Heat transfer mesoscale model

The mathematical modeling of polymerization reactions can be classified into three levels microscale, mesoscale, and macroscale. In microscale modeling, polymerization kinetics and mechanisms are modeled on a molecular scale. The microscale model is represented by component population balances or rate equations and molecular weight moment equations. In mesoscale modeling, interfacial mass and heat transfer... 

The process of formulating mesoscale models from the microscale equations is widely used in transport phenomena (Ferziger Kaper, 1972). For example, heat transfer between the disperse phase and the fluid depends on the Nusselt number, and mass transfer depends on the Sherwood number. Correlations for how the Nusselt and Sherwood numbers depend on the mesoscale variables and the moments of the NDF (e.g. mean particle temperature and mean particle concentration) are available in the literature. As microscale simulations become more and more sophisticated, modified correlations that are based on the microscale results will become more and more common (Beetstra et al, 2007 Holloway et al, 2010 Tenneti et al, 2010). Note that, because the kinetic equation requires mesoscale models that are valid locally in phase space (i.e. for a particular set of mesoscale variables) as opposed to averaged correlations found from macroscale variables, direct numerical simulation of the microscale model is perhaps the only way to obtain the data necessary in order for such models to be thoroughly validated. For example, a macroscale model will depend on the average drag, which is denoted by... 

This polymerization process can be separated into three different levels as proposed by Ray [22]. First this is the microscale level, modeling all processes at the surface and inside the growing polymer particle. The next level is the mesoscale level, describing all mass and heat transfer processes inside the three-phase slurry containing gas bubbles, hydrocarbon diluent with the dissolved aluminumalkyl compound, and the solid growing polymer particles loaded with the active sites. Finally, there is the macroscale level comprising the polymerization vessel as a whole, with sensors to control this slurry polymerization process. These three levels are shown in Fig. 4. 

Cluster/mesoscale To develop a general theory to link the discrete and continuum approaches, so that particle scale heat transfer information, generated from DEM-based simulation, can be quantified in terms of (macroscopic) energy conservation equations, constitutive relations, and boundary conditions that can be implemented in continuum-based process modeling of thermochemical behaviors. 

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