Heat transfer in packed beds

For heat and mass transfer through a stationary or streamline fluid to a single spherical particle, it has been shown in Volume 1, Chapter 9, that the heat and mass transfer coefficients reach limiting low values given by  

Kramers 41) has shown that, for conditions of forced convection, the heat transfer coefficient can be represented by  

This expression has been obtained on the basis of experimental results obtained with fluids of Prandtl numbers ranging from 0.7 to 380. 

For natural convection, Ranz and Marshall142 have given  

Results for packed beds are much more difficult to obtain because the driving force cannot be measured very readily, Gupta and Thodos(43) suggest that the. /-factor for heat transfer, ju (Volume 1, Chapter 9), forms the most satisfactory basis of correlation for experimental results and have proposed that  

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Correlations for heat transfer in packed-beds are still being developed. The current state of the art is represented by... 

Heat transfer in packed beds. Effective thermal conductivity as a function of Reynolds number. Curve 1 Coberly and Marshall. Curve 2 Campbell and Huntington. Curve 3 Calderbank and Pogorski. Curve 4 Kwong and Smith. Curve 5 Kunii and Smith. (From G. F. Froment, Chemical Reaction Engineering, Adv. Chem. Ser., 109, 1970.)... 

Argo and Smith (106, 107) have presented a detailed discussion of heat transfer in packed beds and have proposed the following relation for the effective thermal conductivity in packed beds ... 

Hunt, M. L. (1989). Comparison of Convective Heat Transfer in Packed Beds and Granular Flows. In Annual Review of Heat Transfer. Ed. C. L. Tien. Washington, D.C. Hemisphere. 

Hunt, M. L, (1989). Comparison of Convective Heat Transfer in Packed Beds and Granular Flows. 

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. 

The choice of a model to describe heat transfer in packed beds is one which has often been dictated by the requirement that the resulting model equations should be relatively easy to solve for the bed temperature profile. This consideration has led to the widespread use of the pseudo-homogeneous two-dimensional model, in which the tubular bed is modelled as though it consisted of one phase only. This phase is assumed to move in plug-flow, with superimposed axial and radial effective thermal conductivities, which are usually taken to be independent of the axial and radial spatial coordinates. In non-adiabatic beds, heat transfer from the wall is governed by an apparent wall heat transfer coefficient. ... 

The orthogonal collocation method using piecewise cubic Her-mite polynomials has been shown to give reasonably accurate solutions at low computing cost to the elliptic partial differential equations resulting from the inclusion of axial conduction in models of heat transfer in packed beds. The method promises to be effective in solving the nonlinear equations arising when chemical reactions are considered, because it allows collocation points to be concentrated where they are most effective. 

Correlations for heat transfer in packed beds are still being developed. Enthusiasts of CFD anticipate using it to model nonisothermal packed beds, but the predictions still need to be tweaked. The more classic and time-tested work is ... 

HEAT TRANSFER IN PACKED BEDS. Data for heat transfer between fluids and beds of various kinds of particles can be obtained from Fig. 21.5 or from Eq. 

B. P. Singh, and M. Kaviany, Independent Theory Versus Direct Simulation of Radiative Heat Transfer in Packed Beds, Int. J. Heat Mass Transfer, (34) 2869-2881,1991. 

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. 

TABLE 13.2 Heat Transfer in Packed Beds (Continued)... 

Advances in fundamental data. Intensive research has led to more extensive and more reliable physicochemical data heat transfer in packed beds has been studied more carefully. Large companies are now well aware of the importance of reliable kinetic data as a basis for design and kinetic studies have benefited... 

Figure II.7m-4 Model for heat transfer in packed bed according to Yagi and Kunii [70].

Lindauer, G.C., Heat transfer in packed beds by the method of cyclic temperature variations, AIChE J., 13(6) 1181-1187, 1967. 

Kwong, S.S. and Smith, J.M., 1957. Radial Heat Transfer in Packed Beds. Industrial and Engineering Chemistry, 49(5) 894-903. 

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