ABSTRACT

Heat transport in fibrous insulation is modelled, emphasis being placed on radiative heat transfer. The model further includes conductive heat transport in the gaseous and fibrous phases. The case is a planar layer of fibrous insulation with a heated and a cooled plate on the two sides as in a standard test apparatus for measuring the apparent thermal conductivity. The absorption and scattering coefficients are calculated using the Mie theory, a measured statistical fibre diameter distribution, and the orientation of the fibres. The radiative heat transfer is modelled using two models: the two-flux model and the spherical harmonics method with arbitrary approximation order. The system of governing equations is discretized using finite differences and the system of algebraic equations is solved by the Newton-Raphson method. The results show that the radiative heat flux, as well as the radiative conductivity calculated from the two-flux model, is approx. 15 % in error while a P-1 equation gives very accurate results compared to higher order spherical harmonics approximations. The computational costs of low-order spherical harmonics are acceptable, although not as low as when using the two-flux model. The costs of using very high approximation orders such as P-21 are considerable. However, the P-1 and P-3 approximations do not model the angular distribution of the intensity at the walls as precisely as do the P-11 and P-21 approximations.