Calculation of heat transfer through a horizontal porous annulus by conduction, radiation and convection using variable properties

The distribution of velocity and temperature in porous media is usually calculated by applying the Darcy law and the Boussinesq approximation. This implies that all properties are set constant except the density in the buoyancy terms. This is approximately true, if temperature differences are small in the area of interest. Nevertheless, in a hot gas duct with internal insulation important temperature differences occur between the inner and the outer wall. The present work therefore investigates the influence of temperature-dependent properties on the calculated results. In particular, the contribution of radiation to the thermal conductivity was studied for a high-temperature fibrous insulation. Measurements of the thermal conductivity in a vacuum show that the specific extinction coefficient is a practicable property to describe radiation in fibrous media. Solving the equations of continuity, momentum and energy with variable properties yields heat transfer coefficients which are up to 20% higher than those calculated by using the Boussinesq approximation. An attempt is sometimes made to improve the results from Boussinesq's approximation by using the temperature-dependent thermal conductivity. It is shown in this paper that this leads to even lower heat transfer coefficients and therefore does not represent an improvement in accuracy. (orig.)