In very low density insulating assemblies, heat transfer occurs mainly by gas phase conduction, by convention, and by radiation. Many attempts have been made to analyze the parameters that control the radiant component of this heat transfer using electromagnetic theory based on the Maxwell equations. Extensive solutions are available in the literature for spheres but few results have been calculated for cylinders (which would model fibrous insulations), although the relevant equations have been given by Van de Hulst and by Larkin and Churchill. Larkin and Churchill give appropriate values for “real” refractive indices only, with zero absorption.
We have now obtained complete “complex” solutions as functions of fiber diameter and the fiber optical properties of refractive index and absorption coefficient (or dielectric constant). These solutions allow a full understanding of the roles of scattering and absorption in radiant energy transfer and show how these can be optimized for various materials as a function of wave-length (or temperature).
Once the radiant heat transfer is minimized for single isolated cylinders, we consider how this translates to a low density assembly of many such cylinders or fibers. The results show that radiant heat transfer can be minimized by the selection of an optimum fiber diameter and that this optimum differs for each material and for different absorption coefficients (as these affect the real and imaginary parts of the refractive index which determine the heat transfer).