Radiation heat-flux distribution

For the short crystal, the radiation flux at the center of the cryslal/melt interface exceeds that at the periphery by a factor of six. At the same time, the distribution of radiation heat flux for the crystal of length 197 mm is nearly uniform and similar to the flux obtained when the crystal surface is diffuse. This effect is mainly related to the specular reflection at the conical part of the crystal (its shoulder) while the contributions of the cylindrical part and the free surface of the melt are less significant. Therefore, it is clear why the effect of the specular reflection depends on the crystal length. The shorter the crystal, the closer is the conical part of the crystal to the crystal/melt interface and the more nonuniform is the radiation heat-flux distribution. 

Results of computations of the radiation heat-flux distribution at the crystal/melt... 

As expected, the perturbations of a specular cylindrical surface lead to significant smoothing of the radiation heat-flux distribution at the interface, while the effect of perturbations of a specular conical surface turns out to be insignificant. For... 

Fig. 8.5 Effect of perturbation of only cylindrical (left) or only conical (right) parts of the crystal side surface on the radiation heat-flux distribution at the crystal/melt interface. The unperturbed part of the side...

From a radiation point of view, the heat flux distribution is a function of the tube spacing given as the ratio between the centre-to-centre distance Ct and the tube diameter dt, so that the ratio of maximum heat flux at the front face to the average heat flux - used on the eatalyst side -is as expressed by Hottel [244] ... 

A different situation is observed in the solid phase. Figure 8.3 shows that owing to specular reflection the distribution of radiation heat flux at the crystal/melt interface can be extremely nonuniform, depending on the crystal length. 

The inclusion of radiative heat transfer effects can be accommodated by the stagnant layer model. However, this can only be done if a priori we can prescribe or calculate these effects. The complications of radiative heat transfer in flames is illustrated in Figure 9.12. This illustration is only schematic and does not represent the spectral and continuum effects fully. A more complete overview on radiative heat transfer in flame can be found in Tien, Lee and Stretton [12]. In Figure 9.12, the heat fluxes are presented as incident (to a sensor at T,, ) and absorbed (at TV) at the surface. Any attempt to discriminate further for the radiant heating would prove tedious and pedantic. It should be clear from heat transfer principles that we have effects of surface and gas phase radiative emittance, reflectance, absorptance and transmittance. These are complicated by the spectral character of the radiation, the soot and combustion product temperature and concentration distributions, and the decomposition of the surface. Reasonable approximations that serve to simplify are ... 

If this excess absorption by clouds is ultimately shown to be a real phenomenon, then an increased cloud formation and extent due to anthropogenic emissions may alter the radiative balance of the atmosphere not only through increased reflectance but also through increased absorption of solar radiation. Such an effect could impact atmospheric temperatures, their vertical distribution, and circulation, as well as surface wind speeds and the surface latent heat flux (Kiehl et al., 1995). Hence establishing if this is truly excess absorption, and if so, its origins, is a critical issue that remains to be resolved. 

The processes of scattering and absorption of radiation in the atmosphere so significantly alter the spectral distribution that any similarity to extra terrestrial radiation is almost coincidental. Experiments with radiation between surfaces have shown that blackbody radiation theory can be extended successfully to many radiation heat transfer situations. In these situations the strict equilibrium requirements of the initial model have so far not proved to be necessary for practical designs. Most importantly the concept of temperature has proved useful in non-equilibrium radiation flux situations(3). 

The flux distribution around the tube is not uniform as well. As indicated in Figure 5.3, the radiating plane is the flame. The diagram on the left shows the flux profile for a single-fired heater. The front of the tube facing the fire picks up most of the heat. The diagram on the right shows the profile for a double-fired heater with flames on both sides of the tubes. The flux pattern is close to uniform. 

The heat transport due to conduction and that due to radiation are not readily separable from the experimental data. Curve A of Fig. 4 shows the measured temperature distribution through a typical sample containing 29 shields per inch. Curve B shows the temperature distribution expected if each sheet of aluminum foil were a floating radiation shield. These results were obtained from Fig. 1. Curve C shows the temperature distribution througji an ideal sample, whose thermal conductivity would be independent of temperature. The observed result is probably a combination of radiation heat transfer and the change in thermal conductivity of the insulation with temperature. The thermal conductivity of most disordered dielectrics is approximately proportional to the first power of the temperature, but the temperature dependence of multiple contacts is not well understood. The fact that the temperature distribution for a sample of this type can be accounted for by a temperature-dependent thermal conductivity is sufficient justification for using Eq. (3), a particular solution of the Fourier equation, rather than Eq. (1), the heat flux equation for radiant heat transport, to represent our results. 

BLACK BODY. This term denotes an ideal body which would, if it existed, absorb all and reflect none of the radiation felling upon it its reflectivity would be zero and its absorptivity would be 100%. Such a body would, when illuminated, appear perfectly black, and would be invisible except its outline might be revealed by the obscuring of objects beyond. The chief interest attached to such a body lies in the character of the radiation emitted by it when heated and the laws that govern the relations of the flux density and the spectral energy distribution of that radiation with varying temperature. 

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