A time-dependent integral formulation is developed for modeling transient radiative transfer. The development is based on a rigorous analysis of the wave propagation process inside the participating media. The physical significance of the present integral formulation is the consideration of the time-dependent domain of computation, which is different from the domain disturbed by radiation (i.e., the wave front envelope). Numerical computations are performed for the medium that is an absorbing and isotropically scattering one-dimensional plane slab geometry. 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.
An Integral Formulation of Transient Radiative Transfer
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division October 11, 1999; revision received June 11, 2000. Associate Editor: P. Menguc.
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Tan, Z., and Hsu, P. (June 11, 2000). "An Integral Formulation of Transient Radiative Transfer ." ASME. J. Heat Transfer. June 2001; 123(3): 466–475. https://doi.org/10.1115/1.1371230
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