A design-oriented matrix formulation is derived for computing script-F radiative interchange factors in an enclosure of arbitrary geometrical and emissive-reflective complexity. Algorithms are presented for enclosures containing surfaces which emit either diffusely or directionally and reflect diffusely, specularly, or bidirectionally. Inputs to the transfer matrix are bidirectional and diffuse reflectances, conventional shape factors, and exchange factors which account for specular reflections. Rules are given to identify the various elements of the transfer matrix so that it may be constructed mechanically without writing complete equations for emergent directional and hemispherical fluxes. The formulation is illustrated with a closed-form solution and numerical results for a three-surface enclosure consisting of a bidirectionally reflecting area, a perfectly specular reflector, and a perfectly diffuse reflector.

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