Multiple radiation shields

(a) Develop an equation for the rate of radiant heat transfer through a series of n very thin, fiat, parallel metal sheets, each having a different emissivity e, when the first sheet is at temperature T₁ and the nth sheet is at temperature T_n. Give your result in terms of the radiation resistances for the successive pairs of planes. Edge effects and conduction across the air gaps between the sheets are to be neglected.

(b) Determine the ratio of the radiant heat transfer rate for n identical sheets to that for two identical sheets.

(c) Compare your results for three sheets with that obtained in Example 16.5-1. The marked reduction in heat transfer rates produced by a number of radiation shields in series has led to the use of multiple layers of metal foils for high-temperatureinsulation.

Ru+1 (T-T+) 1,1+1