Heterogeneities temperature fields

The aforementioned heterogeneous temperature field in the autoclave and its temporal evolution may significantly affect the inactivation process of enzymes. For enzymes diluted in pressure-transmitting media, Rauh et al. have numerically studied inactivation and its heterogeneity in the presence of the spatiotemporal... 

The temperature distribution in the capillary slot is presented in Fig. 10.18. These data show the wall superheat influence on temperature fields in liquid and vapor domains. In these cases, significant heterogeneity of temperature fields is observed. 

This study was carried out to simulate the 3D temperature field in and around the large steam reforming catalyst particles at the wall of a reformer tube, under various conditions (Dixon et al., 2003). We wanted to use this study with spherical catalyst particles to find an approach to incorporate thermal effects into the pellets, within reasonable constraints of computational effort and realism. This was our first look at the problem of bringing together CFD and heterogeneously catalyzed reactions. To have included species transport in the particles would have required a 3D diffusion-reaction model for each particle to be included in the flow simulation. The computational burden of this approach would have been very large. For the purposes of this first study, therefore, species transport was not incorporated in the model, and diffusion and mass transfer limitations were not directly represented. 

The simulation of reacting flows in packed tubes by CFD is still in its earliest stages. So far, only isothermal surface reactions for simplified geometries and elementary reactions have been attempted. Heterogeneous catalysis with diffusion, reaction, and heat transfer in solid particles coupled to the flow, species, and temperature fields external to the particles remains a challenge for the future. 

The mathematical model comprises a set of partial differential equations of convective diffusion and heat conduction as well as the Navier-Stokes equations written for each phase separately. For the description of reactive separation processes (e.g. reactive absorption, reactive distillation), the reaction terms are introduced either as source terms in the convective diffusion and heat conduction equations or in the boundary condition at the channel wall, depending on whether the reaction is homogeneous or heterogeneous. The solution yields local concentration and temperature fields, which are used for calculation of the concentration and temperature profiles along the column. 

The component of error, stipulated by the thermoelectric effect, appears at the heterogeneity of the temperature field of the SEC ... 

A punch-die-two step system has been developed to further increase the homogeneity of the sintered product with complex shapes [33]. The strategy proposed is the reduction in heterogeneity of temperature field distribution inside the samples, as shown in Fig. 6.11. The material is pure Ti powder with average particle of 35 pm. The compact has a length of 10 cm, with two steps of 15 and 30 mm in diameter, at a relative density of 100 %. Ti powder is filled into the... 

Of course also the differential balances represent a simplification, based on the idea of a material continuum. TTie continuum is characterized by certain fields of scalar quantities (temperature, concentrations, ) and vector quantities (local velocity of mass flow, diffusion fluxes, — ). Generally, the continuum is heterogeneous the fields are continuous in any of the phases, possibly discontinuous at interfaces. Imagine a distillation or absorption column, or a heterogeneous reactor. 

FIG. 9 Changes of the monolayer film critical temperature with the concentration of impurities obtained from the Monte Carlo simulations (open circles) and resulting from the mean field theory (solid line). (Reprinted from A. Patrykiejew. Monte Carlo studies of adsorption. II Localized monolayers on randomly heterogeneous surfaces. Thin Solid Films, 205 189-196, with permision from Elsevier Science.)... 

In this chapter, we Hmit ourselves to the topic of zeolite membranes in catalysis. Many types of membranes exist and each membrane has its specific field where it can be appHed best. Comparing polymeric and inorganic membranes reveals that for harsher conditions and high-temperature applications, inorganic membranes outperform polymeric membranes. In the field of heterogeneous catalYsis, elevated temperatures are quite common and therefore this is a field in which inorganic membranes could find excellent applications. 

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