An analysis is presented for the transient cooling or heating of a stagnant layer of hot radiating gas surrounded by a cold gas capable of absorbing and emitting radiation. Scattering of radiation is neglected, and energy transfer by conduction and convection is considered to be negligible compared with radiation. The gas is assumed to be perfect and in local thermodynamic equilibrium. The heating of a cold gas by a diffuse and a collimated radiation flux incident on the boundary of the gas from some external source is considered, and the dependence of physical and radiative properties on temperature is taken into account. The problem is formulated exactly using radiative transfer theory. A scheme is developed for the numerical solution of the nonlinear integrodifferential equations of energy conservation. Starting with arbitrary, but given, initial temperature profiles, temperature distributions and local radiative fluxes are predicted as a function of time for a wide range of physically interesting conditions. ยง I. Introduction High temperature phenomena such as are encountered in shock waves, arcs, plasmas, atomic explosions, planetary re-entry, and other recent technological developments have stimulated interest in radiative transfer. An analysis is presented in this paper for unsteady energy transfer in a stagnant layer of hot radiating gas surrounded by a colder gas capable of absorbing and emitting radiation. The objective is to predict the temperature distribution as well as the local radiative flux and to determine the effect of the *