Radiator, diffuse Lambert

The body has a diffuse radiating surface (Lambert radiator) then eA = eA(A, T) is valid. 

For opaque materials, the reflectance p is the complement of the absorptance. The directional distribution of the reflected radiation depends on the material, its degree of roughness or grain size, and, if a metal, its state of oxidation. Polished surfaces of homogeneous materials reflect speciilarly. In contrast, the intensity of the radiation reflected from a perfectly diffuse, or Lambert, surface is independent of direction. The directional distribution of reflectance of many oxidized metals, refractoiy materials, and natural products approximates that of a perfectly diffuse reflector. A better model, adequate for many calculational purposes, is achieved by assuming that the total reflectance p is the sum of diffuse and specular components p i and p. ... 

This simple relationship between incident and transmitted light is well known as the Boguert-Lambert-Beer law. This expression renders positive values for Ij < Iq. In case of scattering material like TLC plates, a part of the scattered light is emitted as reflectance J from the plate surface to the top. For the hrst approximation of a parallel incident light beam with the intensity /g, some radiation may be scattered inside the layer and some radiation may be absorbed either by the sample or by the layer itself. According to the Schuster equations and with the abbreviation R (the diffuse reflectance of an infinitely thick layer). 

An infrared spectrum can be analysed quantitatively by studying the variations in absorption wave-numbers, which reflect a change in environment, or the variations in the line intensities. To measure the latter it is necessary to use, depending on the transparency of the sample to the radiation, respectively, the Beer-Lambert law for transmission measurements and the Kubelka-Munk law for measurements using diffuse reflectance. 

In radiative exchange calculations, it is preferable to use the model, described in the previous section, of a grey, diffuse radiating body as a simple approximation for the radiative behaviour of real bodies. As Lambert s cosine law is valid for this model, we denote these bodies as grey Lambert radiators. The energy radiated from them is distributed like that from a black body over the directions in... 

Surfaces with low emissivities often exhibit approximately mirrorlike or specular reflection rather than diffuse reflection. We want to investigate how the assumption of mirrorlike reflection affects the heat transfer. The assumptions regarding the emission of diffuse and grey radiation remain unaltered. Grey Lambert radiators with mirrorlike reflection are therefore assumed. 

Two main types of models for tubular lamps (the most widely used) will be described. There are lamps that produce an arc that emits radiation and, consequently, photons come out directly from such an arc. Emission is made by the whole lamp volume. We call this process Voluminal Emission. There are other types of lamps in which the discharged arc between electrodes induces an emission produced by some particular substance that has been coated on the lamp surface. We call this process Superficial Emission. Voluminal emission may be safely modeled as an isotropic emission in this case the specific intensity associated with each bundle of radiation originated in some element of volume of the lamp is independent of direction, and the associated emitted energy (per unit time and unit area) is also isotropic (Figure 6.6). On the other hand, it seems that superficial emission can be better modeled by a diffuse type of emission that is also known as one that follows the Lambert s cosine law of emission in this case the emitted intensity is independent of direction but the emitted energy depends on the surface orientation and follows the cosine law equation (Figure 6.7). The following assumptions are made (Irazoqui etal., 1973) ... 

One can distinguish the surface and volume components in the diffuse transmission /dt and the diffuse reflection /dr (Fig. 1.22) [224-227]. The surface component, which is referred to as Fresnel diffiise reflectance, is the radiation undergoing mirrorlike reflection and still obeying the Fresnel reflection law but arising from randomly oriented faces. This phenomenon was first described by Lambert in 1760 [228] to account for the colors of opaque materials. The volume, or Kubelka-Munk (KM), component is the radiation transmitted through at least one particle or a bump on the surface (Fig. 1.22). 

In the case of samples that produce scatter in transmission or diffuse reflectance spectra, a number of factors corrupt the linearity of the Beer-Lambert absorbance concentration relationship. Sample scattering of radiation results in an alteration of the proportion of absorbed and reflected radiation so that pathlength becomes another unknown in the Beer-Lambert relationship. Particle size, particle shape, crystalline form, bulk, density, and the nature of the pore space (filled with air, water, or oil) are all variables that dictate the effective pathlength of the radiation. Sample surfaces also reflect specular energy that has not interacted with molecular structures. This form of energy has an overall effect on spectra, contributing primarily to the curvilinearity of the spectral baseline. 

The phenomenon of diffuse reflection is easily observed in everyday life. Consider for example the intensity of radiation reflected from a completely matte surface such as a sheet of white paper. The remitted radiation is everywhere of the same intensity no matter what the angle of observation or angle of incidence is. It was the same observation that led Lambert [1] to be the first to attempt a mathematical description of diffuse reflection. He proposed that the remitted radiation flux Ir in an area/ cm and solid angle a> steradians (sr) is proportional to the cosine of the angle of incidence a... 

Light induced degradative effects on the polymeric materials are visible on then-surfaces and the depth at which their properties are affected represents an interesting subject [7]. It is why the most affected materials are the transparent or translucid ones. Systems which totally absorb luminous radiation, without occurring of diffusion phenomena, respect the Lambert-Beer law, where Zq is the incident light intensity, I is light intensity at depth x and a is light absorptivity ... 

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