Radiative cooling of a layer with nonuniform velocity - A separable solution

Analyzed here is the cooling of a flowing plane layer filled with hot particles or liquid droplets that emit, absorb, and scatter radiation. The velocity distribution is nonuniform across the layer and the specified shape of this distribution affects the layer temperature distribution and emittance. The velocity distribution determined is one that will cause the layer to cool at a uniform temperature. Thus, if the layer initially has a uniform temperature, it will retain the same emittance throughout its length. A separable solution is found that applies in a 'fully developed' region following an initial cooling length. In this developed region, the solution shows that there is a constant emittance based on the local heat loss and local bulk mean layer temperature. This emittance is a function of the velocity distribution, optical thickness, and scattering albedo.