Radiant heat transfer analysis

This is not to say that the measurement of emissivity is unimportant. For example, the spectral emissivity of materials is an important property for calculations of radiant heat transfer. Radiant heat transfer analysis is critical to designing the temperature-control systems of satellites and spacecraft, since convection and conduction are negligible in outer space. Radiant heat transfer analysis is also important... 

At the conditions reported in this paper where the total pressure is closer to 1000 psig and the feed gas to the FDP reactor is an approximately equimolar mixture of hydrogen and methane, the total carbon conversions are closer to the fraction of carbon that instantaneously reacts and kinetic interpretation is even more difficult. Therefore the kinetic analysis is not yet complete. However for the purposes of FDP reactor simulation, a mathematical model was used that assumed all the carbon reacts at a rate dictated by Equation 1 rather than assuming a portion of this carbon reacts instantaneously. This assumption is felt to be conservative because it does not allow for the fraction of carbon that may react at a considerably faster rate than the final amount of carbon conversion which was used to evaluate the rate constant k. The temperature dependency of k used for our initial reactor simulation studies (11) has been reported (I). While the more detailed kinetic analysis may result in a modified rate equation, the results of our simulation study (11) indicate that radiant heat transfer plays a dominant role in small FDP reactors such as the one used in this study. Because the effect of radiant heat transfer from the reactor walls diminishes as the diameter of the reactor increases, temperature profiles in commercial reactors will be considerably different from those existing in our present 3-inch id FDP reactor this indicates the necessity of using larger diameter pilot plants to obtain reliable scaleup data. 

Develop a heat-transfer analysis for radiant heating of a coextruded sheet of plastic material (example thickness of 0.5 cm of polymethyl methacrylate and 0.75 cm of acrylonitrile-butadiene-styrene, or ABS). Assume that the heating flux to each side is the same. 

The calculation of the radiation heat transfer between black surfaces is relatively easy because all the radiant energy which strikes a surface is absorbed. The main problem is one of determining the geometric shape factor, but once this is accomplished, the calculation of the heat exchange is very simple. When nonblackbodies are involved, the situation is much more complex, for all the energy striking a surface will not be absorbed part will be reflected back to another heat-transfer surface, and part may be reflected out of the system entirely. The problem can become complicated because the radiant energy can be reflected back and forth between the heat-transfer surfaces several times. The analysis of the problem must take into consideration these multiple reflections if correct conclusions are to be drawn. 

Unlike the radiant loss from an optically thin flame, conductive or convective losses never can be consistent exactly with the plane-flame assumption that has been employed in our development. Loss analyses must consider non-one-dimensional heat transfer and should also take flame shapes into account if high accuracy is to be achieved. This is difficult to accomplish by methods other than numerical integration of partial differential equations. Therefore, extinction formulas that in principle can be used with an accuracy as great as that of equation (21) for radiant loss are unavailable for convective or conductive loss. The most convenient approach in accounting for convective or conductive losses appears to be to employ equation (24) with L(7 ) estimated from an approximate analysis. The accuracy of the extinction prediction then depends mainly on the accuracy of the heat-loss estimate. Rough heat-loss estimates are readily obtained from overall balances. 

The thermal system model for radiant-tube continuous furnace involves integration of the mathematical models of the furnace enclosure, the radiant tube, and the load. The furnace enclosure model calculates the heat transfer in the furnace, the furnace gas, and the refractory walls. The radiosity-based zonal method of analysis [159] is used to predict radiation heat exchange in the furnace enclosure. The radiant-tube model simulates the turbulent transport processes, the combustion of fuel and air, and the convective and radiative heat transfer from the combustion products to the tube wall in order to calculate the local radiant-tube wall and gas temperatures [192], Integration of the furnace-enclosure model and the radiant-tube model is achieved using the radiosity method [159]. Only the load model is outlined here. 

One cautionary note should be kept in mind when using Eqs. (42)-(45) and (71) to calculate radiative heat transfer in FFB. The bed s absolute temperature 1), is normally assumed to be uniform across the bed and is used as the source or sink temperature in Eqs. (42) and (43). This assumption may be inappropriate in those cases in which a dense aimular region of particles shields the FFB wall from the bulk bed. In sueh situations, it is the average temperature of the particles in the annular layer that should be taken as the source/ sink temperature for ealeulation of radiant heat flux to/from the wall. This requires a mass and heat balance analysis for the material flowing in the annulus, and the reader is referred to Chapter 19 for necessary hydrodynamic models. 

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