Absorptivity hemispherical total

Fig. 5.16 shows the spectral irradiance E according to (5.37) for T = 1000 K and T = 5777 K. Here, the proportionality constants c were each chosen so that for both temperatures the maximum of E, which appears at Amax = C2/5T, was the same. The hatched areas in Fig. 5.16 are proportional to the absorbed fraction of the incident radiation flow, whilst the areas under the E curves correspond to the irradiance E. The desired hemispherical total absorptivity a T) is, according to (5.28) and (5.36) the ratio of these areas. For T = 1000 K an absorptivity close to a 2 will be expected. In contrast the largest portion of the solar radiation (T = 5777 K) falls in the region of small wavelengths... 

The results found from Fig. 5.16 can be confirmed by the following calculations. According to Table 5.1 the hemispherical total absorptivity is obtained to be... 

The hemispherical total absorptivity is not only a property of the absorbing surface. Rather, it depends on the spectral distribution of the incident radiation energy. This is shown by the different values of a for the mainly short-wave solar radiation, in which the absorption properties at small wavelengths are decisive, and for the incident radiation from an earthly source, for which the long-wave portion of the absorption spectrum a (X,T) is of importance. 

If the bodies participating in radiative exchange cannot be assumed to be black bodies, then the reflected radiation flows also have to be considered. In hollow enclosures, multiple reflection combined with partial absorption of the incident radiation takes place. A general solution for radiative exchange problems without simplifying assumptions is only possible in exceptional cases. If the boundary walls of the hollow enclosure are divided into isothermal zones, like in 5.5.2, then a relatively simple solution is obtained, if these zones behave like grey Lambert radiators. Each zone is characterised purely by its hemispherical total emissivity si — whilst at = is valid for its absorptivity, and for the reflectivity... 

Here, a (T, T2) is the hemispherical total absorptivity of body 1 for black radiation at temperature T2. This gives... 

According to section 5.3.2.2, the hemispherical total absorptivity of a body with any radiative properties is equal to its hemispherical total emissivity, if radiation from a black body at the same temperature strikes the body. This is the case here. It therefore follows from (5.160) that A2F21 = A. This corresponds to the reciprocity rule (5.132) with F 2 = 1. Its application to this case was however not assured from the start as the intensity of body 1 is not constant. 

A plate which allows radiation to pass through with a hemispherical total absorptivity a = 0.36, is irradiated equally from both sides, whilst air with = 30 °C flows over both surfaces. They assume a temperature = 75 °C at steady-state. The heat transfer coefficient between the plate and the air is a = 35W/m2K. Using a radiation detector it is ascertained that the plate releases a heat flux qstr = 4800 W/m2 from both sides. Calculate the irradiance E and the hemispherical total emissivity of the plate. 

The hemispherical total absorptivity a represents an integrated average over both direction and wavelength ... 

Finally, integrating the absorbed energy over both wavelength and direction and comparing with the integrated incident energy gives hemispherical total absorptivity. 

This relation is known as Kirchhoff s law. Equation 7.27 may be substituted into the various relationships for the integrated emissivity or absorptivity. However, it does not follow that such quantities as directional total, hemispherical-spectral, or hemispherical total emissivity and absorptivity are necessarily equal. In fact, the integrated properties are only equal if certain restrictions are met. These are given in Table 7.1. 

Emittance and Absorptance The ratio of the total radiating power of a real surface to that of a black surface at the same temperature is called the emittance of the surface (for a perfectly plane surface, the emissivity), designated by 8. Subscripts X, 0, and n may be assigned to differentiate monochromatic, directional, and surface-normal values respectively from the total hemispherical value. If radi-... 

Tlial is, the total hemispherical emissivity of a surface at temperature T is equal to its total hemispherical absorptivity for radiation coming from a blackbody at the same temperature. This relation, which greatly simplifies the radiation analysis, was first developed by Gustav Kirchhoff in 1860 and is now called Kirchlioff s law. Note that tliis relation is derived under the condition that the... 

Now, by putting these absorbed energy flows in relation to the associated incident radiation flows d2 n from (5.30) and dabsorptivities presented in Table 5.1 are obtained. These describe either the absorption of radiation coming from all directions in the hemisphere or over all wavelengths or finally the absorption of the total radiation on the surface element. 

Besides, according to Kirchhoff s law, the total hemispherical emissivity of the surface equals the total hemispherical absorptivity. Therefore, e = a, e = a, ... 

TABLE 2.4. Total hemispheric emittances (and absorptances) of metals and their oxides, selected from references 42,51, and 70. Emittances of refractories and miscellaneous nonmetals are listed in chapter 4 of reference 51. 

Another thermal property that atFects the response of a polymer to the exposure from an external heat source is the surface absorptivity. It is generally assumed that polymers behave as gray surfaces, ie that the total hemispherical surface absorptivity is equal to the total hemispherical emissivity, e. Hallman (23) measured e for many polymers and different radiant heat soin-ces. Some of Hallman s measurements are given in Table 5. These values are applicable prior... 

The thermal performance of a solar collector is closely related to the thermal properties of the absorber. Within this framework, many measurements are necessary, more particularly the conductivity, but also emissivity and absorptivity to solar radiation. The aim of this paper is to study the thermal properties of the PLA bio-polymer charged of exfoliated graphite and/or CNT. Thereafter, the total hemispherical absorptivity, an estimation of the total hemispherical emissivity and the thermal conductivity coefficient were measured for different load rates, we will conclude on the interest and the potentialities of tested materials. 

As noted above, the best spatial resolution of a microscope is ultimately determined by diffraction of the radiation. Thus, the spatial resolution is limited by the radius r of the Airy disk for the longest wavelength in the spectrum and hence depends on n, the refractive index of the medium in which the optics are immersed, for example, 1.0 for air and up to 1.56 for oils. Oil immersion is almost never used for infrared microspectroscopy because of absorption by the oil but has occasionally been used to improve the spatial resolution in Raman microspectroscopy. Immersion oils have been shown to be essential in order to obtain good depth resolution with confocal Raman microscopy [21]. Of greater importance from a practical standpoint for infrared microspectroscopy is the improvement in spatial resolution that is achieved in an attenuated total reflection (ATR) measurement with a hemispherical IRE, especially when the IRE is fabricated from germanium ( = 4.0) or silicon (n = 3.4.)... 

A specimen is heated by electrical self-resistance in vacuum. Total hemispherical emittance is determined from the Stefan-Boltzmann law of radiation, knowing the power input, the total surface area, and the temperature. By using a solar simulator, as in method 3, the difference in electric power required to maintain a given temperature with the solar simulator on and off determines the solar absorptance. 

In the last two decades of the past century, the presence in the atmosphere of ozone-depleting substances (CFCs, HCFCs, halons, carbon tetrachloride, etc.) has been reducing the ozone concentration in the stratosphere over high and mid-latitudes of both hemispheres. Ozone concentration in the atmosphere is very low (about 3 parts in 10 millions), and that of the total ozone column is equivalent to that of 3 mm at standard temperature and pressure. Nevertheless, its optical density is about 45 at the absorption maximum around 255 nm, about 13 at 280 nm, and goes to 0 at 320 run. Therefore, the stratospheric layer, which contains approximately 90% of the total ozone, has the function of a protective filter for the Earth s surface, fully cutting off solar radiation under 280 nm and greatly reducing UV-B radiation (280 to 315 nm). 

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