Transient thermal analysis of parallel translucent layers by using Green'sfunctions

An analysis is developed for computing transient thermal behavior in a comp osite of two parallel translucent layers with a space between them. The rad iative two-nux equation is coupled with the transient energy equation, and both equations are solved by using Green's functions. Illustrative results are provided for transient heating of two parallel translucent layers that exchange radiation. The external boundaries of the two-layer combination ar e each exposed to a radiative environment, and all boundaries can be convec tively heated or cooled. The layer refractive indices are larger than one, and internal reflections are included with boundaries assumed diffuse. The analysis includes internal emission, absorption, isotropic scattering, and heat conduction. Transient results from the present method are verified for a single gray layer by comparison with a finite difference solution that i ncorporates a numerical solution of the exact radiative transfer equations for the radiative heat source. Illustrative transient temperature distribut ions show the effects of an insulating gap between layers, when one side of the two-layer composite is subjected to heating by radiation and convectio n, while the other side is being cooled.