Packed beds radiation heat transfer

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,... 

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 ... 

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. 

The combined conduction and radiation heat transfer through a packed bed of spheres is more often studied because of its practical importance. The quasi-homogeneous theories predict that ETC (fee) is the sum of the effective conductivity feg,c without radiation contributions and the radiative conductivity fer without conduction contributions (Vortmeyer, 1978). That is... 

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. 

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... 

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. 

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 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 packed bed systems at moderate temperatures convection is the predominant mode of heat transfer however, thermal radiation may become significant at elevated temperatures, in particular when the gas flow rate through the system is small. Following the work of Baddour and Yoon [24], Downing [25] proposed the following expression for the effective thermal conductivity of a packed bed at high temperatures in the absence of fluid motion ... 

Figure 1 Heat transfer mechanisms in a packed bed Conduction (1 heat transfer through soiid 2 heat transfer through the contact surface of soiid 5 heat transfer through the fiuid fiim near the contact surface and 6 heat transfer through soiid-fiuid-soiid between noncontacting soiid), convection (7 heat transfer by iaterai mixing of fiuid), and radiation (3 radiant heat transfer between surfaces of soiid and 4 radiant heat transfer between adjacent voids). Reprinted from Yogi andKunii (1957) with permission from John Wiley and Sons.

The heat transfer in fluidized beds of monodisperse particle has been extensively investigated in the past. Heat transfer in a packed/fluidized bed with an interstitial fluid may involve many mechanisms as shown in Fig. 1 (Yagi and Kunii, 1957). These mechanisms can be classified into three heat transfer modes in fluidized beds fluid—particle or fluid—wall convection particle-particle or particle—wall conduction and radiation. Different heat transfer models are developed for these mechanisms, as described in the following. 

The combined CFD-DEM approach, incorporated with heat transfer models of convection, conduction, and radiation, has been developed and can be used in the study of heat transfer in packed and fluidized beds. It has various advantages over the conventional experimental techniques and continuum simulation approaches. For example, the detailed conductive heat transfer between particles can be examined and the factors such as local particle-fluid structure and materials properties in determining heat transfer can be investigated. 

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