Conduction and Radiation Heat Transfer in High-Porosity Fiber Thermal Insulation

Nomenclature a, b = partial wave coefŽ cients C = radiative cross section F = orientation distribution function fv = Ž ber volume fraction G k = asymmetry scattering factor; Eq. (23) Ib = black-body radiation Ib k = Planck function i k = Ž ber-scattering intensity distribution K k = extinction coefŽ cient kr = radiative conductivity k0 = propagation constant L = specimen thickness M = number of Ž ber polar orientations mg = molecularmass of gas-phasematerial ms = molecularmass of solid-phasematerial N = number of Ž ber sizes n = real part of complex refractive index P = size of the equivalent pore spaces inside aerogel pk = scattering phase function q = heat  ux r = radius of Ž ber T = temperature xi = fractional volume of Ž bers of radius ri a = size parameter, 2p r / k C k = modiŽ ed extinction coefŽ cient; Eq. (22) c = ratio of speciŽ c heats at constant pressure and constant volume d s = solid fraction of matrix medium g = scattering angle