View factors for radiation

Figure 4.11-6. View factor for radiation from a small element to a parallel disk for Example 4.11-3.

Equations similar to equation 9.158 may be obtained for each of the surfaces in an enclosure, 1 = 1,1 = 2, 1 = 3, 1 = n and the resulting set of simultaneous equations may then be solved for the unknown radiosities, qoi,qm- qun The radiation heat transfer is then obtained from equation 9.140. This approach requires data on the areas and view factors for all pairs of surfaces in the enclosure and the emissivity, reflectivity and the black body emissive power for each surface. Should any surface be well insulated, then, in this case, Qj — 0 and ... 

Radiation heat transfer is assumed to be significant between each portion of the cells and those portions of other cells that are in the same plane, in the upper plane and in the lower plane. The error associated with this assumption increases when small vertical portions are considered. Figure 7.26 shows the view factors, for a cavity constituted of four cells, as the function of the length of the cell slice (vertical discretization). The four view factors have the following meaning (1) Fap - view factor between a cell and the two adjacent cells in the same horizontal plane (2) Fop - view factor between opposite cells in the same horizontal plane (3) Fad - view factor between a cell and the two adjacent cells in the upper and lower plane (4) Fod -view factor between opposite cells in the same horizontal plane. When the element length is larger than 0.04 m, the summation of these coefficients is about 0.97, which means that the error is less than 3%. The calculation of these coefficients is shown in Section 7.4.2.2. 

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

Krishna, S.M. 1987. Geometric view factors for thermal radiation hazard assessment. Fire Safety Journal... 

IB Derivation of View Factors in Radiation for Various Geometries... 

View factor for infinite parallel black planes. If two parallel and infinite black planes at T and Tj are radiating toward each other, plane 1-emits aradiation to plane 2, which is all absorbed. Also, plane 2 emitsaTj radiation to plane 1, which is all absorbed. Then for plane 1, the net radiation is from plane 1 to 2,... 

View factor for infinite parallel gray planes. If both of the parallel plates /I, and A2 are gray with emissivities and absorptivities ofe, = a, andcj = 2. respectively, we can proceed as follows. Since each surface has an unobstructed view of each other, the view factor is 1.0. In unit time surface A, emitse,/l,CTT J radiation toAj- Of this, the fraction 62 (where 2 = 2) absorbed ... 

EXAMPLE 4.11-3. Radiation Between Parallel Disks In Fig. 4.11-6 a small disk of area /I, is parallel to a large disk of area A and /I, is centered directly below Aj- The distance between the centers of the disks is R and the radius of/lj is a. Determine the view factor for radiant heat transfer from /I, to /Ij. 

Hence, one selects the surface whose view factor can be determined most easily. For example, the view factor F12 for a small surface /I completely enclosed by a large surface /I2 is 1.0, since all the radiation leaving Aj is intercepted by /Ij. In Fig. 4.11-7 the view factors Fij between parallel planes are given, and in Fig. 4.11-8 the view factors for... 

A small cold package having an area /Ij and emissivity j is at temperature T. It is placed in a warm room with the walls at Tj and an emissivity ,. Derive the view factor for this using Eq. (4.11-45), and the equation for the radiation heat transfer. 

FIG. 5-17 Distribution of radiation to rows of tubes irradiated from one side. Dashed lines direct view factor F from plane to tubes. Solid lines total view factor F for black tubes backed by a refractory surface. 

Here, Qr is the energy loss per second by a surface at temperature to its suiToundings at temperature T, , the emissivity of the subsU ate being e, the view factor F being the fraction of tire emitted radiation which is absorbed by the cool sunoundings, and a being tire Stefan-Boltzmairn radiation constant (5.67 X 10 Jm s In the present case, tire emissivity will have a value of about 0.2-0.3 for the metallic subsU ates, but nearly unity for the non-metals. The view factor can be assumed to have a value of unity in the normal situation where the hot subsU ate is enclosed in a cooled container. 

In all of these systems, the rate of generation at the gas-solid interface is so rapid that only a small fraction is canied away from the particle surface by convective heat uansfer. The major source of heat loss from the particles is radiation loss to tire suiTounding atmosphere, and the loss per particle may be estimated using unity for both the view factor and the emissivity as an upper limit from tlris source. The practical observation is that the solids in all of these methods of roasting reach temperatures of about 1200-1800 K. 

Radiation effects from a fireball of the size calculated above, and assumed to be in contact with the ground, have been calculated by Pietersen (1985). A fireball duration of 22 s was calculated from the formula suggested by Jaggers et al. (1986). An emissive power of 350 kW/m was used for propane, based on large-scale tests by British Gas (Johnson et al. 1990). The view factor proposed in Section 6.2.5. 

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. 

The amount of calculation involved here can be very considerable and use of a computer is usually required. A simpler approach is to make use of the many expressions, graphs and tables available in the heat transfer literature. Typical data, presented by Incropera and DE Witt(45) and by Howell(47), are shown in Figures 9.38-9.40, where it will be seen that in many cases, the values of the view factors approach unity. This means that nearly all the radiation leaving one surface arrives at the second surface as, for example, when a sphere is contained within a second larger sphere. Wherever a view factor approaches zero, only a negligible part of one surface can be seen by the other surface. 

For a given geometry, view factors are related to each other, one example being the reciprocity relationship given in equation 9.126. Another important relationship is the summation rule which may be applied to the surfaces of a complete enclosure. In this case, all the radiation leaving one surface, say i, must arrive at all other surfaces in the enclosure so that, for n surfaces ... 

This means that the sum of the exchange areas associated with a surface in an enclosure must be same as the area of that surface. The principle of the summation rule may be extended to other geometries such as, for example, radiation from a vertical rectangle (area 1) to an adjacent horizontal rectangle (area 2), as shown in Figure 9.40iii, where they are joined to a second horizontal rectangle of the same width (area 3). In effect area 3 is an extension of area 2 but has a different view factor. 

The target for optimization in FTA with CL detection is to adjust all experimental factors in such a way so that the detector views as much radiation as possible while the chemiluminescent solution flows through the cell. Hence the kinetics of the flow and detector system should be monitored to match the kinetics of the reaction and generate maximum intensity inside the cell. The effect of experimental variables on the CL signal cannot be exactly predicted in advance and there is not enough theoretical background to support any suggestion. 

Classical heat transfer provides expressions for quantities such as view factors, radiation and temperature fields in semi—infinite bodies. The lining materials studied here were treated as semi-infinite bodies since the test duration is relatively short. 

This energy balance also assumes that the absorbtivity and emissivity ofthe target surface are nominally equal and for simplicity are considered as one. The view factor associated with the re-radiation from the target to the surroundings has been assumed to be one for simplicity. This assumption will lead to higher estimated temperatures, particularly as the fire encompasses more ofthe field of view of the target. 

Utilizing ionization efficiency curves to determine relative populations of vibrationally excited states (as in the photoionization experiments) is a quite valid procedure in view of the long radiative lifetime that characterizes vibrational transitions within an electronic state (several milliseconds). However, use of any ionization efficiency curve (electron impact, photon impact, or photoelectron spectroscopic) to obtain relative populations of electronically excited states requires great care. A more direct experimental determination using a procedure such as the attenuation method is to be preferred. If the latter is not feasible, accurate knowledge of the lifetimes of the states is necessary for calculation of the fraction that has decayed within the time scale of the experiment. Accurate Franck -Condon factors for the transitions from these radiating states to the various lower vibronic states are also required for calculation of the modified distribution of internal states relevant to the experiment.991 102... 

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