Consideration is given to the radiant interchange in a circular cylindrical cavity of finite length for the condition wherein there is an axially increasing or decreasing temperature along the cavity wall. The mathematical formulation of the problem leads to a linear integral equation which has been solved in closed form. The solution yields expressions for the local apparent emittance and for the over-all radiant energy transfer. These quantities fully specify the emission characteristics of the cavity.
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E. M. Sparrow (1965) studied this question.
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