Parameter Estimation in a Two-Layer Planar Gray Participating Medium

Abstract

An inverse analysis is reported for simultaneous estimation of absorption and scattering coefficients for an inhomogeneous plane-parallel anisotropically scattering participating medium between isothermal, diffuse parallel plates from the knowledge of known temperature profile. A finite volume method is used to discretize the equation governing radiative heat transfer through the participating medium, and the inverse problem is solved through the minimization of the sum of square of residuals between the calculated and observed temperatures, utilizing the conjugate gradient method. The calculations are carried out for homogeneous and inhomogeneous media, and the effects of measurement errors on the accuracy of the estimated parameters are investigated. Nomenclature A = area, m 2 c, d = gradient vector I = radiation intensity, Wm −2 sr −1 ¯ I = in-scattering term, Wm −2 sr −1 J = objective function L = characteristic length of the domain (L1 + L2), m L 1= thickness of the top layer of the participating medium, m L 2= thickness of the bottom layer of the participating medium, m M = number of directions in γ direction m = location from the reference z axis mp = total number of measured points N = number of control volumes n = unit vector normal to a control volume surface P = parameter vector q = total heat transfer rate per unit width from the hot wall, W · m −1