Radiation and velocity fields induced by localized temperature fluctuations

A theory describing the coupling between radiative transport, thermal conduction, and velocity fluctuations in postcombustion gases is described. The emission and absorption of radiant energy are taken to be dominated by soot, distributed uniformly in space. The theory is local in the sense that the gas is assumed to be unbounded. However, die temperature, velocity, and radiation fields can be both three-dimensional and time-dependent. Moreover, the model can be thought of as describing any postcombustion scenario in which the absorption coefficient is spatially uniform. Within the framework of the low Mach number combustion equations. an exact representation of the velocity and radiation fields instantaneously induced by fluctuations of any magnitude in the temperature is presented. This result is used to derive a single scalar integro-differential equation for die temperature that incorporates the conservation of mass and energy, together with an exact solution of the radiative transport equation. Some consequences of the theory are illustrated by studying the response generated by a spherically burning fuel mass.