Shape factor for radiation

Fig. 8-12 Radiation shape factor for radiation between parallel rectangles...

Some useful relations between shape factors may be obtained by considering the system shown in Fig. 8-19. Suppose that the shape factor for radiation from A3 to the combined area A,.2 is desired. This shape factor must be given very simply as... 

F - or F Radiation shape factor for radiation from surface m to surface n... 

F1.2 view factor (geometric shape factor for radiation from one blackbody to... 

Lenenberger, H. and Pearson, R. A., Compilation of Radiation Shape Factors for Cylindrical Assemblies, Paper 56-A-144, ASME, New York, 1956. 

B shape the shape factors for the interstitial energy transport by radiation and molecular flow, respectively. The values of the relative particle to particle contact surface area, and the three shape factors, and must be... 

Determination of the radiation shape factor for a given system is a complex problem. Some results (see Figures 9-3, 9-4, and 9-5) have been published for straightforward cases. 

Since radiation arriving at a black surface is completely absorbed, no problems arise from multiple reflections. Radiation is emitted from a diffuse surface in all directions and therefore only a proportion of the radiation leaving a surface arrives at any other given surface. This proportion depends on the relative geometry of the surfaces and this may be taken into account by the view factor, shape factor or configuration F, which is normally written as F, for radiation arriving at surface j from surface i. In this way, F,y, which is, of course, completely independent of the surface temperature, is the fraction of radiation leaving i which is directly intercepted by j. 

It is important to note here that if an element does not radiate directly to any part of its own surface, the shape factor with respect to itself, F]t, Fu and so on, is zero. This applies to any convex surface for which, therefore, Fu =0. 

In a series of papers, Derby and Brown (144, 149-152) developed a detailed TCM that included the calculation of the temperature field in the melt, crystal, and crucible the location of the melt-crystal and melt-ambient surfaces and the crystal shape. The analysis is based on a finite-ele-ment-Newton method, which has been described in detail (152). The heat-transfer model included conduction in each of the phases and an idealized model for radiation from the crystal, melt, and crucible surfaces without a systematic calculation of view factors and difiuse-gray radiative exchange (153). 

From the form of Eq. (2.33) it becomes understandable why the anisotropy of polarization 7Z is sometimes called the degree of alignment. From the point of view of the determination of the magnitude of the polarization moments bPo the measurement of 71 is preferable, as compared with that of V, all the more so if one bears in mind that the population bPo appears only as a normalizing factor for all other bPQ and does not influence the shape of the probability density p(B,multipole moment dependence of V and 71 for various types of radiational transition (A = 0, 1) can be obtained using the numerical values of the Clebsch-Gordan coefficient from Table C.l, Appendix C. 

Consider two black surfaces Ai and A2, as shown in Fig. 8-8. We wish to obtain a general expression for the energy exchange between these surfaces when they are maintained at different temperatures. The problem becomes essentially one of determining the amount of energy which leaves one surface and reaches the other. To solve this problem the radiation shape factors are defined as... 

Other names for the radiation shape factor are view factor, angle factor, and configuration factor. The energy leaving surface 1 and arriving at surface 2 is... 

The calculation of the radiation heat transfer between black surfaces is relatively easy because all the radiant energy which strikes a surface is absorbed. The main problem is one of determining the geometric shape factor, but once this is accomplished, the calculation of the heat exchange is very simple. When nonblackbodies are involved, the situation is much more complex, for all the energy striking a surface will not be absorbed part will be reflected back to another heat-transfer surface, and part may be reflected out of the system entirely. The problem can become complicated because the radiant energy can be reflected back and forth between the heat-transfer surfaces several times. The analysis of the problem must take into consideration these multiple reflections if correct conclusions are to be drawn. 

If the emissivities of all surfaces are equal, a rather simple relation may be derived for the heat transfer when the surfaces may be considered as infinite parallel planes. Let the number of shields be n. Considering the radiation network for the system, all the surface resistances would be the same since the emissivities are equal. There would be two of these resistances for each shield and one for each heat-transfer surface. There would be n + I space resistances, and these would all be unity since the radiation shape factors are unity for the infinite parallel planes. The total resistance in the network would thus be... 

