Packed beds radiation

Cheng GJ, Yu AB Particle scale evaluation of the effective thermal conductivity from the structure of a packed bed radiation heat transfer, Ind Eng Chem Res 52 12202—12211,... 

Hlavacek (1970) has shown that radiation between the solid catalyst and gas can significantly affect the temperature dynamics in packed bed systems operating in excess of 673 K. Since most packed bed systems usually operate well below these conditions, radiation terms are not explicitly included in the model. However, their effect can to some degree be accounted for in the overall heat transfer coefficients.4... 

Extensive experimental determinations of overall heat transfer coefficients over packed reactor tubes suitable for selective oxidation are presented. The scope of the experiments covers the effects of tube diameter, coolant temperature, air mass velocity, packing size, shape and thermal conductivity. Various predictive models of heat transfer in packed beds are tested with the data. The best results (to within 10%) are obtained from a recently developed two-phase continuum model, incorporating combined conduction, convection and radiation, the latter being found to be significant under commercial operating conditions. 

A two-flux radiation field model for an annular packed bed photocatalytic oxidation reactor was presented by Raupp et al. (1997). Similar to other annular flow reactors, the UV source was located at the center of the cylindrical reactor. Yet, the photocatalyst was not introduced in the form of a thin film but rather as spherules filling the annular space between the lamp and the housing. The principal assumptions made in this model included a steady state, isothermal operation, cylindrical symmetry. 

Due to the Langrangian formulation applied to the solid phase, the use of an effective thermal conductivity as usually applied to porous media is not necessary. In a packed bed heat is transported between solid particles by radiation and conduction. For materials with low thermal conductivity, such as wood, conduction contributes only to a minor extent to the overall heat transport. Furthermore, heat transfer due to convection between the primary air flow through the porous bed and the solid has to be taken into account. Heal transfer due to radiation and conduction between the particles is modelled by the exchange of heat between a particle and its neighbours. The definition of the neighbours depends on the assembly of the particles on the flow field mesh. 

A numerical model is presented to describe the thermal conversion of solid fuels in a packed bed. For wood particles it can be shown, that a discretization of the particle dimensions is necessary to resolve the influence of heat and mass transfer on the conversion of the solid. Therefore, the packed bed is described as a finite number of particles interacting with the surrounding gas phase by heat and mass transfer. Thus, the entire process of a packed bed is view as the sum of single particle processes in conjunction with the interaction of the gas flow in the void space of a packed bed. Within the present model, neighbour particles exchange heat due to conduction and radiation with each other. 

In order to avoid geometrical difficulties an ideal model of the packed bed will be employed to evaluate the heat transfer through the particle. The methods by which heat can enter a particle from its inner side are radiation, convection from the gas stream, and conduction through point contacts and stagnant fillets, as indicated in Fig. 13-8. Heat is transferred Through the particle and leaves the other side by the same three mechanisms. The three processes are in series, and the whole will be designated as the series mechanism. Hence... 

The convection coefficient can be predicted from the data on heat transfer between solids and fluids flowing in packed beds. Such data were given in Fig. 10-2. The radiation and conduction coefficients, and hp, depend on the value of (AT) defined by Eq. (13-34). A derivation based on the same assumptions employed in obtaining Eq. (13-33) leads to the results... 

Models have been constructed describing each of these heat transfer mechanisms. Yagi and Kunii [10] developed generalized resistance models for packed beds which others adapted for application to metal hydride beds [9,11-13]. For lower and moderate temperature applications of these models, radiation heat transfer can be neglected [9, 11, 12, 14, 15]. In general, the resistance model of effective thermal conductivity of a packed metal hydride bed can be described as ... 

Figure 9.14 shows a map of independent/dependent scattering for packed beds and suspensions of spherical particles [59]. The map is developed based on available experimental results. The experiments are from several investigators, and some of the experiments are reviewed later. The results show that for relatively high temperatures in most packed beds, the scattering of thermal radiation can be considered independent. 

Knowledge of the heat transfer characteristics and spatial temperature distributions in packed beds is of paramount importance to the design and analysis of the packed-bed catalytic or non-catalytic reactors. Hence, an attempt is made in this section to quantify the heat transfer coefficients in terms of correlations based on a wide variety of experimental data and their associated heat transfer models. The principal modes of heat transfer in packed beds consist of conduction, convection, and radiation. The contribution of each of these modes to the overall heat transfer may not be linearly additive, and mutual interaction effects need to be taken into account [23,24]. Here we limit our discussion to noninteractive modes of heat transfer. 

Investigator Type of correlation Phases involved Mohamad et al. [36] Packed-bed effective thermal conductivity due to radiation Fluid-solid... 

Heat transfer from gases to solids and vice versa occurs efficiently in packed beds, mainly by conduction and radiation. In some kilns, notably the rotary, heat transfer is less efficient and relies to a greater extent on radiation. This places considerable emphasis on burner design and on the shape and emissivity of the flame [16.1]. 

Heat transfer in the bed of a rotary kiln is similar to heat transfer in packed beds except that in addition to the heat flow in the particle assemblage of the static structure (Figure 8.3), there is an additional contribution of energy transfer as a result of advection of the bed material itself. The effective thermal conductivity of packed beds can be modeled in terms of thermal resistances or conductance within the particle ensemble. As shown in Figure 8.3 almost all the modes of heat transfer occurs within the ensemble, that is, particle-to-particle conduction and radiation heat transfer as well as convection through the interstitial gas depending upon the size distribution of the material and process temperature. Several models are available in the literature for estimating the effective thermal conductivity of packed beds. 

N. Wakao. "Effect of radiating gas on effective thermal conductivity of packed beds," Chem. Eng. Sci., 28, 1117-1118, 1973. 

Heat conduction, convection, boiling heat transfer, radiation, transient heat transfer, forced flow in pipes and packed beds, mass transfer by diffusion, and diffusion in porous solids. 

In contrast, the wall structure of a circulating fluidised bed consists of clusters or streamers whose properties are poorly understood. There is a distribution of voidages and thermal properties, and it would be incorrect to arbitrarily ascribe loose packed bed properties to these structures since they are expanded and likely contain many fewer particle-particle and particle-wall contact points than a loose packed b. The clusters are also convectively mixed by gas and wall shear, and have complex cloud-like radiation transfer properties. In combination, these lead to a pronounced thermal boundary layer of substantial thickness and complexity (Chen et al, 1988). This has been measured by Leckner (1991) and is illustrated in Figure 20. 

There are three mechanisms of heat bransfer heat conduction, heat radiation and h t convection. Usually they take place together but for better understanding they are considered separately. Because the heat radiation is of importance at temperatures much higher than duise in the packed bed column, this phenomenon is not considered in this book. 

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