A Moments Method for Describing the Diffusion of Radiation from a Cavity. II

摘要

In an earlier paper the diffusion of radiation from a cavity was treated in the case that the transport of energy is purely radiative and the radiation mean free path in the cavity is infinite. In this paper we reconsider the same problem allowing for a finite mean free path in the cavity. For short times this problem admits a similarity transformation and the resulting equations are solved by a combination of series expansion and perturbation theory methods. Comparison with exact numerical results in special cases shows that a second‐order calculation gives quite good accuracy. These short‐time results, together with the known long‐time results, are incorporated into a moments‐method solution of the cavity problem valid for all times. Typical numerical results are presented which confirm the expectation that the improved model presented here differs from the earlier model mainly in its predictions of the short‐time characteristics of the solution.