How to Calculate Temperature Distribution or Heat Flux Distribution on a Surface in Radiation Space

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When radiant energy is emitted in the space which is composed of surfaces 1 to n and gases 1'to l' as shown in Fig. 1,the temperature of each surface has been already obtained, assuming that both distributions of the temperature and the heat flux on it are uniform. In this paper, I will show a method by which, on the same assumption, both distributions of the temperature and/or the heat flux on each surface may be calculated as the second approximation. The distributions may be obtained by considering heat balance, when overall interchange factor between an infinitesimal surface p on a surface m and a surface or gas x, (x, p) are determined. (x, p) may be obtained as follows. [numerical formula] where Δx_m/A_m represents <x, p>^^^-/A_p-<x, m>^^^-/A_m, and 1,2,……, i, ……, m, ……, n specify n surfaces, respectively. x represents an arbitrary surface or gas, which composes the space, and p an infinitesimal surface on m. (x, m) and <x, m>^^^- mean overall and one-way interchange factor between a surface m and a surface or gas x, respectively. εis emissivity.
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