Mickley-Fairbanks model

This packet renewal model has been widely accepted and in the years since 1955 many researchers have proposed various modifications in attempts to improve the Mickley-Fairbanks representation. Several of these modifications dealt with the details of the thermal transport process between the heat transfer surface and the particle packet. The original Mickley-Fairbanks model treated the packet as a pseudo-homogeneous medium with a constant effective thermal conductivity, suggesting that... 

The Mickley-Fairbanks model was found to overpredict heat transfer coefficients, and Baskakov (1964) suggested that this was due to an additional resistance, 1 /h(, caused by the presence of a thin gas layer between the packet and the wall. 

The first type of model considers the heat transfer surface to be contacted alternately by gas bubbles and packets of closely packed particles. This leads to a surface renewal process whereby heat transfer occurs primarily by transient conduction between the heat transfer surface and the particle packets during their time of residence at the surface. Mickley and Fairbanks (1955) provided the first analysis of this renewal mechanism. Treating the particle packet as a pseudo-homogeneous medium with solid volume fraction, e, and thermal conductivity (kpa), they solved the transient conduction equation to obtain the following expression for the average heat transfer coefficient due to particle packets,... 

In the emulsion phase/packet model, it is perceived that the resistance to heat transfer lies in a relatively thick emulsion layer adjacent to the heating surface. This approach employs an analogy between a fluidized bed and a liquid medium, which considers the emulsion phase/packets to be the continuous phase. Differences in the various emulsion phase models primarily depend on the way the packet is defined. The presence of the maxima in the h-U curve is attributed to the simultaneous effect of an increase in the frequency of packet replacement and an increase in the fraction of time for which the heat transfer surface is covered by bubbles/voids. This unsteady-state model reaches its limit when the particle thermal time constant is smaller than the particle contact time determined by the replacement rate for small particles. In this case, the heat transfer process can be approximated by a steady-state process. Mickley and Fairbanks (1955) treated the packet as a continuum phase and first recognized the significant role of particle heat transfer since the volumetric heat capacity of the particle is 1,000-fold that of the gas at atmospheric conditions. The transient heat conduction equations are solved for a packet of emulsion swept up to the wall by bubble-induced circulation. The model of Mickley and Fairbanks (1955) is introduced in the following discussion. 

Figure 12.6. Conceptual representation of the emulsion-contact model of Mickley and Fairbanks (1955).

An important variation of the model of Mickley and Fairbanks is the film penetration model developed by Yoshida et al. [48] by treating packets as a continuum with a finite thickness (8em). The film penetration theory includes two extremes of emulsion behavior. On one extreme, the packet contacts the heating surface for a short time so that all the heat entering the packet is used to heat up the packet (penetration theory) while none passes through it. On the other extreme, the packet stays at the surface long enough to achieve steady state and simply provides a resistance for heat conduction. 

With an exothermic reaction in the bed, clusters or packets of hot solid come in contact with the cooler surface of the wall or the tubes, and they give up some of their heat in the short time before they are swept away. A model based on the penetration theory of unsteady-state heat transfer and some supporting data were presented by Mickley and Fairbanks [26]. The average coefficient is predicted to vary with the square root of the thermal conductivity, density, and heat capacity of the clusters and inversely with the square root of the average contact time. The fraction of the surface in contact with clusters is taken to be (1 — a), where a is the volume fraction bubbles in the bed. Heat transfer to the bare surface... 

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... 

---