Radiation analysis

Oppenheim— Radiation Analysis by the Network Method, in Hartnett et al.—Recent Advances in Heat and Mass Transfer, McGraw-Hill. 

Tlial is, the total hemispherical emissivity of a surface at temperature T is equal to its total hemispherical absorptivity for radiation coming from a blackbody at the same temperature. This relation, which greatly simplifies the radiation analysis, was first developed by Gustav Kirchhoff in 1860 and is now called Kirchlioff s law. Note that tliis relation is derived under the condition that the... 

It is very tempting to use Kirchhoff s law in radiation analysis since the relation c - a together with p = 1 - a enables us to determine all three properties of an opaque surface from a knowledge of only one property. Although Eq. 12-47 gives acceptable results in most cases, in practice, carp should be exercised when there is considerable dilference between the surface temperature and the temperature of the source of incident radiation. 

The view factor has proven to be very useful in radiation analysis because it allows us to express the fraction of radiation leaving a surface that strikes another surface in terms of Ihe orientation of these two surfaces relative to each other. The underlying assumption in this process is that the radiation a surface receives from a source is directly proportional to the angle the surface subtends when viewed from the source. This would be the case only if the radiation coming off the source is uniform in all directions throughout its surface and the medium between the surfaces does not absorb, emit, or scatter radiation. That is, it is the case when Ihe surfaces are isothermal and diffuse emitters and reflectors and the surfaces are separated by a iioiiparticipating medium such as a vacuum or air. 

Radiation analysis on an enclosure consisting of N surfaces requires the evaluation of view factors, and this evaluation process is probably the most time-consuming part of a radiation analysis. However, it is neither practical nor necessary to evaluate all of the view factors directly. Once a sufficient number of view factors are available, the rest of them can be determined by utilizing some fundamental relations for view factors, as discussed ne,xt. 

Discussion Note that when the outer sphere is much larger than the inner sphere > ri), Fsa approaches one. This is expected, since the fraction of radiation leaving the outer sphere that is intercepted by the inner sphere will be negligible in that case. Also note that the two spheres considered above do not need to be concentric. Hovrever, the radiation analysis will be most accurate for the case of concentric spheres, since the radiation is most likely to be uniform on the surfaces in that case. 

Analysis (a) The geometry involves six surfaces, and thus we may be tempted at first to treat the furnace as a six-surface enclosure. However, the four side surfaces possess the same properties, and thus we can treat them as a single side surface in radiation analysis. We consider the base surface to be surface 1, the top surface to be surface 2, and the side surfaces to be surface 3. Then the problem reduces to determining Qj Qi and Qj. 

The analysis of radiation transfer in enclosures consisting of black surfaces is relatively easy, as we have seen, but most enclosures encountered in practice involve nonblack surfaces, which allow multiple reflections to occur. Radiation analysis of such enclosures becoroe.s very complicated unless some simplifying assumptions are made. 

To make a simple radiation analysis possible, it is common to assume the surfaces of an enclosure to be opaque, diffuse, and gray. That is, the siirface.s arc nontransparent, they are diffuse emitters and diffuse reflectors, and their radiation properties are independent of wavelength. Also, each surface of the enclosure is isothennal, and both the incoming and outgoing radiation are uniform over each surface. But first vve review the concept of radiosity introduced in Chap. 12. 

In Ihe radiation analysis of an enclosure, either the temperature or the net rate of heat transfer must be given for each of the surfaces to obtain a unique solution for the unknown surface temperatures and heal transfer rales. There are two methods commonly used to solve radiation problems. In the first method, Eqs. 13 32 (for surfaces with specified heat transfer rales) and 13-33 (for surfaces with specified temperatures) are simplified and rearranged as... 

The presence of a participating medium complicates the radiation analysis considerably for several reasons ... 

Radiaton heal transfer between surfaces depends on the orientation of the surfaces relative to each other. In a radiation. analysis, this effect is accounted for by the geometric parameter vie.iv facior. The vretv factor ftoni a surface i to a. surface j is denoted by or F j, and is defined as the fraction of the radiation leaving surface i that strikes surface j directly. The view factors between differential and finite surfaces are expressed as... 

C Why is the radiation analysis of enclosures that consist of hlaek surfaces relatively easy How is the rale of radiation heal transfer between iwo surfaces expressed in this... 

C What are the two methods used in radiation analysis How do these two methods differ ... 

C What is a reradialing surface Wllat simplifications does a reradiating surface offer in the radiation analysis ... 

Oppenheim, K.A. Radiation analysis by the network method. Trans. Amer. Soc. Mech. Engrs. 78 (1956) 725-735... 

Smart, J. E. 1998. Real-time airborne radiation analysis and collection (RTARAC) searching for airborne species characteristic to nuclear proliferation. 7 Radioanal Nucl Ch. 235, 105-108. 

Figure 5 A multidetector setup used in combination with a nuclear microprobe. Types of spectra obtained are indicated. PIGE, particle-induced y-ray emission and PBA, prompt radiation analysis. See text for further explanation.

In addition to NAA, neutrons are widely used in prompt radiation analysis for the determination of concentration and spatial distribution of elements in different matrices. For example, a track-etched detector (LR-115, Makrofol KG, CR 39, mica) placed on the polished surface of a sample is irradiated with fast or thermal neutrons then etched with a suitable chemical to deduce the concentration profiles from the track distributions. This method can also be used for the detection of suspended and dissolved U, Th, and Pu in water by (n,f) reactions N in polymers by the N(n,p) C reaction B and Li in semiconductors or glasses by the B(n,a) Li and Li(n,ot) H reactions, respectively. For the detection of fission fragments the use of mica is recommended. 

There are many more new fields in the utilization of neutrons produced mainly by small D-D and D-T accelerators (IAEA 2000). Some typical fields of activation and prompt radiation analysis are summarized in Table 32.1. 

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