Exact Solution of the Radiation Heat Transport Equation in a Gas-Filled Spherical Cavity

by Eugene C. Gritton, Anthony Leonard

Download

Download eBook for Free

FormatFile SizeNotes
PDF file 1 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Purchase

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback49 pages $23.00 $18.40 20% Web Discount

This memorandum treats the case of steady-state, radiative heat transport through an absorbing, emitting, and heat-generating gray gas contained inside a black-wall spherical cavity. An exact analytical solution to the radiative transport equation is obtained for the case of uniform heat generation throughout the gaseous medium. The problem is formulated in terms of an integral equation with a difference kernel over a finite interval. A complex function is introduced for the source function. This in turn leads to a singular integral equation of the principal-value type that can be solved by standard techniques. An exact solution is found that yields the entire distribution of the gas emissive power. When this exact transport theory solution is compared with the Rosseland diffusion theory, the latter is shown to be capable of describing only the overall spatial dependence of the emissive power distribution. The solution has applications for high-temperature systems such as military rockets, reentry vehicles, gaseous-fueled cavity reactors, and modern power plants.

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

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.