Gray surface

Sin e-Gas-Zone/Two-Surface-Zone Systems An enclosure consisting of but one isothermal gas zone and two gray surface zones can, properly specified, model so many industrially important radiation problems as to merit detailed presentation. One can evaluate the total radiation flux between any two of the three zones, including multiple reflec tion at all surfaces. 

The more common approach is to treat the particle-gas suspension as an equivalent gray surface parallel to the heat transfer surface. Equation (11) would than be used with Ftaken as unity. Grace (1986) suggests that the emissivity of the particle-gas suspension can be approximated as,... 

Trim oxidized (faded brown or gray) surfaces of a meat sample and dice a lean portion into 2- to 3-mm cubes. 

Fig. 5.4 Dual -shell representation of the receptor surrogate by Raptor [24]. During the steric adaptation process, the fields generated by the protein binding site on to the ligand s solvent accessible surface (SAS, gray surface) are computed by linear interpolation between inner and outer shell, if...

Scheme 2. Critical reaction steps during C-H activation and consecutive selective oxidation. The gray surface represents the matrix of an active site of a metal oxide catalyst. The first product desorbing from such a catalyst...

Figure 5 (a) Stimulated photon echo signal of the azide ion (N3 ) in D2O at 2043 cm-1 as a function of r and T for the — kj + k2 + k3 (gray surface) and the +ki — k2 + k3 (white surface) phase matching directions, (b) Representative traces for four selected values of T. The solid lines represent a global fit of all the scans to the model correlation function Equation (20). (From Ref. 41.)... 

We have mentioned that a blackbody is a body which radiates energy according to the T4 law. We call such a body black because black surfaces, like as a piece of metal covered with carbon black, approximate this type of behavior. Other types of surfaces, like a glossy painted surface or a polished metal plate, do not radiate as much energy as the blackbody however, the total radiation emitted by these bodies still generally follows the T proportionality. To take account of the gray nature of such surfaces we introduce another factor into Eq. (1-9), called the emissivity c, which relates the radiation of the gray surface to that of. an ideal black surface. In addition, we must... 

In summary, we outline the computational procedure to be followed for numerical solution of radiation heat transfer between diffuse, gray surfaces. This basic procedure is the same for a hand computation, calculation with a minicomputer, or a large computer. 

Fig. 10.9. Isosurface representation of the 3D distribution function of water oxygen around the low-pressure (3 MPa) and high-pressure (300 MPa) structures of ubiqui-tin. The dark gray surfaces show the area where the distribution function is larger than 2. This is a top-view representation, in which the upper parts (the front parts in the figure) are clipped to bring the internal cavity (marked by dashed circle) into...

FIG. 5-19 Generalized electrical network analog for a three-zone enclosure. Here Ai and A2 are gray surfaces and Ar is a radiatively adiabatic surface. (Hot-tel, H C. and A. F. Sarojim, Radiative Transfer, McGraw-Hill, New York, 1967, p. 91.)... 

Figure 11. Schematic view of a TS (thick black line), with the same type of view as in Fig. 10. The equilibrium point is in the middle with its stable manifold and unstable manifold extending as straight lines. Trajectories in dot-dashed lines are reactive (inside the tubes) and cross TS trajectories in dashed lines are not reactive. The whole gray surface is the energy level. For a linear motion, it takes the form of a parabolic hyperboloid.

The effect of the gray approximation on emissivity and emissive power of a real surface is illustrated in Fig. 12 27. Note that the radiation emission from a real surface, in general, differs from the Planck distribution, and the emission curve may have several peaks and valleys. A gray surface should emit as much radiation as the real surface it represents at the. same temperature. Therefore, the areas under the emission curves of the real and gray surfaces must be equal. 

Coiiiparisoii of the emissivity (o) and emissive power ( >) of a real surface with those of a gray surface and a blackbody at the same temperature. 

That is, the surface will emit as much radiation energy at 800 K as a gray surface having a constant emissivity of e = 0.621. The emissive power of the surface is... 

C Wliai is a graybody How does it differ from a blackbody What is a diffuse gray surface ... 

We now consider an enclosure consisting of three opaque, diffuse, and gray surfaces, as shown in Fig. 13-26. Surfaces 1, 2, and 3 have surface areas Aj, and A3 cmissivities C, e, and 3 and uniform temperatures T, T , and T 3. respective . The radiation network of this geometry is constructed by following the standard procedure draw a surface resistance associated with each of the three surfaces and connect these surface resistances with space resistances, as shown in the figtire. Relations for the surface and space resistances are given by Fqs. 13-26 and 13-31. The three endpoint potentials and... 

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 a gray surface 6i = ai = Ex- A selective surface is one for which ex(T,X) exhibits a strong dependence on wavelength. If the wavelength dependence is monotonic, it follows from Eqs. (5-107) to (5-10 that 6i and ai can differ markedly when 7 and Tj are widely separated. For example, in solar energy applications, the nominal temperature of the earth is Ti = 294 K, and the sun may be represented as a blackbody with radiation temperature T2 = 5800 K. For these temperature conditions, a white paint can exhibit Ei = 0.9 and tti 2 = 0.1 to 0.2. In contrast, a thin layer of copper oxide on bright aluminum can exhibit 6i as low as 0.12 and tti 2 greater than 0.9. 

This relationship is true for gray surfaces in terms of total hemispherical radiation and that the emitting body sees the entire enclosure. In engineering, this relationship can be used to estimate the amount of radiative heat loss from a refractory wall to the surroundings, for example. 

A gray surface may be defined as a surface for which a. and ex are independent of A over the relevant spectral regions of the irradiation and the surface emission. 

A special case that occurs frequently in engineering practice involves radiation exchange between a small surface at Tg and a much larger, isothermal surface that completely surrounds the smaller one. The surroundings could be a furnace whose temperature Tgur differs from that of an enclosed surface ( sur — Tg). For such a condition, the irradiation may be approximated by emission from a blackbody at Tsud in which case G = crT. If the surface is assumed to be one for which a = e (a gray surface), the net rate of radiation heat transfer from the surface, is ... 

Enclosure with N Diffuse-Gray Surfaces—The Net Radiation Method.579... 

The and e defined above are hemispherical emissivities. The directional emissivities may be defined based on the ratio of the emitted (spectral or total) intensity to the blackbody (spectral or total) intensity. For a diffnse emitter, the emissivity is independent of the direction. For a gray surface, the emissivity is independent of wavelength, e = In practice, the surface may be considered gray if the emissivity is independent of the wavelength over the spectral regions of irradiation and emission. 

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