Absorption of thermal radiation in a semi-transparent spherical droplet: a simplified model

The boundary-value problem for calculation of differential absorption of thermal radiation is formulated based on the modified DP₀ approximation. The solution of this problem is supplemented by simple analytical approximations for the normalised absorbed radiation power. The latter is used together with the analytical approximation for the efficiency factor of absorption, suggested earlier. The resulting simplified model is applied to the specific problem of absorption of thermal radiation by a diesel fuel droplet. Two types of diesel fuel have been considered. It is pointed out that the radial distribution of absorbed thermal radiation power is non-monotonic. The power absorbed in the droplet core is shown to be rather large and almost homogeneous. Also, the absorbed power is large in the vicinity of the droplet surface, but is minimal in the intermediate region. It is pointed out that the variations of the refractive index of diesel fuel with wavelengths can smooth the predicted radial dependence of the thermal radiation power, absorbed in diesel fuel droplets.