Radiation heat transfer view factors

Equations similar to equation 9.158 may be obtained for each of the surfaces in an enclosure, 1 = 1,1 = 2, 1 = 3, 1 = n and the resulting set of simultaneous equations may then be solved for the unknown radiosities, qoi,qm- qun The radiation heat transfer is then obtained from equation 9.140. This approach requires data on the areas and view factors for all pairs of surfaces in the enclosure and the emissivity, reflectivity and the black body emissive power for each surface. Should any surface be well insulated, then, in this case, Qj — 0 and ... 

Radiation heat transfer is assumed to be significant between each portion of the cells and those portions of other cells that are in the same plane, in the upper plane and in the lower plane. The error associated with this assumption increases when small vertical portions are considered. Figure 7.26 shows the view factors, for a cavity constituted of four cells, as the function of the length of the cell slice (vertical discretization). The four view factors have the following meaning (1) Fap - view factor between a cell and the two adjacent cells in the same horizontal plane (2) Fop - view factor between opposite cells in the same horizontal plane (3) Fad - view factor between a cell and the two adjacent cells in the upper and lower plane (4) Fod -view factor between opposite cells in the same horizontal plane. When the element length is larger than 0.04 m, the summation of these coefficients is about 0.97, which means that the error is less than 3%. The calculation of these coefficients is shown in Section 7.4.2.2. 

To account for the effects of orientation on radiation heat transfer between two surfaces, we define a new parameter called the vieu factor, which is a purely geometric quantity and is independent of the surface properties and temperature. It is also called the shape factor, configuration factor, and angle factor. The view factor based on the assumption that the surfaces are diffuse emitters and diffuse reflectors is called the diffitse view factor, and the view factor based on the assumption that the surfaces are diffuse emitters but specular reflectors is called the specular view factor. In lliis book, we consider radiation exchange between diffuse surfaces only, and ihu.s the term view factor simply means diffuse view factor. 

Consider two black surfaces of arbitrary shape maintained at uniform temperatures T and Ti, as shown in fig. 13 -18, Recognizing that radiation leaves a black surface at a rate of E/, - crT" per unit surface area and that the view factor i, 2 represents the fraction of radiation leaving surface 1 that strikes surface 2, the net rate of radiation heat transfer from surface 1 to surface 2 can be expressed as... 

Tliis question deals with sicady-siatc radiation heat transfer between a sphere = 30 ctii) and a circular disk (r2 = 120 cm), which are separated by a ceiiler-to-center distance h = 60 cm. When the normal to the center of disk passes through the center of sphere, the radiation view factor is given by... 

Consider a veiiical 2 m-diameler cylindrical furnace whose stiifaces closely approximate black surfaces. The base, top, and side surfaces of the furnace are maintained at 400 K, 600 K, and 900 K, respectively. If the view factor from the base surface to the top surface is 0.2, the net radiation heat transfer between the base and the side suifaces is (a)22.5kW (b)38.6kW (c) 60.7 kW... 

Consider an enclosure consisting of W diffuse and gray surfaces. The emissivity and tempetature of each surface as well as the view factors between the surfaces are specified. Write a program to determine the net rate of radiation heat transfer for each surface. 

For multimode problems, it is sometimes advantageous to use a dual grid technique in order to minimize the computational expense associated with storing and evaluating view factors. A course mesh can be used for the radiation heat transfer, while finer meshes can be used for the conduction and/or convection heat transfer. This technique is discussed in detail, and associated computational error (which is small) is reported in Zhao [178]. 

A small cold package having an area /Ij and emissivity j is at temperature T. It is placed in a warm room with the walls at Tj and an emissivity ,. Derive the view factor for this using Eq. (4.11-45), and the equation for the radiation heat transfer. 

The amount of calculation involved here can be very considerable and use of a computer is usually required. A simpler approach is to make use of the many expressions, graphs and tables available in the heat transfer literature. Typical data, presented by Incropera and DE Witt(45) and by Howell(47), are shown in Figures 9.38-9.40, where it will be seen that in many cases, the values of the view factors approach unity. This means that nearly all the radiation leaving one surface arrives at the second surface as, for example, when a sphere is contained within a second larger sphere. Wherever a view factor approaches zero, only a negligible part of one surface can be seen by the other surface. 

Classical heat transfer provides expressions for quantities such as view factors, radiation and temperature fields in semi—infinite bodies. The lining materials studied here were treated as semi-infinite bodies since the test duration is relatively short. 

In all of these systems, the rate of generation at the gas-solid interface is so rapid that only a small fraction is carried away from the particle surface by convective heat transfer. The major source of heat loss from the particles is radiation loss to the surrounding atmosphere, and the loss per particle may be estimated using unity for both the view factor and the emissivity as an upper limit from this source. The practical observation is that the solids in all of these methods of roasting reach temperatures of about 1200-1800 K. 

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). 

The surfaces of a two-surface enclosure exchange heat with one another by thermal radiation. Surface 1 has a tempetature of 400 K, an area of 0.2 m, and a total emissivity of 0.4. Surface 2 is black, has a temperature of 600 K. and an area of 0.3 ntl If the view factor is 0.3, the rate of radiation heal transfer between the two surfaces is ( ) 87W (h) I35W (c) 244W... 

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)... 

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. 

The surface temperature of a cylinder of diameter D =2R and emissivity em is to be kept at Tm (Fig. 9P-16). (a) Find the radiant heat transfer from the cylinder to the ambient, (b) Let three different insulated radiation shields separately surround the cylinder. For each case, find the view factors and the radiant heat transfer. 

N. H. Juul, View Factors in Radiation between Two Parallel Oriented Cylinders, J. Heat Transfer, 104, p. 235,1982. 

The emissivity accounts for the properties of a radiating surface. An ideal radiator, or black body, has a value of e = 1. The rate of radiative heat transfer between two bodies is proportional to the difference between the fourth powers of their temperatures. In most commercial apparatus, not all the radiation from one body reaches the second. Radiation goes out in all directions, and only some of it reaches the intended receiver. The fraction that does is called the area factor or the view factor. Thus,... 

The type of heat transfer at the surface is determined by the value of z. Suppose the height of the cooling liquid metal surface is h, when z>h, the surface element radiates with the furnace wall, a Monte Carlo algorithm is applied to calculate the view factor varying with withdrawal distance. When zfollowing equation is used to calculate the heat transfer ... 

EXAMPLE 4.11-3. Radiation Between Parallel Disks In Fig. 4.11-6 a small disk of area /I, is parallel to a large disk of area A and /I, is centered directly below Aj- The distance between the centers of the disks is R and the radius of/lj is a. Determine the view factor for radiant heat transfer from /I, to /Ij. 

A very important aspect of radiative heat transfer is the system geometry. This is accounted for by using radiation shape factors, also called view factors, angle factors, or configuration factors and defined as follows... 

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