Reradiating surface

Note that Qj = 0 for insulated (or reradiating) surfaces, and crTj = J for black surfaces since e, - 1 in that case. Also, the term corresponding to j = i drops out from either relation since Jj - J- = Ji — - 0 in that case. 

The equations above give AMincar algebraic equations for the deieiinination of the N unknown radiosities for an A -surface enclosure. Once Ihe radiosities J, fr , Jn 3te available, the unknown heat transfer rates can be determined from Eq. 13-34 while the unknown surface temperatures can be determined from Eq, 13-3, 5. The temperatures of insulated or reradiating surfaces can be delei mined from ffT/ 7,. A positive value for Qj indicates net radiation heal transfer from surface i to other surfaces in the enclosure while a negative value indicates net radiation heat transfer lo Ihe surface. 

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... 

C What is a reradialing surface Wllat simplifications does a reradiating surface offer in the radiation analysis ... 

Neglect convection heat transfer, and assume all surfaces are diffuse, gray, and of infinite extent. Since the bottom wall (A3) is insulated, the net radiative heat flux at that surface must be zero. This type of surface is called a reradiating surface. The radiation network is shown in Figure 7.14. For an area of 1 nf, Aj = A3 = 1 m, the number of tubes is M = 10, and the length of each tube is L = 1 m. Hence, Aj = MtzDL = 1.57 nd (the surface area of the tubes). If there were only one tube and the plates were infinitely large, the view factor between the tube and each plate would be 0.5. 

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. 

Note that the emissivity value of the reradiating surface does not affect the results. If surfaces A, and A2 are treated as blackbodies, gj = 2 = 1, then the predicted net radiative heat transfer rate q 2 would be 97.3 kW/m, which is almost twice the value calculated in part (a). 

For a lunar colony to be established on the moon, the intensity of the solar radiation at high noon is a concern (Fig. 9P-19). A sun shade , consisting of two thin metal plates separated by insulation, is 4 m by 4 m square and is mounted parallel to and 2 m from the lunar surface. The solar radiation is perpendicular to the lunar surface and parallel such that a shadow 4 m x 4 m is cast beneath the shade. The moon s surface acts as a reradiating surface. The irradiation from the sun is G — 1,400 W/m2, while it may be assumed that space behaves as a black body at 0 K. Find temperatures 1), T%, T3, and T4. 7) is the temperature of the lunar surface far from the shade. 

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)... 

If an enclosure may be divided into several radiant-heat sources or sinks Ai, A2, etc, and the rest of the enclosure (reradiating refractoiy surface) may be lumped together as A at a uniform temperature Tr, then the total interchange area for zone pairs in the black system is given by... 

In rotary devices, reradiation from the exposed shelf surface to the solids bed is a major design consideration. A treatise on furnaces, including radiative heat-transfer effects, is given by Ellwood and Danatos [Chem. Eng., 73(8), 174 (1966)]. For discussion of radiation heat-transfer computational methods, heat fliixes obtainable, and emissivity values, see Schornshort and Viskanta (ASME Paper 68-H 7-32), Sherman (ASME Paper 56-A-III), and the fohowing subsection. 

Equation (12-57) does not account for gas radiation at high temperature when the kiln charge can see the burner flame hence, the method will yield a conservative design. When a kiln is fired internally, the major source of heat transfer is radiation from the flame and hot gases. This occurs directly to both the sohds surface and the wall, and from the latter to the product by reradiation (with some conduction). 

The rate of heat transfer by radiation between two surfaces may be reduced by inserting a shield, so that radiation from surface 1 does not fall directly on surface 2, but instead is intercepted by the shield at a temperature Tsh (where 7, > T,h > T2) which then reradiates to surface 2. An important application of this principle is in a furnace where it is necessary to protect the walls from high-temperature radiation. 

Incoming radiation from the Sun and backradiation emitted by Earth interacts with the atmosphere. Although about half of the Sun s radiation passes directly to Earth s surface, a portion is reflected back directly into space, while another portion is absorbed by atmospheric gases and reradiated. Figure 18.3 shows the fate of radiation intercepting Earth. About half of the incoming solar radiation actually reaches the surface of Earth. The rest is reflected or absorbed by the atmosphere or clouds. Infiared radiation reflected from Earth s surface is partially absorbed and reflected by the atmosphere and clouds. Some of this radiation is reradiated back toward Earth s... 

Tfb = temperature, °F, of the radiant surface, which is essentially the firebox temperature. The reason for this latter value, 7, is that the flames heat not so much the tubes as the refractory, and the refractory then reradiates the heat to the tubes, so the main heat source becomes the refractory. 

Radiation from the sun is in part reradiated as long wavelength (infrared) radiation from the Earth s surface and is absorbed by small amounts of water vapor, carbon dioxide, ozone, and other compounds in the atmosphere (Table 9.4). The ability of these components to intercept infrared radiation is shown in Figure 9.3. The upper boundary of the stippled area is the emission of the ocean s surface, whereas the lower boundary is the radiation measured at the distance of satellites. The difference is the net energy absorbed and trapped in the lower atmosphere. On a global average annual basis, this trapped infrared radiation is equal to 153 watts per square meter of the Earth s surface. 

The reradiation of the absorbed energy leads to an observed warming of Earth s surface environment of about 35°C that is, an average surface temperature... 

The external heat flux (q"x) from the cone heater does not exclusively determine the heat flux important for samples pyrolysis in the cone calorimeter, since the reradiation from the hot sample surface (q"eTad), the loss by thermal conductivity into the specimen and the surroundings ( I SS), and the heat flux from the flame (q Lmt) are also of the same order of magnitude.82 85 Thus, the heat flux effective with respect to pyrolysis during a cone calorimeter run (qeii) is the result of the external heat flux and the material s response (qeB = q L + < L - gCad - qLs). 

Shielding effects are observed, especially in the case of effective insulation accompanied by increased reradiation due to high surface temperatures. Indeed, optimizing the barrier properties so that the HRR drops below a critical value characteristic for passing a test, or even reducing the HRR... 

The diffusivity, a2, is subsequently determined under the condition that the intercepts of the linear fits for the thermally thick and thin conditions are equal. For the PA6 nanocomposite, when the diffusivity is equal to 0.9 x 10 7m2/s, the intercepts are almost the same at about 11.5kW/m2. These intercepts are equal to the 0.64 fraction of the critical heat flux (below which there is no ignition) for ignition [21], and thus the critical heat flux can be calculated equal to 11.5/0.64 = 17.9 kW/m2. The ignition temperature can then be calculated by considering the critical heat flux equal to surface reradiation and convection losses ... 

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