Role of mass and heat transfer

Zhang et al. (1989) treated the interplay between diffusion and interface reaction during the initial and transient stages of crystal dissolution in a silicate melt. Using the interface reaction rate of diopside, they found that the period for 

the melt consumption rate u is distinguished from the crystal growth rate (they differ by the density ratio), and the concentration in terms of kg/m (denoted as C) is also distinguished from mass fraction (the same as weight percent, denoted as w). 

Crystal growth Consider the case for crystal growth along one direction (hence a one-dimensional problem). Define the initial interface to be at x = 0 and the crystal is on the side with negative x (left-hand side) and the melt is on the positive side (Section 3.4.6). Due to crystal growth, the interface advances to the positive side. Define the interface position at time t to be at x = Xq, where Xq 0 is a function of time. Let w be the mass fraction of the main equilibriumdetermining component then the diffusion equation in the melt is 

Mass balance at the boundary provides an equation relating crystal growth rate to other parameters  

The new reference frame is known as the interface-fixed reference frame, and the old reference frame is called the laboratory-fixed reference frame. The melt consumption rate u depends on whether the growth is controlled by interface reaction, or by diffusion, or by externally imposed conditions such as cooling. 

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Most of the actual reactions involve a three-phase process gas, liquid, and solid catalysts are present. Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well known since the days of Thiele [43] and Frank-Kamenetskii [44], but transport phenomena coupled to chemical reactions are not frequently used for complex organic systems, but simple - often too simple - tests based on the use of first-order Thiele modulus and Biot number are used. Instead, complete numerical simulations are preferable to reveal the role of mass and heat transfer at the phase boundaries and inside the porous catalyst particles. 

RELATIVE ROLES OF MASS AND HEAT TRANSFER IN INTERNAL AND EXTERNAL DIFFUSION... 

Chapter 7 Catalysis by Solids, 2 The Catalyst and Its Microenvironment, 171 Modeling of Solid Catalyzed Reactions, 171 Role of Diffusion in Pellets Catalyst Effectiveness, 183 Effect of External Mass and Heat Transfer, 201 Combined Effects of Internal and External Diffusion, 204 Relative Roles of Mass and Heat Transfer in Internal and External Diffusion, 205 Regimes of Control, 206... 

Relative roles of mass and heat transfer in internal and external diffusion... 

The last step to bring a hydrogen storing system to the consumer is probably the most important. Here, safety is the first concern but utilization conditions, cycle life, cost, and so on, have to be considered. A crucial step is the design of the tank itself where problems of mass and heat transfer will have to be resolved. We should not forget that all benefits from an optimum alloy and catalyst could be easily destroyed by a poorly designed reservoir. Here, computer simulation will play an important role in the development of a safe and optimal hydrogen tank. 

For many processes performed in supercritical fluids, the transport properties of the medium will play an important role. For polymerizations, this includes mass transfer for mixing reactants and to allow proper contact between monomer and catalyst. Polymerization reactions are usually highly exothermic, so that the heat of reaction needs to be absorbed and transported through the supercritical fluid. Virtually aU studies described in the literature have been performed on a relatively small scale, and scale-up aspects, for which mass and heat transfer are major issues, have generally been disregarded. This chapter will describe an experimental study of some aspects of mass and heat transfer in supercritical CO2 (SCCO2), and a comparison will be made with the behavior of standard liquid systems. 

On an individual particle level, particle size and density play a dominant role in dictating the heat and mass transfer rates and hydrodynamics. Usually, particle sizes are chosen so that resistance of mass and heat transfer between particles and surrounding flow is negligible. Mass transfer between the gas and a single sphere can be estimated by (Froessling, 1938) ... 

