SOLUTION OF THE INTEGRATED RADIATIVE TRANSFER EQUATION FOR GRAY AND NONGRAY MEDIA M. F. G. Cremers, M. J. Remie, K. R. A. M. Schreel, and L. P. H. de Goey Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands In this article a spectrally resolved solution of the integrated radiative transfer equation for the discrete transfer method with linear temperature interpolation is presented. Combined with the discrete ordinate method, the radiative heat fluxes are determined for use in the finite-volume energy equation. The spectral dependence of the absorption coefficient is approximated as a series of bands of constant value and scattering is neglected. The method is shown to be computationally efficient when applied to a course mesh typical for conduc- tion problems and at the same time to be accurate for both optically thin and thick media, including semitransparent media. 1. INTRODUCTION Optically thick or semitransparent objects at high temperatures suffer from sig- nificant radiative heat loss at the surfaces. Apart from heat loss at the surface, inter- nal temperature gradients result in internal conductive and radiative heat fluxes, and the ratio between the conductive and radiative heat flux depends on the thermal and optical properties of the object. The redistribution of energy by conductive and radi- ative transport increases with increasing temperature gradient. Doornink et al. [1] showed that in a semitransparent material such as glass, thermal energy is redistrib- uted by radiation and is transferred from the interior of the material to surroundings by ‘‘long-range’’ radiative transfer. Therefore, it is important to estimate the radiat- ive heat fluxes accurately when the medium is absorbing and the temperature gradi- ents are large. Different methods have been developed to estimate the radiative heat flux in gray media. Siegel and Howell [2] and Modest [3], e.g., provide overviews of the dif- ferent well-known solution methods for simplified conditions. Among them are the Rosseland diffusion approximation for the optically dense case, and different meth- ods using a mean absorption coefficient when radiative heat transfer is not the domi- nant heat transfer mechanism and may be calculated with limited accuracy. Received 1 October 2005; accepted 23 November 2005. Financial support by Philips Lighting B.V. is gratefully acknowledged. Address correspondence to K. R. A. M. Schreel, Department of Mechanical Engineering, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: k.r.a.m.schreel@tue.nl 205 Numerical Heat Transfer, Part A, 50: 205–228, 2006 Copyright # Taylor & Francis Group, LLC ISSN: 1040-7782 print=1521-0634 online DOI: 10.1080/10407780600602465