Radiation heat transfer reradiating surface

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. 

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. 

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. 

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... 

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. 

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)... 

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. 

---