The Sparrow-Galerkin solution of radiation exchange and transition to finite element

This paper presents a historical perspective on the development of the Gale rkin-type and finite-element calculations of radiation exchange between sur faces. It is shown that the formulation of the variational solution of radi ation exchange introduced by Sparrow in the 1950s is similar to that used b y Galerkin to solve differential equations. The extension of Galerkin's met hod to the integral equations of the Fredholm type yields the formulations developed by Sparrow using the variational method. For this reason, the Gal erkin-type solutions of radiation exchange will be referred to as the Sparr ow-Galerkin method. The Sparrow-Galerkin solution technique, in most cases, provides highly accurate results. However, for a certain set of parameters , the series solutions may not converge. This leads to formulation of a fin ite-element technique as the discretized form of the Sparrow-Galerkin metho d evolves into the finite-element method. (C) 1998 Elsevier Science Ltd. Al l rights reserved.