Particle—fluid convection

It should be noted that a fluid bed has many particles. A hmited number of hot spheres cannot fuUy represent the averaged thermal behavior of all particles in a bed. Thus, Zhou et al. (2009) further examined the HTCs of all the particles and found that the features are similar to those observed for hot spheres (Fig. 17). The similarity illustrates that the hot sphere approach can, at least partially, represent the general features of particle thermal behavior in a particle—fluid bed. Overall, the particles in a uniformly fluidized bed behave similarly. But a particle may behave differently from another at a given time. The probabiHty density distributions of time-averaged HTCs due to particle—fluid convection and particle conduction are obtained, respectively (Fig. 18). The convective HTC in the packed bed varies in a small range due to the stable particle structure. Then, the distribution curve moves to the r ht as U increases, indicating the increase of convective HTC. The distribution curve also becomes wider. It is explained that, in a fluidized bed, clusters and bubbles can be formed, and the local flow... 

Notably, the approach has taken into account almost aU the known heat transfer mechanisms including particle-fluid convection, particle-particle conduction, and radiative heat transfer between solid particles and surrounding environment. It can be tested through various comparisons of the predicted and measured results. The approach has a good capability in describing heat transfer in packed and fluidized beds at a particle scale. 

Specific correlations of individual film coefficients necessarily are restricted in scope. Among the distinctions that are made are those of geometry, whether inside or outside of tubes for instance, or the shapes of the heat transfer surfaces free or forced convection laminar or turbulent flow liquids, gases, liquid metals, non-Newtonian fluids pure substances or mixtures completely or partially condensable air, water, refrigerants, or other specific substances fluidized or fixed particles combined convection and radiation and others. In spite of such qualifications, it should be... 

Uf Uf] f = Uf (8 Uf. However, in general, the fluid velocity seen by a particle may fluctuate due, for example, to the momentum coupling with the particle phase. As in Eq. (4.85), the terms Gp]p and S]p result from mass transfer between phases. Letting f2 again be the fluid mass seen by a particle, the convection term can be written as... 

Individual adsorbent particles within a packed bed are surrounded by a boundary layer, which is looked upon as a stagnant liquid film of the fiuid phase. The thickness of the film depends on the fluid distribution in the bulk phase of the packed bed. Molecular transport toward the boundary layer of the particle by convection or diffusion is the first step (1) of the separation process. 

When hydrocarbons are used as the stabilizing liquid in the plasma burner, even the coarser silica particles in the feed are reduced to SiO vapor, according to Kugler, Sins, and Silberger (453), who disclosed a burner design. A fluid convection electrode was described by Korman et al. (454). The so-called arc-silicas, which appear to be simply volatilized, are probably at least partly converted to SiO by the carbon vapor of the arc and then reoxidized. A series of products sold as Arc Silicas are described as 2-3 micron clusters of 15 nm particles (455). 

Figure 18 Probability density distributions of time-averaged heat transfer coefficients of particles at different gas superficial velocities (A) fluid convection and (B) particle conduction (Zhou et al., 2009).

The combined CFD-DEM approach, incorporated with heat transfer models of convection, conduction, and radiation, has been developed and can be used in the study of heat transfer in packed and fluidized beds. It has various advantages over the conventional experimental techniques and continuum simulation approaches. For example, the detailed conductive heat transfer between particles can be examined and the factors such as local particle-fluid structure and materials properties in determining heat transfer can be investigated. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

Convection occurs in a moving fluid, generally from the fluid to a solid surface or vice versa. Although heat transfer between single particles is by conduction, it is the energy transfer with the matter that governs the heat transfer. The basic laws of heat and mass transfer have to be considered in order to describe convection mathematically. 

Convective heat transmission occurs within a fluid, and between a fluid and a surface, by virtue of relative movement of the fluid particles (that is, by mass transfer). Heat exchange between fluid particles in mixing and between fluid particles and a surface is by conduction. The overall rate of heat transfer in convection is, however, also dependent on the capacity of the fluid for energy storage and on its resistance to flow in mixing. The fluid properties which characterize convective heat transfer are thus thermal conductivity, specific heat capacity and dynamic viscosity. 

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