Radiative Heat Transport

Heat radiation consists of electromagnetic waves with a wavelength (X) range of 0.5 to 10 microns. All bodies emit electromagnetic waves as a result of the thermal agitation of their molecules. The rate at which a body emits radiant energy depends mostly on its temperature. Between two surfaces, an exchange of radiation can take 

The rate of emission of radiant energy is given by the Stefan-Boltzmann law  

For a black body, the spectral distribution of energy flux is given by Planck s law of radiation. The wavelength at which this intensity is maximumal is inversely proportional to the absolute temperature. This is Wien s law it can be formulated as  

At room temperature Vai = 10 pm (infrared) and at 6000 °K = 0.5 pm (green). The fact that the color of a body depends on its temperature is used in optical temperature measurements. This is often referred to as infrared temperature measurement even though some measurements may occur outside the infrared region of the spectrum. The infrared region ranges from a wavelength of 0.7 pm to about 400 pm. 

A perfectly black body emits the maximum amount of radiation based on its temperature its emissivity is unity. According to Kirchhoff s law, its absorptivity will also be unity. In reahty, surfaces have emissivities and absorptivities for infrared radiation that are less than unity. The actual value will depend on the material, the surface roughness, the temperature, and the wavelength of the radiation. 

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Atherton et al. (153) have extended the calculations to include diffuse-gray radiation between components of the enclosure and reached essentially the same conclusions regarding the stability of the process. However, they discovered a new mechanism for the damped oscillation of the crystal radius caused by the radiative interaction between the crystal surface just above the melt level and the hot crucible wall. These oscillations are especially apparent when the vertical temperature gradient in the crystal is low, so that radiative heat transport has a dominating influence. 

Radiative heat transport through olivine has been discussed extensively (e.g., Fukao et al., 1968 Shankland, 1970 Schatz and Simmons, 1972 Scharmeli, 1979 Shankland et al., 1979). The radiative thermal conductivity, Kt of forsteritic olivine increases with rising temperature and would contribute to heat flow in the Upper Mantle (Shankland et al., 1979). However, values of Kt for olivine are considered to be rather low to satisfactorily explain the dissipation of the Earth s internal heat by radiation and lattice conduction alone. Note, however, that Fe2 CF transitions in almandine, pyroxenes (M2 site) and, perhaps, silicate perovskites absorb strongly in the wavelength range 1,250 to... 

Shankland, T. J. (1970) Pressure shift of infrared absorption bands in minerals and the effect on radiative heat transport. J. Geophys. Res., 75,409-13. 

J. T. Farmer and J. R. Howell, Monte Carlo Algorithms for Predicting Radiative Heat Transport in Optically Thick Participating Media, Proc. 10th International Heat Transfer Conference, Brighton, England, 1994. 

DBE-4 is initiated by a spurious control rod group withdrawal, as in DBE-3. However, in this case both the HTS and SCS fail to provide forced heliiom circulation. Core heat removal is accomplished by conductive and radiative heat transport to the RCCS. The initial phase of this event is identical to AOO-3 and DBE-3, but the subsequent temperature history is that of a pressurized conduction cooldown. The effects on the core are therefore the same as for DBE-3 during the initial phase and the same as for SRDC-1 during the later phase. (The SRDCs are evaluated in Section 4.2.5.5.)... 

The dip in the temperature at the reactor end is observed because the wall loses energy by radiation to the surroundings. In this case, a thermal reservoir for radiative heat transport at the reactor end was assumed to be at ambient (low) temperature. On the other hand, it is common to use a thermal reservoir temperature... 

At room temperature and relatively small temperature differences, the value of h will be above 5 W/m °C. This value is large enough that it cannot be neglected relative to free convection. Obviously, at higher temperatures the contribution of the radiative heat transport increases substantially. 

Intermediate Cases (0.01 < D < 100) For growth of optical crystals such as sapphire, BGO, YAG, fluorides, the material is neither transparent (D 1) nor optically very thick (D 1) in the whole infrared spectram. Therefore, more complex models have to be appHed in order to compute the radiative heat transport in such materials. Three kinds of models are frequently used ... 

