This work develops analytical solutions that converge rapidly for all optical thicknesses. For the case of an optically thick medium, such as the gaseous-fuel in a cavity reactor, solutions are found in a closed form. Consideration is given to the problem of an absorbing, emitting and heat generating gray gas contained inside a black wall spherical cavity of given radius. A solution to the problem is obtained through the use of singular integral equation theory based on methods just developed for use in neutron transport theory and Couette flow. 5 pp. Refs. (KB)
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.