The Two-Zone Enclosure

The Two-Zone Enclosure Figure 5-18 depicts four simple enclosure geometries which are particularly useful for engineering calculations characterized by only two surface zones. For M = 2, the reflectivity matrix R is readily evaluated in closed form since an explicit algebraic inversion formula is available for a 2 X 2 matrix. In this case knowledge of only E = 1 direct exchange area is required. Direct evaluation of Eqs. (5-122) then leads to... 

Physically, a two-zone speckled enclosure is characterized by the fact that the view factor from any point on the enclosure surface to the sink zone is identical to that from any other point on the bounding surface. This is only possible when the two zones are intimately mixed. The seemingly simplistic concept of a speckled enclosure provides a surprisingly useful default option in engineering calculations when the actual enclosure geometries are quite complex. 

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. 

The second conversion of GS to (GSi)r will be Case 4 of Table 5-10, the two-surface-zone enclosure with computation simphfied by assuming that the direct-view fac tor from any spot to a surface equals the fraction of the whole enclosure that the surface occupies (the speckled-furnace model). This case can be considered an ideahzation of many processing furnaces such as distilling and cracking coil furnaces, with parts of the enclosure tube-covered and part left refrac-toiy. (But the refractory under the tubes is not to be classified as part of the refractory zone.) Again, one starts with substitution into Eq. (5-173) of the terms GSi, GS, and S Si from Table 5-10, Case 4, with all terms first converted to their gray-phis-clear form. To indicate the procedure, one of the components, S Si, wil be formulated. 

Combined construction, process-related, and ventilation measures include air locks between two zones (Fig. 7A09f) and process equipment enclosures with air exhaust from the enclosures (Fig, 7.109g). 

The indium studs 30 are used for connection of the n-type zones by cold welding with corresponding input studs 31 of a silicon integrated circuit formed in a silicon wafer 15. The two wafers 2 and 15 are disposed on a cooled surface 16 in a cryogenic enclosure 17. 

Total Exchange Areas When an enclosure contains reflective surface zones, allowance must be made for not only the radiant energy transferred directly between any two zones but also the additional transfer attendant to however many multiple reflections which occur among the intervening reflective surfaces. Under such circumstances,... 

Zone Methodology and Conventions For a transparent medium, no more than E = M(M —1)/2 of the M2 elements of the ss array are unique. Further, surface zones are characterized into two generic types. Source-sink zones are defined as those for which temperature is specified and whose radiative flux Q, is to be determined. For flux zones, conversely, these conditions are reversed. When both types of zone are present in an enclosure, Eq. (5-118) may be partitioned to produce a more efficient computational algorithm. Let A/ M t M. represent the total number of surface zones where A/ is the number of source-sink zones and Mf is the number of flux zones. The flux zones are the last to be numbered. Equation (5-118) is then partitioned as follows ... 

Zone Method Let a zone of a furnace enclosure be an area small enough to make all elements of itself have substantially equivalent views of the rest of the enclosure. (In a furnace containing a symmetry plane, parts of a single zone would lie on either side of the plane.) Zones are of two classes source-sink surfaces, designated by numerical subscripts and having areas Ai, Aa,. . ., and emissivities El, and surfaces at which the net radiant-heat flux is zero (ful-... 

The two balance equations (5.144) and (5.145) can be established for each zone (i = 1,2,. ..n). Therefore, 2 n equations are available for the n unknown radiosities Hi and the n required values for and 7) respectively. Before we go into this equation system in 5.5.3.4, the next section offers solutions for the more simple case of enclosures bounded by only two or three zones. 

The relationships derived in the last section for the heat flow, Qx, transferred from a radiation emitter 1 to a receiver 2, are also valid for an enclosure that is only bounded by these two zones. As no reradiating zone is present, with 1R = 0 and F2R = 0 from (5.149), F12 = F12 is obtained. The heat flow transferred from 1 to 2 is... 

Type e is also called increased safety and intended for apparatus that is to be installed in a Zone 1 area. Two of the allowable features of the type d enclosures, namely permitting sparking components and no Temperature Class hmit to the internal components, cannot be incorporated into the type e designs. The practical aspect of this is the removal of a source of ignition i.e. a spark or a hot surface. In many types of equipment e.g. luminaries, terminal boxes, junction boxes, some designs of motor control stations, telephones and public address speakers, the elimination of these two sources of ignition is not a difficult problem. 

Many furnace problems are adequately handled by dividing the enclosure into but two source-sink zones Ai and A9 and any number of no-flux zones A, A .. . . For this case Eq, (5-130) yields... 

Of a more complete approach are the zone models [3], which consider two (or more) distinct horizontal layers filling the compartment, each of which is assumed to be spatially uniform in temperature, pressure, and species concentrations, as determined by simplified transient conservation equations for mass, species, and energy. The hot gases tend to form an upper layer and the ambient air stays in the lower layers. A fire in the enclosure is treated as a pump of mass and energy from the lower layer to the upper layer. As energy and mass are pumped into the upper layer, its volume increases, causing the interface between the layers to move toward the floor. Mass transfer between the compartments can also occur by means of vents such as doorways and windows. Heat transfer in the model occurs due to conduction to the various surfaces in the room. In addition, heat transfer can be included by radiative exchange between the upper and lower layers, and between the layers and the surfaces of the room. 

Figure 2.5 The zone 2 concept according to VDE 0165/1991-02. Requirements for electrical apparatus with arcs or sparks in normal operation and/or temperatures exceeding a defined limit/temperature class. Two types of protection are defined here the schwadensicheres Gehause , comparable with a restricted breathing enclosure , and simple pressurization .

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