Thermal analysis of multiple, infinite, parallel plates with thin film coatings
Zalta, Karen Loftus
Chapman, Alan J.
Master of Science
Multiple, infinite, parallel plates, with or without thin surface films, in a known thermal environment are analyzed. Several assumptions are made to render the problem tractable. A two wavelength band approximation is employed. The two bands considered are the solar band, which includes the shorter wavelengths, and the infrared band, which includes the longer wavelengths. This approximation is essential in that it allows the solar and infrared radiosity equations to be mathematically unlinked. This further allows the solar radiosities to be independent of temperature. In the solar band, thin films are assumed to absorb a negligible amount of radiation as compared to the substrate, due to the relative thicknesses. Thus, the solar optical properties may be calculated using Fresnel's equations. The effective optical properties of a plate (substrate and thin films) are calculated using equations based on ray-tracing. These effective optical properties, functions of thin film optical properties, substrate index of refraction, substrate extinction coefficient, and substrate thickness, include all inner reflections within a plate. Once the effective optical constants for each plate are known, a method is established for calculating solar radiosities. This method has two parts. First, a recursive algorithm is established for calculating the percentage of environmental radiation which eventually falls on each surface (irradiation factors). Then, the radiosities may be predicted by a superposition of the irradiation factors. The algorithm is unique in that it requires a one-time solution of four equations. Then the solution of the (N-l) plate case predicts the solution of the N plate case. Also, all inner reflections between plates are considered. This is clearly a great advantage over direct methods which require the simultaneous solution of (4N-2) equations. In the infrared band, radiation is absorbed and emitted in a diffuse manner. The plates are assumed to be gray and opaque. Infrared radiosities may not be calculated directly since they depend upon temperature. An energy balance is made on each side of every plate yielding 2N equations which are functions of the 2N unknown temperatures. An iterative scheme is employed whereby subsequent "guesses" are made for the temperatures until convergence is achieved. Though this analysis could conceivably be performed using a programmable pocket calculator, a Digital PDP-11 computer was used to run Program PLATES which performed the analysis.