Processes in which solids play a rate-determining role have as their principal kinetic factors the existence of chemical potential gradients, and diffusive mass and heat transfer in materials with rigid structures. The atomic structures of the phases involved in any process and their thermodynamic stabilities have important effects on drese properties, since they result from tire distribution of electrons and ions during tire process. In metallic phases it is the diffusive and thermal capacities of the ion cores which are prevalent, the electrons determining the thermal conduction, whereas it is the ionic charge and the valencies of tire species involved in iron-metallic systems which are important in the diffusive and the electronic behaviour of these solids, especially in the case of variable valency ions, while the ions determine the rate of heat conduction. 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

MJ Pikal, ML Roy, S Shah. Mass and heat transfer in vial freeze-drying of pharmaceutical Role of the vial. J Pharm Sci 73 1224-1237, 1984. 

From our current knowledge, it is suggested that intrinsic kinetics typically plays a minor role in hydrate formation in real systems (turbulent pipeline flow), and instead mass and heat transfer may play a larger role in determining the rate of hydrate formation. 

Pikal, M.J., Roy, M.L., Shah, S. Mass and heat transfer in vial freeze-drying pharmaceuticals role of vial. J. Pharm. Sci. 73,1224-1237,1984... 

The first role of agitation is to keep the catalyst particles uniformly suspended in the reaction medium. When gas and liquid reactants are simultaneously used, agitation plays an essential role in facilitating the gas to liquid mass transfer.1201 Moreover, an efficient stirring is needed to avoid external (i.e. from the organic phase to the external surface of the catalyst particles) mass and heat transfer limitations.1113-151... 

Solvents are widely used in the chemical industry and play a variety of roles e.g. mass and heat transfer (Adams et al, 2004). They are conventionally volatile organic compounds (VOC) that lead to significant emissions to the atmosphere and possess substantial risks such as flammability and toxicity. Some of these solvents are already banned in the pharmaceutical industry (e.g. benzene) and others... 

Since industrial catalysts are employed as pellets, the mass- and heat-transfer effects can play an important role. The internal diffusion is often the critical step controlling the overall process rate. The use of an efficient catalyst is the decisive element in designing a competitive process. 

Voidage profiles represent one of the most important aspects of the flow structure of fast fluidization, which play an important role in gas and solids mixing, mass and heat transfer, and conversion in a chemical reactor. Considerable efforts have been given to studying the axial and radial variation of solids concentration axially, dilute at the top and dense at the bottom, and radially, dilute in the center and dense in the vicinity of the wall. As already mentioned in Section II, these variations depend mainly on gas velocity and solids circulation rate and are also influenced by the configuration of the apparatus. 

The preceding chapters in Parts I and 11 show that the value of micro-instrumentation is being demonstrated broadly and that recent research results continue to improve on the ability of these devices to play an increasingly important role in both research and manufacturing environments. As the value of micro-unit operations is realized, there will be an increased evaluation of these devices to replace macro-units or to be incorporated within macro-imit operations. The superior mass and heat transfer capability frequently leads to significant quality, energy and environmental benefits. 

Several elementary aspects of mass diffusion, heat transfer and fluid flow are considered in the context of the separation and control of mixtures of liquid metals and semiconductors by crystallization and float-zone refining. First, the effect of convection on mass transfer in several configurations is considered from the viewpoint of film theory. Then a nonlinear, simplified, model of a low Prandtl number floating zone in microgravity is discussed. It is shown that the nonlinear inertia terms of the momentum equations play an important role in determining surface deflection in thermocapillary flow, and that the deflection is small in the case considered, but it is intimately related to the pressure distribution which may exist in the zone. However, thermocapillary flows may be vigorous and can affect temperature and solute distributions profoundly in zone refining, and thus they affect the quality of the crystals produced. 

For a collection of droplets, the evaporation process of one particular drop can be influenced by the neighboring droplets depending on their distance and relative location. The study of Bellan and Harstad [6] concluded that in a dense droplet cluster, evaporation occurs primarily due to diffusion effects (that is when Sh 2), while convection plays a dominant role in the more dilute regions of a spray. A detailed discussion of the mass and heat transfer of a collection of drops, together with appropriate references, can be found in the text of Sirignano [25]. 

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