Radiative cooling of a solidifying droplet layer including absorption and scattering

A simple solution for the transient cooling of a solidifying layer filled with drops that can emit and scatter radiation is discussed, with application to a liquid drop radiator proposed for the Space Station (Mattick and Hertzberg, 1981). The layer remains at uniform temperature during solidification, and the outer portions rapidly lose heat, producing a variation along the length of the layer in the distribution of liquid concentration across the layer. The analysis is used to obtain both the amount of energy dissipated by the two-phase system at uniform temperature and the velocity distribution necessary to maintain a uniform liquid fraction across the entire layer at all locations along the layer length.