Numerical Solution of the Radiation Transport Equation at an Air-Water Interface for a Stratified Medium - Judd, K. Peter; Handler, Robert A. (Frontiers in Mechanical Engineering, 2019)
This paper is a continuation of previous work that analytically examined the strength of radiation leaving an air-water interface. The approach here is to numerically integrate the radiation transport equation in order to capture the non-linear features of the problem, and also to include more realistic models for the thermal boundary layer. The radiation intensity of the photons emitted from the interface, relative to that of thermal radiation at the temperature of the interface, is defined here as the signal. This signal was computed for constant surface temperature and constant heat flux boundary conditions. As expected, the numerical computations show that the signal increased as the air-water temperature difference increased. The results are shown to form a hierarchy of signal strengths based on the chosen thermal stratification model. However, for both boundary conditions, the numerical results for a linear temperature profile compared very favorably with the simplified analytical linearized model over the thermal wavebands of 3-5 and 8-14 microns. In addition, the linearized model compared favorably with the most realistic models of thermal stratification.