Temperature jump boundary conditions in radiation diffusion

Technical Report · Wed Dec 01 04:00:00 EST 1976

DOI:https://doi.org/10.2172/7306201· OSTI ID:7306201

Alonso, C. T.

The radiation diffusion approximation greatly simplifies radiation transport problems. Yet the application of this method has often been unnecessarily restricted to optically thick regions, or has been extended through the use of such ad hoc devices as flux limiters. The purpose of this paper is to review and draw attention to the use of the more physically appropriate temperature jump boundary conditions for extending the range of validity of the diffusion approximation. Pioneering work has shown that temperature jump boundary conditions remove the singularity in flux that occurs in ordinary diffusion at small optical thicknesses. In this review paper Deissler's equations for frequency-dependent jump boundary conditions are presented and specific geometric examples are calculated analytically for steady state radiation transfer. When jump boundary conditions are applied to radiation diffusion, they yield exact solutions which are naturally flux- limited and geometry-corrected. We believe that the presence of temperature jumps on source boundaries is probably responsible in some cases for the past need for imposing ad hoc flux-limiting constraints on pure diffusion solutions. The solution for transfer between plane slabs, which is exact to all orders of optical thickness, also provides a useful tool for studying the accuracy of computer codes.

• Research Organization: California Univ., Livermore (USA). Lawrence Livermore Lab.
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 7306201
• Report Number(s): UCID-17359
• Country of Publication: United States
• Language: English

Related Subjects

654001* -- Radiation & Shielding Physics-- Radiation Physics
Shielding Calculations & Experiments
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUNDARY CONDITIONS
DIFFUSION
RADIATION TRANSPORT
SLABS
TEMPERATURE EFFECTS