Reradiating wall

In a radiation dominated kiln environment, with hot combustion gases and reradiating walls, the characteristic time is... 

If the kiln may be considered an enclosure bounding an isothermal gray gas of emissivity, S, with two bounding surfaces consisting of reradiating walls of area, and of bed soHds (the radiation sink) of area, then the expression for R becomes (19)... 

A zone with Qt > 0 is called a (net) radiation source, as it emits more radiation than it absorbs. A zone with Qt < 0 is a (net) radiation receiver, that absorbs more radiation than it emits. An adiabatic zone (Q = 0) with respect to the outside is known as a reradiating wall. Its temperature is such that it emits just as much radiation as it absorbs from radiation incident upon it (radiative equilibrium). 

Fig. 5.56 Enclosure formed from radiation source 1, radiation receiver 2 and reradiating walls with Qr = o...

An enclosure with only three zones is often a good approximation for the case of a radiation source of area A and temperature T in radiative exchange with a radiation receiver of area A2 and temperature T2 < T, cf. Fig. 5.56. In addition to this walls that axe adiabatic with respect to the outside also participate in the radiative exchange. These can be roughly assigned a unified temperature, Tr. The reradiating walls that enclose the space are combined here into a single zone with Tr and Qr = ° ... 

As comparison with (5.134) shows, the heat flow Qi transferred from 1 to 2 is increased compared to the net radiation flow )2 due to the reradiating walls, because Fi2 > Fi2. If the radiation source and receiver have flat or convex surfaces (Fn = 0, F22 = 0), then the view factors Fir and F2r can lead back to F 2 and instead of (5.140)... 

Radiative exchange between a radiation source, a radiation receiver mid a reradiating wall... 

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. 

No current, QR = 0, flows between the nodes with the potentials crTR and HR, cf. Fig. 5.62. The resistance (1 — R)/ RJ4R therefore has no effect and crTR = HR is valid. The temperature TR of a reradiating wall presents itself independent of its emissivity R. The radiosity HR required for its determination is found from the balance... 

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 4.11-2. Radiation between two black surfaces (a) two planes alone, (b) two planes connected by refractory reradiating walls.

C View Factors When Surfaces Are Connected by Reradiating Walls... 

If the two black-body surfaces /I, and A2 are connected by nonconducting (refractory) but reradiating walls as in Fig. 4.1 l-2b, a larger fraction of the radiation from surface 1 is intercepted by 2. This view factor is called Fjj. The case of two surfaces connected by the walls of an enclosure such as a furnace is a common example of this. The general equation for this case assuming a uniform refractory temperature has been derived (Ml, C3) for two radiant sources A and /12, which are not concave, so they do not sec themselves. 

The factor F,2 for parallel planes is given in Fig. 4.11-7 and for other geometries can be calculated from Eq. (4.11-36). For view factorsF,2 andFj2 for parallel tubes adjacent to a wall as in a furnace and also for variation in refractory wall temperature, see elsewhere (Ml, P3). If there are no reradiating walls. 

A general and more practical case, which is the same as for Eq. (4.11-40) but with the surfaces A, and Aj being gray with emissivities ei and 2, will be considered. Nonconducting reradiating walls are present as before. Since the two surfaces are now gray, there will be some reflection of radiation which will decrease the net radiant exchange between the surfaces below that for black surfaces. The final equations for this case are... 

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