated as a functional of the local temperature.