Analysis of conduction‐radiation problem in absorbing and emitting nongray materials

The purpose of this paper is to present a computationally efficient model to solve combined conduction/radiation heat transfer problems in absorbing, emitting, non‐scattering, non‐gray materials.

The model is formulated for steady‐state condition and based on an iterative approach where the medium is discretized into finite strips and the extinction spectrum is divided into finite bands to consider the extinction coefficient variation with the wavelength.

Temperature fields and heat flux distributions are presented to demonstrate the capability of the formulation. It is shown that the model is quite accurate and efficient even for the cases of pure radiation. Differently from other models, the number of iterations required by the model for convergence is very low, even in the cases dominated by radiation.

The model has great potential to contribute with the evaluation and design of materials for thermal insulation, where radiation heat transfer can be the dominant mechanism, such as aerogel materials which are recognized as the solids with the lowest thermal conductivity and are intended to be used in building and construction, aerospace, transportation and other applications.