Abstract
Numerical computations are performed for the transient radiative transfer equation within the one-dimensional parallel plate geometry using an integral formulation obtained in a prior work. The medium under consideration is absorbing and isotropically scattering. One boundary is a black emitting surface or a transparent surface subjected to the collimated incident radiation. The incident intensity is applied at the start of the transient. The other boundary is a cold and black or specularly reflecting surface. The spatial and temporal incident radiation and radiative flux distributions are presented for different boundary conditions and for uniform and nonuniform property distribution. The transient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. The solutions of reflecting boundary condition exhibit distinctive behavior from that of the non-reflecting boundary. The integral formulation is extended to handle the transient transfer within the nonhomogeneous participating media. The integral formulation has several advantages over the differential treatment of the hyperbolic wave of the radiative transport; among others: (1) The avoidance of using a high order upwind difference scheme in resolving the wave front; (2) Providing a sound basis for physical interpretation as the radiative transfer is a volumetric process; and (3) Many integral equation numerical methods that have previously been developed for the steady state integral formulation can be re-applied to treat the transient problem.
