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 (SCI-Expanded) identifier identifier


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.