Radiant heat-transfer rate

Derive an expression for the radiant heat transfer rate per unit area between two large parallel planes of emissivities e and en and at absolute temperatures T and 73 respectively. 

The goal of the present study is to provide the information needed for design of a practical underwater propulsion system utilizing powdered aluminum burned with steam. Experiments are being conducted in atmospheric pressure dump combustors using argon/oxygen mixtures and steam as oxidizers. Spectrometer measurements have been made to estimate combustion temperatures and radiant heat transfer rates, and samples of combustion products have been collected to determine the composition and particle size distribution of the products. 

It will be assumed here that the convective heat transfer rates are high enough to allow the effects of radiation on the convective motion to be ignored, i.e., to assume that the convection and the radiation can be considered separately and that the total heat transfer rate will be the sum of the separately evaluated convective and radiant heat transfer rates. 

A body that emits the maximum amount of heat for its absolute temperature is called a blackbody. Radiant heat transfer rate from a blackbody to its surroundings can be expressed by the following equation ... 

Heat Recovery and Seed Recovery System. Although much technology developed for conventional steam plants is appHcable to heat recovery and seed recovery (HRSR) design, the HRSRhas several differences arising from MHD-specific requirements (135,136). First, the MHD diffuser, which has no counterpart ia a conventional steam plant, is iacluded as part of the steam generation system. The diffuser experiences high 30 50 W/cm heat transfer rates. Thus, it is necessary to allow for thermal expansion of the order of 10 cm (137) ia both the horizontal and vertical directions at the connection between the diffuser and the radiant furnace section of the HRSR. 

In essence, one properly located low-emissivity shield can reduce the radiant heat transfer to around one-half of the rate without the shield, two shields can reduce this to around one-fourth of the rate without the shield, and so on. 

A horizontally fired burner is located at one end of the heater. The flame extends along the central longitudinal axis of the heater. In this way the wickets are exposed to the open flame and can be subjected to a maximum rate of radiant heat transfer. The tubes should be sufficiently far away from the flame to prevent hot spots or flame pinching. 

In the radiant section of a boiler the fourth power of the wall temperature is typically less than 2 per cent of the fourth power of the mean flame and gas temperature. The effects of waterside conditions and wall thickness on the heat transfer rate are therefore negligible. 

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 ... 

The last point is worth considering in more detail. Most hydrocarbon diffusion flames are luminous, and this luminosity is due to carbon particulates that radiate strongly at the high combustion gas temperatures. As discussed in Chapter 6, most flames appear yellow when there is particulate formation. The solid-phase particulate cloud has a very high emissivity compared to a pure gaseous system thus, soot-laden flames appreciably increase the radiant heat transfer. In fact, some systems can approach black-body conditions. Thus, when the rate of heat transfer from the combustion gases to some surface, such as a melt, is important—as is the case in certain industrial furnaces—it is beneficial to operate the system in a particular diffusion flame mode to ensure formation of carbon particles. Such particles can later be burned off with additional air to meet emission standards. But some flames are not as luminous as others. Under certain conditions the very small particles that form are oxidized in the flame front and do not create a particulate cloud. 

Other factors being constant, the rate of vaporization from a large exposed liquid surface is proportional to the area of the surface. This may also be true for droplets 67, 96) if radiant heat transfer is predominant 17). Under normal circumstances, however, the rate of vaporization of a droplet at rest with respect to its environment is proportional to the droplet diameter 3). This comes about because the vaporization rate is controlled by the rate of conduction of heat or of mass through the gas film surrounding the droplet. The appropriate equation is ... 

Smoke (carbon) formation, which apparently is due to incomplete combustion of portions of the fuel-air mixture (i.e., rich combustion), also can pose a serious public relations problem at civilian airports and, by radiant-heat transfer from incandescent carbon particles, can shorten the endurance life of combustion-chamber liners and adjacent parts (0). Smoke would also constitute a serious problem in the case of automotive gas turbines, because accumulation of carbon and other nonvolatile fuel components on the intricate passages of the heat exchanger could reduce turbine and heat-exchanger efficiency by reducing heat-transfer rate and increasing the pressure drop across the... 

The radiation contribution for highly evacuated powders near room temperature is larger than the solid-conduction contribution to the total heat transfer rate. On the other hand, the radiant contribution is smaller than the solid-conduction contribution for temperatures between 77 and 20 or 4 K. Thus, evacuated powders can be superior to vacuum alone (for insulation thicknesses greater than 0.1 m) for heat transfer between ambient and liquid nitrogen temperatures. Conversely, since solid conduction becomes predominant at lower temperatures, it is usually more advantageous to use vacuum alone for reducing heat transfer between two cryogenic temperatures. 

In some cases it is not possible to consider the modes separately. For example, if a gas, such as water vapor or carbon dioxide, which absorbs and generates thermal radiation, flows over a surface at a higher temperature, heat is transferred from the surface to the gas by both convection and radiation. In this case, the radiant heat exchange influences the temperature distribution in the fluid. Therefore, because the convective heat transfer rate depends on this temperature distribution in the fluid, the radiant and convective modes interact with each other and cannot be considered separately. However, even in cases such as this, the calculation procedures developed for convection by itself form the basis of the calculation of the convective part of the overall heat transfer rate. 

It should be noted that when the enclosure contains a gas, the convective heat transfer rates can be low and radiant heat transfer can be significant. Some gases, such as carbon dioxide and water vapor, absorb and emit radiation and in such cases the energy equation has to be modified to account for this. However, even when the gas in the enclosure is transparent to radiation, there can be an interaction between the radiant and convective heat transfer. For example, for the case where the end walls can be assumed to be adiabatic, if grab and qKm are the rates at which radiant energy is being absorbed and emitted per unit wall area at any point on these end walls then the actual thermal boundary conditions on these walls are ... 

Another major area for further research in the use of OEC is the design of the combustion chambers. In nearly all cases, OEC has been adapted and retrofitted to existing furnace designs. In the future, the design of new furnaces that will use OEC should be investigated to optimize the increased radiant heat transfer, reduced convective heat transfer, and reduced gas volume flow rates. 

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