Radiative heat load

One operating concern for a rich combustor is the occurrence of high combustor wall temperatures. In a fuel-rich combustor, air cannot be used to film-cool the walls and other techniques (e.g., fin cooling) must be employed. The temperature rise of the primary combustor coolant was measured and normalized to form a heat flux coefficient which included both convective and radiative heat loads. Figure 7 displays the dependence of this heat flux coefficient on primary combustor equivalence ratio. These data were acquired in tests in which the combustor airflow was kept constant. If convective heat transfer were the dominant mechanism a constant heat flux coefficient of approximately 25 Btu/ft -hr-deg F would be expected. The higher values of heat flux and its convex character indicate that radiative heat transfer was an important mechanism. 

Radiation can be reduced by reducing the emissivity of the cold and warm surfaces that face each other, and by introducing an intermediate temperature surface between the coldest and warmest surfaces. The radiative heat load to a spherical or cylindrical container of area A temperature Ty, and emissivity from a surrounding container of temperature T2 and emissivity 3 is given by Scott (1959) ... 

Items 1-4 determine the degree to which the radiation source and material load are thermally coupled and can be addressed with the heat transfer analysis methods outlined in Chap. 7 of this handbook. Items 5 and 6 may be quantified with an analysis, which takes into account the multimode heat transfer effects discussed elsewhere in this handbook. Because of the nonlinear nature of radiative heat transfer, few correlations exist that can be applied to relevant materials processing situations. 

Semitransparent Material. When the load is not opaque, radiative heat transfer occurs within the material in conjunction with conduction and/or advective transfer (if the load is moved with respect to a coordinate system). The thermal response of the load is, therefore, determined in part by volumetric radiation heat transfer, necessitating prediction or measurement of the relevant radiative properties. 

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. 

Direct Fired Furnaces. For direct fired furnaces, radiative heat transfer from the flame and combustion products as well as from the walls to the load is usually the dominant heat transfer mode. Convection from the combustion gases makes a much smaller contribution. The radiative transfer within the furnace is complicated by the nongray behavior of the combus-... 

Radiative heat transfer from the flame to the load Heat delivery to the load Physical modeling Sensors and controls... 

Conceptual models for the DST were evaluated by comparing simulated temperatures with temperatures measured at three boreholes. The models with the best agreement between calculated and measured temperatures included dual continua (matrix and fracture) and active fracture, to reflect actual heat loads. The canister heat load was decreased by 20 percent to account for radiative and conductive heat loss through the thermal bulkhead. 

Total incident heat flux (kW/m ) 180 250 300 350 Increased heat loadings up to 400kW/m (280kW/m radiative, 120kW/m convective), e=0.75, h = 0.09kW/m K... 

Relatively few studies have been carried out at temperatures high enough (>— 600°C) that radiation plays a significant role. Basu and Konuche (1988) and Wu et al. (1989) found that the radiative heat transfer coefficient increased with increasing temperature, while the contribution of radiation to the total heat transfer increased with decreasing suspension density. In different studies, the radiative component has been found to contribute more than 50% of the total heat transfer at low particle loadings (e.g., Basu and Konuche, 1988), whereas the contribution is 15 to 40% for higher suspension densities (e.g., Han and Cho, 1999 Luan et al., 1999). 

The thermal properties of a glass melt are very difficult to simulate or measure experimeutaUy. This is because the overall heat transfer behavior is a combination of all three possible mechanisms conduction, convection, and radiation (and in a glass melt, all can be significant). Conduction and convection are fairly straightforward to model at all scales however, the radiative heat transfer mechanism is very much harder to describe. This is exacerbated (or perhaps simplified—see later discussiou) in the case of waste loaded melts, as the transparency of the glass melt reduces and the absorption characteristics change. 

The actual flame temperature is lower than the adiabatic equilibrium flame temperature because of heat loss from the flame. The actual flame temperature is determined by how well the flame radiates its heat and how well the combustion system, including the load and the refractory walls, absorbs that radiation. A highly luminous flame generally has a lower flame temperature than a highly nonluminous flame. The actual flame temperature will also be lower when the load and the walls are more radiatively absorptive. This occurs when the load and walls are at lower temperatures and have high radiant absorptivities. These effects are discussed in more detail in Chapter 4. As the gaseous combustion products exit the flame, they... 

Skocypec and Buckius [180,181] presented an analytical formulation to obtain the radiation heat transfer from a mixture of combustion gases and scattering particles. They considered band models for the gases and accounted for the absorption and scattering by particles. They developed charts similar to Hottel charts for combustion gases. The results presented can be used to obtain the average radiative properties if the particle loading information is not known accurately. (See also Refs. 182-184 for a discussion on the limits of this formulation.)... 

The boundary condition at the inner (top) surface of the load is exposed to the radiative and convective heat q"ot such that... 

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