Conditions for supersonic bent Marshak waves

Supersonic radiation diffusion approximation is a useful way to study the radiation transportation. Considering the bent Marshak wave theory in 2-dimensions, and an invariable source temperature, we get the supersonic radiation diffusion conditions which are about the Mach number \(M>8(1+\sqrt{\e...

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Bibliographic Details
Published in:arXiv.org 2014-10
Main Authors: Xu, Qiang, Xiao-dong, Ren, Li, Jing, Jia-kun, Dan, Wang, Kun-lun, Shao-tong, Zhou
Format: Article
Language:English
Subjects:
Density
Diffusion
High temperature
Internal energy
Mach number
Online Access:Get full text
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Summary:Supersonic radiation diffusion approximation is a useful way to study the radiation transportation. Considering the bent Marshak wave theory in 2-dimensions, and an invariable source temperature, we get the supersonic radiation diffusion conditions which are about the Mach number \(M>8(1+\sqrt{\ep})/3\), and the optical depth \(\tau>1\). A large Mach number requires a high temperature, while a large optical depth requires a low temperature. Only when the source temperature is in a proper region these conditions can be satisfied. Assuming the material opacity and the specific internal energy depend on the temperature and the density as a form of power law, for a given density, these conditions correspond to a region about source temperature and the length of the sample. This supersonic diffusion region involves both lower and upper limit of source temperature, while that in 1-dimension only gives a lower limit. Taking \(\rm SiO_2\) and the Au for example, we show the supersonic region numerically.
ISSN:2331-8422
DOI:10.48550/arxiv.1410.4035