A 2D Improvement of Radiative Heat Transfer with the P1 Approximation and a Statistical Narrow Band Model

• Published in: Fluid dynamics & materials processing 2012-01, Vol.8 (3), p.323-338
• Main Authors: Khourchafi, A, El Alami, M, Najam, M, Belhaq, M
• Format: Article
• Language: English
• Subjects: Absorptivity; Anisotropy; Approximation; Correlation; Mathematical analysis; Mathematical models; Radiative heat transfer; Real gases; Sharpness; Spectra; Spectral correlation
• ISSN: 1555-256X; 1555-2578
• DOI: 10.3970/fdmp.2012.008.323

A spectral radiation study has been carried out in the framework of a statistical narrow-band model based on an inverse-tailed exponential law and the socalled P1 approximation. This new spectral formulation, which may be also regarded as a grey band formulation with a local absorption coefficient, leads to two implementation methods: a non correlated form in which the averaged formulation of the P1 approximation does not take into account the correlation between fundamental quantities and a pseudo-correlated variant consisting basically of a technique for improving the anisotropy of the radiative intensity. Real gases (H sub(2)O, CO sub(2)) are considered. The resulting tests show the limitation of the method in radiative heat transfer. A proper consideration of the spectral correlation with the technique of of the correlation "indicator", however, leads to an appreciable increase of the accuracy. Since the thermal discontinuity near the corners is known to penalize the P1 method, it is expected that the present formulation may give even better results in more general cases (for which the sharpness of thermal gradients near the walls is less pronounced).