Radiative exchange

As an introduction, a simple case of radiative exchange will be looked at. A radiator with area A, and at temperature T, is located in surroundings which are at temperature Ts, see Fig. 1.11. The medium between the two shall have no effect on the radiation transfer it shall be completely transparent for radiation, which is a very good approximation for atmospheric air. The surroundings shall behave like a black body, absorbing all radiation, as = 1. 

The net flow of heat Q, from the radiator to the surroundings enclosing it is 

In many cases a simple assumption is made about the radiator it is treated as a grey radiator. This is only an approximation but it simplifies matters greatly. The absorptivity of a grey radiator does not depend on the type of incident radiation, and it always agrees with the emissivity, such that a = e. 

The difference between the fourth power of the temperature of the emitter and that of the body which receives the radiation, is characteristic of radiative exchange. This temperature dependence is found in numerous radiative heat transfer problems involving grey radiators. 

In many applications heat transfer by convection must be considered in addition to radiative heat transfer. This is, for example, the case where a radiator releases heat to a room which is at a lower temperature. Radiative heat exchange takes place between the radiator and the walls of the room, whilst at the same time heat is transferred to the air by convection. These two kinds of heat transfer are parallel to each other and so the heat flow by convection and that by radiation are added together in order to find the total heat exchanged. The heat flux then becomes 

---

Radiative Exchange between Gases or Suspended Matter... 

Consider radiative exchange between a body of area A i and temperature Ti and black surroundings at To. The net interchange is given by... 

RADIATIVE EXCHANGE BETWEEN GASES OR SUSPENDED MATTER AND A BOUNDARY... 

Local Radiative Exchange The interchange rate Q between an isothermal gas mass at Tq and its isothermal black bounding surface of area Ai is given by... 

Note that though S Si is never used in calculating radiative exchange, its value is necessary for use of Eq. (5-159) to calculate GS. 

Treatment of Refractory Walls Partially Enclosing a Radiating Gas Another modification of the results in Table 5-10 becomes important when one of the surface zones is radiatively adiabatic the need to find its temperature can be eliminated. If surface A9, now called A, is radiatively adiabatic, its net radiative exchange with Aj must equal its net exchange with the gas. 

This has to be considered when splitting walls or floors into several elements, because in such models, these elements have a direct radiative exchange, while in reality there is no exchange or only an indirect one via opposite surfaces. 

Figure 3.10. Configuration for radiative exchange between two differential elements.

A special care is to be devoted to the control that all the parts of the apparatus have reached the desired temperature when parts remain at higher temperature, due to the high value of the specific heat, the cooling only by radiative exchange is usually impossible. To open a gas heat switch, several hours of pumping are usually necessary to reduce the pressure to a value suitable for the thermal isolation. An insufficient pumping leads to a time-dependent heat leak due to desorption and condensation of the residual gas at the coldest surfaces. 

Heat conduction takes mainly place along solid materials as electric wires or along the walls of the cryostat, by radiative exchanges, and through gases. 

Among the shunt spurious contribution, the power exchanged through the residual gas in the vacuum chamber does not represent usually a problem. The shunt conductances are always to be compared with the thermal conductance of the sample. At temperatures above 77 K, the thermal contact drawback vanishes (see Section 4.4), but the problem of the radiative exchange (a T4) becomes very important. 

It appears at this time that one of the most important mechanisms involved in the luminescence of rare earth ions is energy exchange between them. One may clearly differentiate between two distinct mechanisms (a) radiative exchange and (b) nonradiative exchange. In the radiative mechanism, a photon emitted by ion A is captured by ion B. Since the photon has left the A system, the capture of it by B cannot decrease the lifetime of A. However, f the photon is shuttled back and forth between similar or dissimilar ions, the fluorescent lifetime could well be increased by radiation trapping. This is an interesting phenomenon and warrants further discussion. 

In a series of papers, Derby and Brown (144, 149-152) developed a detailed TCM that included the calculation of the temperature field in the melt, crystal, and crucible the location of the melt-crystal and melt-ambient surfaces and the crystal shape. The analysis is based on a finite-ele-ment-Newton method, which has been described in detail (152). The heat-transfer model included conduction in each of the phases and an idealized model for radiation from the crystal, melt, and crucible surfaces without a systematic calculation of view factors and difiuse-gray radiative exchange (153). 

There is no net radiative exchange between the enclosing walls (fire-box), and the radiating gas and tubes. Heat is lost from the enclosing wall to the surroundings only. 

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. 

Radiative Exchange Between Two Differential Area Elements... 

Figure 12.1 Radiative exchange between two differential area elements.

We first look at the radiative exchange between differential elements. Then the relations will be developed for exchange between areas of finite size. Two differential black elements are shown in Fig. 12.1. The elements dAi and dA2 are at temperatures Ti and T2 respectively their normals are at angles Pi and p2 to the line of length R joining them. 

Fig. 1.11 Radiative exchange between a body at temperature T and black surroundings at temperature...

---