Divergence of Radiative Heat Flux in Ultra-Short Time Scale in Axisymmetric Geometry With its Implications

An axisymmetric transient radiative heat transfer model is developed taking into account the new formulation of divergence of radiative heat flux in ultrashort time scale. In order to predict the medium temperature, divergence of radiative heat flux is coupled with the energy equation. The conventional quasi steady divergence of radiative heat flux is modified taking into account the transient effect of photon transport. An axisymmetric domain is taken as a physical model in the present analysis. A critical examination revealed that even for pure scattering medium, the diveregence of flux is a non-zero quantity due to the inclusion of the new term called as propagation term in the formulation of the divergence of radiative heat flux in ultrashort time scale. A two-dimensional scheme is proposed to solve the radiative transfer equation (RTE) in an axisymmeric cylindrical domain. The step spatial scheme is used for discretizing the spatial term in the RTE. The medium is assumed to be absorbing, emitting and isotropically scattering. The walls are assumed as diffuse and gray. It is observed that the conventional quasi-steady divergence of radiative heat flux underpredicts the temperature of the medium in the time scale of the order of characteristic time scale of photon where transient radiation effect is predominant.