Heat transfer mechanistic model

Celata, G. P, M. Cumo, A. Mariani, M. Simoncini, andG. Zummo, 1994a, Rationalization of Existing Mechanistic Models for the Prediction of Water Subcooled Flow Boiling CHF, Int. J. Heat Mass Transfer 57(Suppl.) 347-360. (5)... 

A mechanistic account of suspension-to-surface heat transfer is necessary to quantify the heat transfer behavior accurately and to assess the form of dependency of dimensionless groups in the correlations. In the following, the modes and regimes of suspension-to-surface heat transfer along with the three mechanistic models accounting for this heat transfer behavior are described. 

Development of a mechanistic model is essential to quantification of the heat transfer phenomena in a fluidized system. Most models that are originally developed for dense-phase fluidized systems are also applicable to other fluidization systems. Figure 12.2 provides basic heat transfer characteristics in dense-phase fluidization systems that must be taken into account by a mechanistic model. The figure shows the variation of heat transfer coefficient with the gas velocity. It is seen that at a low gas velocity where the bed is in a fixed bed state, the heat transfer coefficient is low with increasing gas velocity, it increases sharply to a maximum value and then decreases. This increasing and decreasing behavior is a result of interplay between the particle convective and gas convective heat transfer which can be explained by mechanistic models given in 12.2.2, 12.2.3, and 12.2.4. 

Mechanistic equations describing the apparent radial thermal conductivity (kr>eff) and the wall heat transfer coefficient (hw.eff) of packed beds under non-reactive conditions are presented in Table IV. Given the two separate radial heat transfer resistances -that of the "central core" and of the "wall-region"- the overall radial resistance can be obtained for use in one-dimensional continuum reactor models. The equations are based on the two-phase continuum model of heat transfer (3). 

In this chapter, emphasis will be given to heat transfer in fast fluidized beds between suspension and immersed surfaces to demonstrate how heat transfer depends on gas velocity, solids circulation rate, gas/solid properties, and temperature, as well as on the geometry and size of the heat transfer surfaces. Both radial and axial profiles of heat transfer coefficients are presented to reveal the relations between hydrodynamic features and heat transfer behavior. For the design of commercial equipment, the influence of the length of heat transfer surface and the variation of heat transfer coefficient along the surface will be discussed. These will be followed by a description of current mechanistic models and methods for enhancing heat transfer on large heat transfer surfaces in fast fluidized beds. Heat and mass transfer between gas and solids in fast fluidized beds will then be briefly discussed. 

A model for predicting the efficiency of dualflow-type trays has been reported and is mechanistic in character. A large efficiency database, provided by Fractionation Research, Inc. (FRl), was used in constracting the model. Efficiency data for counterflow baffle tray columns are sparse, and the only model available is based largely on a heat transfer database, using the appropriate analogies. 

Cluster Renewal Models Most mechanistic models for heat transfer in CFBs are extensions of the model of Mickley and Fairbanks (1955). Descending clusters and strands in the vicinity of the wall surface are modeled as homogeneous semi-infinite... 

This review, therefore, will not attempt to cover the gamut of heat transfer models proposed in the literature and reviewed elsewhere [l]. Rather it will concentrate on those few models most widely used in industrial applications and attempt to lay emphasis on their reliability, on parameter values to employ and mechanistic, rather than empirical, methods of prediction, wherever possible. Some closing remarks on future trends in heat transfer research straight out of the crystal ball will be tentatively suggested. 

Fig. 2 The dependence of the overall heat transfer coefficient on particle diameter [4]. Reprinted with permission ACS Symp. Series 196, 527. Copyright (1982) ACS. irrespective of d or G, and our own data bears this out reasonably well. However, no explanation was offered. The mechanistic model presented in Section 4 predicts the continuous curves, which follow the data fairly well. It would suggest that the major thermal resistance shifts from effective conduction through the bed to, ultimately, heat transfer at the wall as the particle size is increased. The radial effective conductivity increases with particle diameter, whereas the wall heat transfer coefficient decreases, hence the existence of an optimum in the overall coefficient, U.

We now turn to the central question concerning the evaluation of mechanistic heat transfer models. It will be prudent to begin with the small tube-to-particle diameter case because of the central role it plays in practice. Here, we shall be concerned primarily with testing the two-phase model predictions given by Eqns (28) and (29). Finally, we shall examine the adequacy of the model for predicting overall U values for narrow diameter tubes and compare it with alternatives claimed to be wide-ranging. 

X-12] KATAOKA, I., et al., Mechanistic modelling of pool entrainment phenomenon, Int. J. Heat Mass Transfer, Vol.27, Noll (1988) pp. 1999-2014. 

In summary, mechanistic modelling of fluid mechanics and heat transfer is still in its infancy. However, gradual progress is being made toward practical design models. 

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