Abstract
An analysis is presented for local radiation equilibrium temperatures in a semigray, nondiffuse conical cavity. The nondiffuse character is taken into account with a specular component of reflection. A simple rule is found to exist among the paths of specularly reflected rays in the cavity. Using this rule, the radiant interchange factors are easily obtained. The kernel of the integral equation for radiant flux takes infinitely large values at the apex. This behavior of the kernel is expressed with the delta function, so that the radiant heat exchange and temperature at the apex can exactly be obtained. The temperature calculated showed to be increased by the specular component of reflection in the short wave range but decreased by that in the long wave range, when the solar absorptance of the surface is large. A general conclusion on the property of the radiosity integral equation is obtained that its kernel takes infinitely large values at an intersection of more than two surfaces as at the apex and this singularity can be expressed in terms of the delta function.
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