Radiant conductivity

Approximate Radiant Conductivity Model. The radiative heat transfer for a onedimensional, plane geometry with emitting particles under the steady-state condition is given by [79] ... 

The approach has many limitations, but the single most important limitation is that the value of F cannot be easily calculated. Of all the methods, the Monte Carlo method can be used for calculating Ffor semitransparent particles. The value of Falso depends upon the value of the conductivity of the solid phase. In the Kasparek experiment [79] infinite conductivity is assumed, which is justified for metals. Similarly, the case of zero conductivity can be easily treated by considering the rays to be emitted from the same point at which they were absorbed. However, the intermediate case, that is, when the conductivity is comparable to the radiant conductivity, shows a strong dependence of radiant conductivity on the solid conductivity. The extent of this dependence may be seen by comparing the difference in the values of Fin Table 9.7 corresponding to low and high emissivities. If the conductivity was small, all the F values would be close to those obtained for the er = 0 case. Thus, a simple tabulation of F as in Table 9.7 is of limited use. On the other hand, this approach is simple. 

Determination of F. Many different models are available for the prediction of F, and these are reviewed by Vortmeyer [79], Here, the main emphasis is on examining the validity of the radiant conductivity approach by comparing the results of some of these models with the Monte Carlo simulations and with the available experimental results. 

The results for e = 0.476 and various values of er and kf have been obtained for both diffusive and specular surfaces. The results are shown in Fig. 9.15a and b. The results for both surfaces are nearly the same. Both low and high kf asymptotes are present. The low kf asymptotes are reached for kf < 0.10 and the high kf asymptote is approached for kf > 10. There is a monotonic increase with er, that is, as absorption increases, the radiant conductivity increases for high kf. 

FIGURE 9.15 Effect of dimensionless solid conductivity on the dimensionless radiant conductivity for (a) diffuse particle surface and (b) specular particle surface [9],... 

The variational upper bound on the radiant conductivity, including the conduction through the particle, has been predicted by Wolf et al. [80]. 

Finally, we note that the thermal conductivity of the solid phase influences the radiation properties. When using the radiant conductivity model, the results show that kr can increase by fivefold for ks < >as compared to that for ks 0 (for er = 1 and typical porosities). 

The primary means of heat transfer in a fired heater are radiant, conduction, and convection. Radiant heat transfer accounts for 60% to 70% of the total heat energy picked up by the charge in the furnace. Convective heat transfer accounts for about 30% to 40% of the total heat energy... 

The variation in total thermal conductivity with density has the same general nature for ah. cellular polymers (143,189). The increase in at low densities is owing to an increased radiant heat transfer the rise at high densities to an increasing contribution of k. ... 

Thermal conductivity of foamed plastics has been shown to vary with thickness (197). This has been attributed to the boundary effects of the radiant contribution to heat-transfer. 

In heavy-metal analysis of the same pigments, metals found were present in only trace amounts. The data Hsted place the products tested in the category of nontoxic materials. The Radiant Color Co. has conducted toxicity tests on its own products similar to the A-Series and has found them to be nontoxic. Heavy metals were found only in trace amounts in these tests. 

A fire tube contains a flame burning inside a piece of pipe which is in turn surrounded by the process fluid. In this situation, there is radiant and convective heat transfer from the flame to the inside surface of the fire tube, conductive heat transfer through the wall thickness of the tube, and convective heat transfer from the outside surface of that tube to the oil being treated. It would be difficult in such a simation to solve for the heat transfer in terms of an overall heat transfer coefficient. Rather, what is most often done is to size the fire tube by using a heat flux rate. The heat flux rate represents the amount of heat that can be transferred from the fire tube to the process per unit area of outside surface of the fire tube. Common heat flux rates are given in Table 2-11. 

Surfaces will absorb radiant heat and this factor is expressed also as the ratio to the absorptivity of a perfectly black body. Within the range of temperatures in refrigeration systems, i.e. - 70°C to + 50°C (203-323 K), the effect of radiation is small compared with the conductive and convective heat transfer, and the overall heat transfer factors in use include the radiation component. Within this temperature range, the emissivity and absorptivity factors are about equal. 

Among the causes producing irreversibility w7e may instance the forces depending on friction in solids, viscosity of liquids imperfect elasticity of solids inequalities of temperature (leading to heat conduction) set up by stresses in solids and fluids generation of heat by electric currents diffusion chemical and radio-active changes and absorption of radiant energy. 

From here the water mixture rises through the water-wall tubes (generator tubes) that constitute the furnace membrane where steam is generated (primarily by radiant energy transfer). The steam-BW mixture is collected in top water-wall headers and conducted through risers (riser tubes) back to the top drum, where the saturated steam separates from the water at the steam-water interface. 

The value of the coefficient will depend on the mechanism by which heat is transferred, on the fluid dynamics of both the heated and the cooled fluids, on the properties of the materials through which the heat must pass, and on the geometry of the fluid paths. In solids, heat is normally transferred by conduction some materials such as metals have a high thermal conductivity, whilst others such as ceramics have a low conductivity. Transparent solids like glass also transmit radiant energy particularly in the visible part of the spectrum. 

A flat-bottomed cylindrical vessel, 2 m in diameter, containing boiling water at 373 K, is mounted on a cylindrical section of insulating material, l m deep and 2 m ID at the base of which is a radiant heater, also 2 m in diameter, with a surface temperature of 1500 K. If the vessel base and the heater surfaces may be regarded as black bodies and conduction though the insulation is negligible, what is the rate of radiant heat transfer to the vessel How would this be affected if the insulation were removed so that the system was open to the surroundings at 290 K ... 

These authors numerically solved the system of equations with appropriate boundary conditions to derive the time-averaged radiant and conductive heat fluxes between the fluidized bed and the heat transfer surface. Using... 

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