In reality, the radiation shape factors F, 2, F( m, and F2 m are unity for this example, so that the expression for the heat flow could be simplified to some extent however, these shape factors are included in the network resistances for the sake of generality in the analysis. 

All the preceding discussions have considered radiation exchange between diffuse surfaces. In fact, the radiation shape factors defined by Eq. (8-21) hold only for diffuse radiation because the radiation was assumed to have no preferred direction in the derivation of this relation. In this section we extend the analysis to take into account some simple geometries containing surfaces that may have a specular type of reflection. No real surface is completely diffuse or completely specular. We shall assume, however, that all the surfaces to be considered emit radiation diffusely but that they may reflect radiation partly in a specular manner and partly in a diffuse manner. We therefore take the reflectivity to be the sum of a specular component and a diffuse component ... 

Making use of Eqs. (8-99) and (8-102) gives the complete network for the system as shown in Fig. 8-61. Of course, all the radiation shape factors in the above network are unity, but they have been included for the sake of generality. In this network Jw refers to the diffuse radiosity on the left side of 2, while J 2D is the diffuse radiosity on the right side of this surface. 

Find the radiation shape factors F, for the situations shown. 

We stait this chapter with one-dimensional steady heat conduction in a plane wall, a cylinder, and a sphere, and develop relations for thennal resistances in these geometries. We also develop thermal resistance relations for convection and radiation conditions at the boundaries. Wc apply this concept to heat conduction problems in multilayer plane wails, cylinders, and spheres and generalize it to systems that involve heat transfer in two or three dimensions. We also discuss the thermal contact resislance and the overall heat transfer coefficient and develop relations for the critical radius of insulation for a cylinder and a sphere. Finally, we discuss steady heat transfer from finned surfaces and some complex geometries commonly encountered in practice through the use of conduction shape factors. 

To account for the effects of orientation on radiation heat transfer between two surfaces, we define a new parameter called the vieu factor, which is a purely geometric quantity and is independent of the surface properties and temperature. It is also called the shape factor, configuration factor, and angle factor. The view factor based on the assumption that the surfaces are diffuse emitters and diffuse reflectors is called the diffitse view factor, and the view factor based on the assumption that the surfaces are diffuse emitters but specular reflectors is called the specular view factor. In lliis book, we consider radiation exchange between diffuse surfaces only, and ihu.s the term view factor simply means diffuse view factor. 

The size of the points, for a perfect crystal, is uniquely determined by instrumental factors (including radiation emission and optics) and absorption, so the diffracted intensity is confined to a small region around each point (Figure 13.2a), and the FWHM is quite small. Instrumental effects on peak broadening and line-shape are described in greater detail in Chapters 4 and 5. 

U. Gross, K. Spindler, and E. Hahne, Shape Factor Equations for Radiation Heat Transfer between Plane Rectangular Surfaces of Arbitrary Position and Size with Rectangular Boundaries, Lett. Heat Mass Transfer, 8, pp. 219-227,1981. 

Brink has derived a formula for the radiation width of a y-ray of energy fi on the basis of the integrated photonuclear cross section (the dipole sum) and the shape predicted for this cross section by Steinwedel and Jensen This cross section refers to absorption by the ground state of the nucleus for the radiation width, we are concerned with the emission of radiation by a state already excited to some 7Mev. Brink assumed nevertheless that the factor f[e, E) in (65.1) can be taken directly from the photonuclear cross section regardless of the fact that the initial state of the nucleus is not the ground state. If... 

Figure 4.11-4. Area elements for radiation shape factor.

A very important aspect of radiative heat transfer is the system geometry. This is accounted for by using radiation shape factors, also called view factors, angle factors, or configuration factors and defined as follows... 

Radiation shape factors can be computed for different situations and then used with the equations... 

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