Estimation of the Mean Thermal Conductivity of Anisotropic Materials

An estimation method of the plane directional thermal conductivity of fibrous insulations using the cyclic heat method and the transient hot-wire method is proposed. By assuming that the thermal conductivity λh of anisotropic materials measured by the transient hot-wire method is equivalent to that of the isotropic materials which have the same bulk density ρ and specific heat c as the anisotropic materials, the thermal conductivity λh is shown to be equal to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt {\lambda _x \lambda _y } $$ \end{document}, which is a geometrical mean of the thermal conductivities in the direction of the plane λx and the thickness λy of the anisotropic materials. For an alumina silica blanket (ρ=125 kg·m−3), the thermal conductivities λh, λx, and λy were measured in the temperature range between −140 and 300°C using the transient hot-wire method for λh and the cyclic heat method for λx and λy. In the same way, the thermal conductivities λh, λx, and λy of a rock wool (ρ=121 kg·m−3) insulation were also measured in the temperature range, 100 to 600°C. From a comparison of the measured results with the estimated values of λx, it is confirmed that the proposed method can estimate the measured values reasonably well.