9.38. As a result of changes in the thermal motions of its constituent particles, which are a function of the temperature, every body emits energy

in the form of electromagnetic radiations over a range of wave lengths; this is called thermal radiation. The amount of energy carried by the ra­diation is unchanged as it passes through a vacuum and is largely unaffected by dry air and many other gases, with the notable exceptions of carbon dioxide and water vapor. But when the radiation falls on a solid body or in its passage through the last-mentioned gases, part or all of the energy is absorbed. The fraction of the incident radiation that is absorbed is called the absorptivity. An ideal material which absorbs all the radiation falling upon it, and thus has an absorptivity of unity, is designated a black body. The emissive power or thermal radiation flux, i. e., the energy radiated in unit time per unit area of a black body, is given by the Stefan-Boltzmann law, namely,

Thermal radiation flux = (тГ4,

where the constant a has the value of 5.68 x 10“8 W/m2 • K4. The ratio of the emissive power of an actual surface to that from a black body is referred to as the emissivity, and for a body in thermal equilibrium, the emissivity and absorptivity are equal (Kirchhoff’s law).

9.39. The emissivity (and absorptivity) of surfaces vary with the nature of the material and its temperature as well as with its physical condition, e. g., roughness, cleanliness, etc. For metals, the emissivity is relatively low; the values generally range from about 0.05 or less for a highly polished surface to 0.2 or 0.3 for a roughened surface. If the metal is covered with an oxide film, the emissivity is greatly increased. Nonmetals have fairly high emissivities, although, in contrast to metals, the values decrease with increasing temperature. The emissivity of graphite, for example, ap­proaches unity at temperatures up to about 800 К (530°C), so that it approximates a black body. It is therefore a good emitter and absorber of thermal radiation. When radiation falls on a body, the proportion which is not absorbed is partly transmitted, e. g., through a “transparent” material such as air, and partly reflected, e. g., by a polished metal surface.

9.40. If two surfaces at different temperatures are separated by a non­absorbing medium, there is an interchange of radiation between them since they both act as absorbers and emitters. However, the net result is the transfer of energy from the hotter to the colder surface, the rate of energy transfer, e. g., in watts, being given by

Я. r ~ ^1Є1,2°"(Ті — Tf),

where 7 and T2 are the absolute temperatures of the hotter and colder bodies, respectively, Ax is the surface area of the former, and г12 is an interchange factor which is related to the emissivities (or absorptivities) of

the two surfaces; if both bodies were black, i. e., perfect absorbers and emitters, e12 would be unity. Certain geometrical factors should be in­cluded in this expression, but they may be disregarded here.

9.41. Even though radiation does not transfer any appreciable amount of energy directly to the coolant in a reactor, it may do so indirectly. In gas-cooled reactors operating at high temperatures, heat is transferred by convection from the fuel to the coolant, which is generally helium gas. The latter is transparent to thermal radiation and so does not absorb any radiant energy directly. However, radiation is transferred through the gas to the moderator (graphite), and this then loses energy by convection to the gaseous coolant. Thus, radiative transfer provides a means for conveying heat from the fuel element to the gas in an indirect manner. Radiation may also be significant in the transfer of heat from one reactor component, such as a fuel element, to another component, thus leading to thermal gradients which must be taken into account in stress analysis.