A variational formulation and Ritz solution of the radiative equilibrium of a plane slab

Derbentli T.

INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, vol.24, no.3, pp.349-356, 1997 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 1997
  • Doi Number: 10.1016/s0735-1933(97)00020-1
  • Title of Journal : INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
  • Page Numbers: pp.349-356

Abstract

Radiative equilibrium problem for an absorbing emitting medium between plane parallel diffuse surfaces can be expressed by the Fredholm equation of the second kind. In this paper a variational formulation of the problem is obtained in terms of a functional. Dimensionless temperatures and heat fluxes for various optical thicknesses are then solved by the Ritz method. Results are expressed in terms of a third order polynomial with two coefficients and are very close to the exact solution of Heaslet and Warming. Copyright (C) 1997 Elsevier Science Ltd.