A polynomial chaos approach to narrow band modeling of radiative heat transfer in non-uniform gaseous media

- Radiative heat transfer in non-uniform media is considered.
- A polynomial chaos approach is developed for this purpose.
- The technique is shown to provide non-parametric copulas.
- Copulas model the dependencies between gas spectra in distinct states.
- The approach is shown to be reliable for radiative heat transfer calculations.

An accurate treatment of non-uniformities is required in many applications involving radiative heat transfer in gaseous media. Usual techniques to handle path non-uniformities rely on simplifying assumptions, such as scaling or correlation of gas spectra. Those approximations are usually accurate but may also fail to provide accurate results, especially when large temperature gradients are considered. The objective of the present work is to show that this problem can be treated rigorously. The proposed method can be applied to any arbitrary narrow band model. It is based on some results from Polynomial Chaos׳ framework and copulas theory. Although the mathematical derivation may appear sophisticated, applying the method is straightforward. It is shown that adding only one coefficient to any uniform narrow band model (for a simple case involving a non-uniform column discretized into two uniform sub-paths) allows to achieve almost LBL accuracy for radiative heat transfer calculations. The technique is described and applied to some “severe” test cases from the literature.