View factor/radiation

Tliis question deals with sicady-siatc radiation heat transfer between a sphere = 30 ctii) and a circular disk (r2 = 120 cm), which are separated by a ceiiler-to-center distance h = 60 cm. When the normal to the center of disk passes through the center of sphere, the radiation view factor is given by... 

Two square plates, with the sides a and b (and h > a), are coaxial and parallel to each other, as shown in Fig. P13-103, and they are separated by a cenicr-to-cenler distance of i. Tjte radiation view factor froiu the sntaller to the larger plate, is given by... 

J. van Leersum, A Method for Determining a Consistent Set of Radiation View Factors from a Set Generated by a Nonexact Method, International Journal of Heat and Fluid Flow, 10(1), p. 83,1989. 

F12 radiation view factor between two contacting spheres... 

A thorough comparison of several computational methods for evaluating diffuse radiation view factors has been made [171]. Figure 18.35 shows several of the geometries considered. As evident, intervening surfaces are present in all of the cases, which range in complexity from the relatively simple six-sided shelf structure to the complicated multiplesided truss. 

Fij radiation view factor between diffuse surfaces i and j... 

F = direct view factor Ey, fraction of isotropic radiation from Aj intercepted directly by Aj. 

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. 

The thermal radiation received from the fireball on a target is given by equation 9.1-31, where Q is the radiation received by a black body target (kW/m ) r is the atmospheric transmissivity (dimensionless), E = surface emitted flux in kW/m", and f is a dimensionless view factor. 

The heat flux, E, from BLEVEs is in the range 200 to 350 kW/m is much higher than in pool fires because the flame is not smoky. Roberts (1981) and Hymes (1983) estimate the surface heat flux as the radiative fraction of the total heat of combustion according to equation 9.1-32, where E is the surface emitted flux (kW/m ), M is the mass of LPG in the BLEVE (kg) h, is the heat of combustion (kJ/kg), is the maximum fireball diameter (m) f is the radiation fraction, (typically 0.25-0.4). t is the fireball duration (s). The view factor is approximated by equation 9.1-34. where D is the fireball diameter (m), and x is the distance from the sphere center to the target (m). At this point the radiation flux may be calculated (equation 9.1-30). 

In the second approach, the energy release is split by a predefined (mostly constant) factor between convection and radiation. The convective part is directly transferred as energy gain to the room air, while the radiative part is distributed to the surrounding walls by the area-weighted method or the view-factor method. 

Form view factor A factor which describes the effects of the relative area of two surfaces, the geometry of the surfaces in relation to each other, and the two emissivities on radiation heat exchange between the surfaces. 

Radiation shape factor The angle factor representing the fraction of the angular field of view from which energy exchange is trading places. 

The view factor is the fraction of the radiation falling directly on the receiving target. The view factor depends on the shapes of the fire and receiving target, and on the distance between them. 

Fn = view factor or geometric configuration factor E = emissive power of emitting surface 2 = incident radiation-receiving surface... 

In order to compute the thermal radiation effects produced by a burning vapor cloud, it is necessary to know the flame s temperature, size, and dynamics during its propagation through the cloud. Thermal radiation intercepted by an object in the vicinity is determined by the emissive power of the flame (determined by the flame temperature), the flame s emissivity, the view factor, and an atmospheric-attenuation factor. The fundamentals of heat-radiation modeling are described in Section 3.5. 

The total radiation received by an object also depends on the fireball s position relative to the object (i.e., the view factor) and radiation adsorption by the atmosphere. 

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. 

Ground Distance (m) View Factor Solid Flame Radiation (kW/m ) Point Source Radiation (Hymes) (kW/ni )... 

View factor The ratio of the incident radiation received by a surface to the emissive power from the emitting surface per unit area. 

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. 

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 ... 

---