Prese nt ed a re methods that avoid th e need to em ploy an extrapolation tec hnique in the region of th e c riti cal points for e valuation of th e apparent e mmissivity of diffu se c ylindrical and coni cal caviti es. Th e meth ods involve appropriate s ubstitutions in the integrand s of integral equations that a re used in a nalytical so lut ions for determ inin g the th erm al radiation c ha racte ri sti cs of diffuse and co ni cal cavi ti es. Equations for ei th e r iso th ermal or noni soth e rm al surface temperature conditi ons a re provid ed in a direc t fo rm for co mputations. N um e ri cal res ults are prese nted for a general lin ea r tem pera ture d istribution along the le ngth of a cylindri ca l cavit y. T he meth od is equally app li cable for th e solut ion of othe r prob le ms in integral eq uation s where discont inuiti es are e nco untered.
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B A Peavy (1966) studied this question.