Three-surface enclosures

In the equations above it must be noted that the summations must be performed over all surfaces in the enclosure. For a three-surface enclosure, with i = 1, the summation would then become... 

Not Radiation Heal Transfer to or from a Surface 727 Net Radiation Heat Transfer betv.een Any Tv-o Surfaces 729 Methods of Solving Radiation Problems 730 Radiation Heal Transfer in Tv/o-Surface Enclosures 731 Radalion Heat Transfer in Three-Surface Enclosures 733... 

Analysis The widths of the sides of the triangular cross section of the duct arc ti, /.7, and Ls, and the surface areas corresponding to them are Ai, A, and As, respectively. Since the duct is infinitely long, the fraction of radiation leaving any surface that escapes through the ends of the duct is negligible. Therefore, the infinitely long duct can be considered to be a three-surface enclosure, Af= 3. 

I he network method is not practical for enclosures with more than three or four surfaces, however, because of the increased complexity of the network. Next we apply the method lo solve radiation problems in two- and three-surface enclosures. 

Radiation Heat Transfer in Three-Surface Enclosures... 

Schematic of a three-surface enclosure and the radiation nehvork associated with it.

Analysis We vnll solve this problem systematically using the direct method to demonstrate its use. The cylindrical furnace can be considered to be a three-surface enclosure with surface areas of... 

Analysis The furnace can be considered to be a three-surface enclosure with a radiation network as shovm in the figure, since the duct is very long and thus the end effects are negligible. We observe that the viev/ factor from any surface to any other surface in the enciosure is 0.5 because of symmetry. Surface 3 is a reradiating surface since the net rale of heat transfer at that surface is zero. Ihen we must have Qi = -Qj, since the entire heat lost by surface 1 must be gained by surface 2. The radiation network in this case is a simple series-parallei connection, and vis can determine Qi directly from... 

FIGURE 7.13 Example 7.4 hot furnace plate (1), tubes (2), and refractory wall (3) form a three-surface enclosure with a reradiating surface. 

FIGURE 7.14 Network representation for a three-surface enclosure. 

Consider an enclosure shown above, consisting of three surfaces which are very long in the direction perpendicular to the plane of the figure. The summation rule for view factors gives... 

Consider an arbitrary three-dimensional enclosure of total volume V and surface area A which confines an absorbing-emitting medium (gas). Let the enclosure be subdivided (zoned) into M finite surface area and N finite volume elements, each small enough that all such zones are substantially isothermal. The mathematical development in this section is restricted by the following conditions and/or assumptions ... 

FIG. 5-19 Generalized electrical network analog for a three-zone enclosure. Here Ai and A2 are gray surfaces and Ar is a radiatively adiabatic surface. (Hot-tel, H C. and A. F. Sarojim, Radiative Transfer, McGraw-Hill, New York, 1967, p. 91.)... 

We now consider an enclosure consisting of three opaque, diffuse, and gray surfaces, as shown in Fig. 13-26. Surfaces 1, 2, and 3 have surface areas Aj, and A3 cmissivities C, e, and 3 and uniform temperatures T, T , and T 3. respective . The radiation network of this geometry is constructed by following the standard procedure draw a surface resistance associated with each of the three surfaces and connect these surface resistances with space resistances, as shown in the figtire. Relations for the surface and space resistances are given by Fqs. 13-26 and 13-31. The three endpoint potentials and... 

In an enclosure bounded by three surfaces there are 9 view factors. Of these only 3 need to be calculated according to (5.130). As the end areas 1 and 2 are flat, we have Fn = 0 and F22 = 0, so that only one view factor has to be determined by evaluating the double integral from (5.130). This is the view factor F12] it is found from Table 5.9 (two equally sized, parallel concentric circular discs) with z = 2 + (h/r)2 = 8.25 to be... 

Sin e-Gas-Zone/Two-Surface-Zone Systems An enclosure consisting of but one isothermal gas zone and two gray surface zones can, properly specified, model so many industrially important radiation problems as to merit detailed presentation. One can evaluate the total radiation flux between any two of the three zones, including multiple reflec tion at all surfaces. 

For small-scale laboratory work, the exhaust surface is often made as a separate section added to the side of a table or put into a large hole in a table. These tables usually have a sheet metal surface that is resistant to the chemicals used and is easily cleaned. Many circular holes are cut into the metal surface to allow for airflow. This perforation makes the pressure difference over the table quite high and at the same time gives an even distribution of the airflow over the entire surface. These types of exhaust surfaces could be formed to suit different working conditions, e.g., the surface could be made to fit into a sink or to be placed below and around a balance. Using side walls that are not too high, on three or four sides, transforms the table to a partial enclosure, which increases... 

An enclosure surrounded by three isothermal surfaces (zones), like that shown schematically in Fig. 5.59, serves as a good approximation for complicated cases of radiative exchange. Zone 1 at temperature 7 and with emissivity is the (net-) radiation source, it is supplied with a heat flow Q1 from outside. Zone 2 with temperature T2 < Tx and emissivity e2 is the radiation receiver, whilst the third zone at temperature TR, assumed to be spatially constant, is a reradiating wall, (Qr = 0). The heat flow Qi = — Q2 transferred by radiative exchange in the enclosure is to be determined. 

The symmetry of the construction means that it is sufficient to just consider the top half of the oven. It forms the schematically illustrated enclosure in Fig. 5.63b. It is bounded at the top by the heated square 1 with j = 0.85, at the side by the rectangular areas 2 with e2 = 0.70, which release heat to the outside, and below by the metal plate R. It is adiabatic as a result of symmetry, and represents a reradiating wall. We will assign the approximately uniform temperatures T), T2 and Tr to these surfaces, such that the radiative exchange in a hollow enclosure bounded by three zones is to be calculated according to (5.148) or (5.151). 

Figure 2.2.1 Cross-section of a three-dimensional conducting phase containing a Gaussian enclosure. Illustration that the excess charge resides on the surface of the phase.

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