| Traditional engineering analysis of transport of thermal radiation, optical intensity, or photons through highly scattering media inevitably use assumptions to simplify the transient terms, such as time derivatives, in transport analysis, even if the boundary conditions and/or sources that are responsible for the radiative intensity or photons vary significantly with time. Such models exhibit infinite speed of propagation of the optical signal and finite transmission values are predicted even at times smaller than that associated with propagation of light. If the hyperbolic or wave nature of the complete transient radiative transfer equation is retained, the resulting models do not exhibit such drawbacks. This work discusses the different methods for determining transient radiative transfer through a scattering absorbing media using radiative transfer formulations. Two types of the incident intensity formulations are considered. For the first case, incident source pulse of the duration of picoseconds or less is used. The incident source pulse travels at the speed of light. For the other case, a boundary driven radiative problem formulation is used. The radiation intensity is incident at the surface and maintained at a constant value at all times in all directions. The different methods of solving the transient radiative transfer equation include the {dollar}Psb1, Psb3{dollar}, and {dollar}Psb5{dollar} approximations, two-flux method, and eight, twelve, and sixteen discrete ordinates methods in one-dimension and {dollar}Psb1{dollar} approximation for the case of two-dimensional geometry. In addition, the general transient radiative transfer equation is also solved by direct numerical integration without any simplifying assumptions for the one-dimension case. Large numbers of independent parameters can influence radiative transfer through a participating medium. But since the emphasis of this work is mainly on the scattering phenomenon, three important parameters associated with it, namely scattering albedo, optical depth, and scattering phase function distribution, are only considered here. Different orders of approximation for the phase function are considered as are a parametric study of wide range of the scattering albedo and optical depth is performed. All of the above mentioned parameters affect the transmitted and back scattered fluxes significantly. Applications where these transient methods are important include nascent field of optical tomography for biomedical imaging, remote sensing of ocean and atmosphere, evaluation of properties of turbid media, in-situ property determination of combustion generated particulates. |
