Energy Balance Models

In this model, energy balances are set up for the reactor and the separator tube separately, and two equations are obtained. The gas holdup can then be obtained from combining these two equations. Details can be found in Zhang et al. [7]. The comparison between the measured and calculated cross-sectional mean gas holdups is shown in Fig. 5. It can be seen that there is a satisfactory agreement between the experimental and calculated gas holdup in the different operating conditions. Therefore, it is reasonable to conclude that the energy balance model used in this work can describe the circulation flow behavior in the novle internal-loop airlift reactor proposed in this work. 

North, G. R., J. G. Mengel, and D. A. Short. 1983. Simple energy balance model resolving the seasons and the continents Application to the astronomical theory of the ice ages. J. Geophys. Res. 88, 6576-86. 

Crowley (2000) estimated the contributions of various factors to climate formation (SAT changes) for the last 1,000 years using an energy-balance model of climate. According to the results obtained... 

Demyshev SG, Korotaev GK (1992) Numerical energy-balanced model of baroclinic currents in no-flat-bottom ocean on C-grid. In Numerical models and results of calibration calculation of the Atlantic Ocean currents. INM RAS, Moscow, p 163... 

More recent work has extended the modelling of reactive extrusion processes to full-scale process modelling by the combination of kinetic, chemorheological and flow/energy-balance modelling. This work is summarized in Table 6.2, highlighting the system used, the model description and the expected model outputs. Full references are provided for readers with further interest in these models. 

Chen et al. (2006) highlight a novel calorimetric method to examine cure during electron-beam processing of epoxy resins via an energy-balance model and use of a novel experimental calorimeter. 

Instead of the GCMs, it has been common to use Energy Balance Models (EBMs) to study changes in climate on orbital timescales. These types of models can be grouped into four categories (1) annual mean atmospheric models (2) seasonal atmospheric models with a mixed layer ocean (3) Northern Hemisphere ice sheet models and (4) coupled climate-ice sheet models, which in some cases include a representation of the deep ocean. 

The ratio of the radiation emitted by a surface to that emitted by a black body at the same temperature, energy balance models... 

Statistical-dynamical or energy-balance models in which only the latitudinally averaged quantities are determined and the effects of the longitudinally varying transports are determined parametrically. Abbreviated as ZAM. zooplankton... 

As pointed out by Pocius [60], the directional stability of cracks is significantly affected by the fracture toughness of adhesive bonds. An energy balance model used to analyze crack propagation predicted that directionally unstable cracks are more unlikely to occur as the fracture toughness of the adhesive bonds increase [32]. This energy balance model will be discussed in this chapter later. 

As seen, even relatively crude analytical energy balance models are helpful in understanding crack stability in adhesive layers. This energy-based perspective provides an intuitive understanding of the effect of in-plane stresses within an adhesive layer on crack path selection. Indeed, residual stresses have been shown to induce some very interesting failure modes in bonded joints, including spiral crack patterns [63]. 

From the preceding one can see the fairly elaborate considerations regarding the role of pressure in heat transfer, flooding, entrainment, and coltimn materid balance. The use of material- and energy-balance models, together with a pressure-relative volatility-separation model, may be required. 

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