Effect of surroundings on the transient energy transfer in a layer of radiating gas

Summary 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.