Packet model

Lee S-Y 1995 Wave-packet model of dynamic dispersed and integrated pump-probe signals in femtosecond transition state spectroscopy Femtosecond Chemistry ed J Manz and L Wdste (Heidelberg VCH)... 

A (>0) is the electronic factor. 1-P is the probability for continuing on the lower PES, which corresponds to ET. If the barrier disappears, the Landau-Zener model should not be used and it may be necessary to include the nuclear coordinates in a wave packet model. 

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. 

As a result of the time-dependent voidage variations near the heating surface, the thermophysical properties of the packet differ from those in the bed, and this difference has not been included in the packet model. The limitation of this model lies in not taking into account the nonuniformity of the solids concentration near the heating surface. Thus, the packet model under this condition is accurate only for large values of Fourier number, in general agreement with the discussion in 4.3.3. 

It should be noted that the preceding treatment of the emulsion phase/packet model is suitable for a system with homogeneous emulsion phase (i.e., particulate fluidization). The model needs to be modified when applied to the fluidized bed with a discrete bubble phase. 

The model based on the concept of pure limiting film resistance involves the steady-state concept of the heat transfer process and omits the essential unsteady nature of the heat transfer phenomena observed in many gas-solid suspension systems. The film model discounts the effects of thermophysical properties such as the specific heat of solids and hence would not be able to predict the particle convective component of heat transfer. For estimating the contribution of the particle convective component of heat transfer, the emulsion phase/packet model given in a subsequent section should be used to describe the temperature gradient from the heating surface to the bed. 

Ozkaynak and Chen (1980) showed that this modified packet model could predict the measured convective heat transfer coefficient with good success, when packet residence time Xpa is known. When Xpa is not known a priori, Kunii and Levespiel (1991) suggest that it can be estimated from bubble frequency (/J,) and the volume fraction of bubbles at the surface (8 ),... 

Heat Transfer Coefficient from Packet Model... 

Use the packet model to estimate the convective heat transfer coefficient for the above case of a horizontal tube in a bubbling bed. Additionally, the bed has a porous plate distributor, and the center line of the heat transfer tube is located of Lt = 0-19m above the distributor. 

To apply the packet model, we first need to ealeulate some bubble charaeteristics, utilizing hydrodynamie theory. The neeessary equations ean be obtained from Chapter 3, or from the book of Kunii and Levenspiel (1991). First, to estimate the bubble diameter ([Pg.282]

For this large Fourier number, Eq. (33) shows C = 1.0. The packet model, Eq. (32), then gives a value for the convective heat transfer coefScient ... 

Packet Models Models featuring packets constitute the most common type of model. These usually assume that the radiative component is the sum of radiation from clusters and from the dispersed phase. The radiative heat transfer between clusters and the... 

Ando K (2012) Electron wave packet modeling of chemical bonding Floating and breathing minimal packets with perfect-pairing valence-bond spin coupling. Chem Phys Lett 523 134— 138... 

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