An integral formulation of transient radiative transfer

A time-dependent integral formulation is developed for modeling transient r adiative transfer. The development is based on a rigorous analysis of the w ave propagation process inside the participating media. The physical signif icance of the present integral formulation is the consideration of the time -dependent domain of computation, which is different from the domain distur bed by radiation (i.e., the wave front envelope). Numerical computations ar e performed for the medium that is an absorbing and isotropically scatterin g one-dimensional plane slab geometry. The spatial and temporal incident ra diation and radiative flux distributions are presented for different bounda ry conditions and for uniform and nonuniform property distribution. The tra nsient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. T he solutions of reflecting boundary conditions exhibit distinctive behavior from that of the non-reflecting boundary.