Optimal porosity distribution of fibrous insulation

The porosity of fibrous materials is an important factor to their insulating performance. This paper considers the optimal porosity distribution of non-uniform fibrous porous medias for thermal insulation. Heat flow through the fibrous porous media is described by a coupled conduction–radiation heat transfer model which is numerically solved by using Finite Volume Method, and the optimal porosity distribution corresponding to the minimum total heat transfer is derived by applying a BFGS quasi-Newton optimization procedure. Variable analysis shows that the optimal porosity distribution is typically piecewise in conductive heat transfer dominated porous medium. For practical reasons, the change of porosity distribution across the thickness of the fibrous porous media may need to be continuous. To derive such a continuous optimal porosity distribution, a small penalty item should be introduced into the objective function. The study shows that, a continuous optimal porosity distribution generally has relatively high porosity at both boundaries and relatively low porosity in the centre region. The optimal distribution depends on many factors such as fibre radius, fibre emissivity, temperature difference, and overall mean porosity.