Famworth [74] presented a model of the combined conductive and radiative heat flow through fibrous material used for clothing insulation. The amount of heat transferred by convective heat transfer is small compared to that of conductive and radiative heat transport and is neglected. In the case where a sample of fibrous material is held between two plates, one cold and one hot, and in the absence of radiative heat, the heat flow is given by ... 

Whereas conductive and radiative heating are useful techniques for some appHcations, convective heating is by far the most common means of supplying the energy needed to evaporate the solvent, because convection is the only means of heating that also provides a means of transporting solvent vapor away from the surface of the coating. 

These two points taken together illustrate that the temperature at the Earth s surface depends on bofh a radiative balance and all of the meteor-ologic processes that transport heat within the lower atmosphere and of course, all the oceanographic factors that transport heat in the ocean as well. So, at this juncture we must abandon the simple picture of a global-mean radiative heat... 

The high filament temperature used causes additional radiative heating of the substrate [530, 531]. Feenstra et al. [531, 548] have developed a heat transport model of their setup (Figure 68). All heat exchange is assumed to occur via ra-... 

We now repeat the derivation of the steady-state heat transport limited moisture uptake model for the system described by VanCampen et al. [17], The experimental geometry is shown in Figure 9, and the coordinate system of choice is spherical. It will be assumed that only conduction and radiation contribute significantly to heat transport (convective heat transport is negligible), and since radiative flux is assumed to be independent of position, the steady-state solution for the temperature profile is derived as if it were a pure conductive heat transport problem. We have already solved this problem in Section m.B, and the derivation is summarized below. At steady state we have already shown (in spherical coordinates) that... 

This solution is composed of simple radiative and conductive heat transport terms. 

In conduction, heat is conducted by the transfer of energy of motion between adjacent molecules in a liquid, gas, or solid. In a gas, atoms transfer energy to one another through molecular collisions. In metallic solids, the process of energy transfer via free electrons is also important. In convection, heat is transferred by bulk transport and mixing of macroscopic fluid elements. Recall that there can be forced convection, where the fluid is forced to flow via mechanical means, or natural (free) convection, where density differences cause fluid elements to flow. Since convection is found only in fluids, we will deal with it on only a limited basis. Radiation differs from conduction and convection in that no medium is needed for its propagation. As a result, the form of Eq. (4.1) is inappropriate for describing radiative heat transfer. Radiation is... 

It was shown by Weaver (2003) that the average annual radiative cooling of clouds in high latitudes has the same order of magnitude as the convergence of vortices-induced meridional heat flux, but of an opposite sign. Since there is a close correlation between CRF and storm track dynamics, we can suppose two ways for the impact of storm tracks dynamics on poleward heat transport ... 

Indirectly via CRF changes. The efficiency of heat transport by vortices is reduced by radiative cloud cooling. Changes in efficiency can be a substantial climate-forming factor. Various levels of efficiency can determine the possibility of the existence of different climatic conditions. 

An element in a thermally radiative environment absorbs, reflects, refracts, diffracts, and transmits incoming radiative heat fluxes as well as emits its own radiative heat flux. Most solid materials in gas-solid flows, including particles and pipe walls, can be reasonably approximated as gray bodies so that absorption and emission can be readily calculated from Stefan-Boltzmann s law (Eq. (1.59)) for total thermal radiation or from Planck s formula (Eq. (1.62)) for monochromatic radiation. Other means of transport of radiative... 

Note that, despite the typically high operating temperatures of fuel cells, radiative heat transfer was neglected. Lee and Aris (16) have discussed such effects in parallel-channel monoliths. The importance of radiative transport depends on the emissivity of the surface for the low (about 0.1) emissivity of Pt-coated catalyst-electrodes, their analysis suggests that radiative effects can be neglected. 

At very low cryogenic temperatures, the best insulation is a vacuum jacket that is silvered to eliminate radiative heat leaks. Various kinds of superinsulation exist and are used to store and transport volatile cyrogens like liquid helium. In one type a fine insulating powder is placed in the vacuum jacket in another type a metallized variety of Kapton film is used. 

Curtis L.J. and Miller D.J. (1988) Transport model with radiative heat transfer for rapid cellulose pyrolysis. Ind. Eng. Chem. Res., 27, 1775-83,... 

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