Application of Ambarzumian’s Method to Radiant Interchange in a Rectangular Cavity

[+] Author and Article Information
A. L. Crosbie, T. R. Sawheny

Thermal Radiative Transfer Group, Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, Mo.

J. Heat Transfer 96(2), 191-196 (May 01, 1974) (6 pages) doi:10.1115/1.3450163 History: Received September 11, 1973; Online August 11, 2010


Ambarzumian’s method had been used for the first time to solve a radiant interchange problem. A rectangular cavity is defined by two semi-infinite parallel gray surfaces which are subject to an exponentially varying heat flux, i.e., q = q0 exp(−mx). Instead of solving the integral equation for the radiosity for each value of m, solutions for all values of m are obtained simultaneously. Using Ambarzumian’s method, the integral equation for the radiosity is first transformed into an integro-differential equation and then into a system of ordinary differential equations. Initial conditions required to solve the differential equations are the H functions which represent the radiosity at the edge of the cavity for various values of m. This H function is shown to satisfy a nonlinear integral equation which is easily solved by iteration. Numerical results for the H function and radiosity distribution within the cavity are presented for a wide range of m values.

Copyright © 1974 by ASME
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