Analysis of nonlocal character of radiation heat transfer in thermal insulations

Insulations are typical participating media were simultaneous radiation ( emission, absorption, anisotropic scattering) and conduction are present with complex interactions between these two modes of heat transfer. In contradiction to heat conduction, thermal radiation is a long-distance interaction process and mathematically is described in a different way. In the case of participating media it is necessary to solve simultaneously the differential heat conduction equation and the radiative transfer equation which is, in general, of integro-differential type. The problem is especially complex when anisotropic scattering and spectral dependence of radiative properties are considered. In the paper a method based on a nonlocal description of radiative heat transfer in the medium is proposed. The method allows to decouple solution of the radiative transfer equation from solution of the heat conduction equation. It is especially suitable for optically thick media to which insulations normally belong. It easily allows to study influence of the boundary (or thickness) effect on heat transfer in insulations. Some examples have been given to illustrate the way of application of the method.