The analysis of thermal phenomena associated with radiation from sources which are imperfectly collimated is presented in a form convenient for engineering calculations. The analysis is developed in terms of beam divergence and directional intensity and applied to an hypothetical solar simulation system. Two different intensity distributions are postulated and expressions are derived for solar constants and solar shape factors. The concept of shadowing is discussed and a procedure is described for calculating both local and mean solar shape factors in penumbral regions. A simple L-shaped configuration is analyzed to illustrate the procedures and to examine the influence of beam divergence on equilibrium temperatures. Results are presented for both diffuse and specular surfaces, and several values of α*/ε.

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