Mass convection external flow

Ary given catalytic material can be abstracted based on the same underlying similar architecture — for ease of comparison, we describe the catalytic material as a porous network with the active centers responsible for the conversion of educts to products distributed on the internal surface of the pores and the external surface area. Generally, the conversion of any given educt by the aid of the catalytic material is divided into a number of consecutive steps. Figure 11.13 illustrates these different steps. The governing transport phenomenon outside the catalyst responsible for mass transport is the convective fluid flow. This changes dramatically close to the catalyst surface from a certain boundary onwards, named the hydrodynamic boundary layer, mass transport toward and from the catalyst surface only takes place... 

Mass-Transfer Coefficient Denoted by kc, kx, Kx, 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 theory, the surface renewal theory and the penetration theory, all of which pertain to idealized cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flow through 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. 

Consider the flow of air over the free surface of a water body such as a lake under isothermal conditions. If the air is not saturated, the concentration of water vapor will vtsry from a maximum at the water surface where the air is always saturated to the free steam value far from the surface. In heat convection, we defined the region in which temperature gradients exist as the thermal boundary layer. Similarly, in mass convection, we define the region of the fluid in which concentration gradients exist as the conceniration boundary layer, as shown in Figure 14 -38. In external flow, the thickness of the concentration boundary layer S,. for a. species A at a. specified location on the surface is defined as the normal distance y from the surface at which... 

An effort or a flow, which is a gate for communicating with the exterior, can be imposed (or supplied) by an external system (another dipole or dipole assembly, for instance). An example of external effort is when a force is imposed on a mass placed in a gravitational field. An external flow may correspond to the convection phenomenon, when a fluid transporting an object imposes its own velocity. 

The convection mass transport of species i may also take place if there exists a bulk fluid motion. The convection mass transfer is analogous to convection heat transfer and occurs between a moving mixture of fluid species and an exposed solid surface. Like hydrodynamic and thermal boundary layers, a concentration boundary layer forms over the surface if the free stream concentration of a species i, differs from species concentration at the surface, Qs, in an external flow over a solid surface as demonstrated in Figure 6.13. 

Table 2.6 Mass transfer correlations relevant for free and forced convection and valid for internal and external flow regimes. 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

So far we have considered an infinite value of the gas-to-particle heat and mass transfer coefficients. One may encounter, however, an imperfect access of heat and mass by convection to the outer geometrical surface of a catalyst. Stated in other terms, the surface conditions differ from those in the bulk flow because external temperature and concentration gradients are established. In consequence, the multiple steady-state phenomena as well as oscillatory activity depend also on the Sherwood and Nusselt numbers. The magnitudes of the Nusselt and Sherwood numbers for some strongly exothermic reactions are reported in Table III (77). We may infer from this table that the range of Sh/Nu is roughly Sh/Nu (1.0, 104). 

The second material property is heat of gasification, L, defined as the net heat flow into the material required to convert one unit mass of solid material to volatiles. The net heat flux into the material can be obtained from an energy balance at the surface of the specimen. Typically, a sample exposed in a bench-scale calorimeter is heated by external heaters and by its own flame. Heat is lost from the surface in the form of radiation. Owing to the small sample size, the flame flux is primarily convective, and flame absorption of external heater and specimen surface radiation can be neglected. Hence, L can be defined as... 

Convective diffusion — The electrochemical - mass transport controlled by both -> convection and - diffusion is called a process by convective diffusion [i]. Convection is caused by externally controlled force or spontaneous force. Convective diffusion has been conventionally used in a strict sense for well-controlled flow such as for -> rotating disk electrodes [ii], - channel elec-... 

To this point we have limited onr consideration to mass diffitsion in a station aiy medium, and thus the only ntotion involved was the creeping motion of molecules in the direction of decreasing concentration, and there was no motion of the mixture as a whole. Many practical problems, such as the evaporation of water from a lake under the iiifliience of the wind or the mixing of two fluids as they flow in a pipe, involve diffusion in a moving medium where the hoik motion i.s caused by an external force. Mass diffusion in such c.nses is complicated by the fact that chemical species are transported both by diffusion and by the bulk motion of the medium (i.e., convection). The velocities and mass flow rates of species in a moving medium consist of two components one due to molecular diffusion and one due to convection (Fig. 14-29). 

Figure 15-17. Block diagram of the thermal flow in a lubricated gear and bearing system. Heat sources.—A oil film at tooth contact B churning of bulk oil C oil film in bearings and bulk churning D oil film at Seals E external sources. Heat transmission.—F m G c H c, m I c J f K m L f M f N m P f Q c, f, r R c S n, f, r T c. c = conduction f = forced convection m = mass transport n = natural convection r = radiation.

The effectiveness factor E is evaluated for the appropriate kinetic rate law and catalyst geometry at the corresponding value of the intrapellet Damkohler number of reactant A. When the resistance to mass transfer within the boundary layer external to the catalytic pellet is very small relative to intrapellet resistances, the dimensionless molar density of component i near the external surface of the catalyst (4, surface) IS Very similar to the dimensionless molar density of component i in the bulk gas stream that moves through the reactor ( I, ). Under these conditions, the kinetic rate law is evaluated at bulk gas-phase molar densities, 4, . This is convenient because the convective mass transfer term on the left side of the plug-flow differential design equation d p /di ) is based on the bulk gas-phase molar density of reactant A. The one-dimensional mass transfer equation which includes the effectiveness factor. 

The /th species mass flux, j, and the total heat flux, q, can be expressed in terms of transfer coefficients. This is useful in situations where the liquid or gas phase is not completely resolved, or when the flow conditions are not exactly known. Often, these transfer coefficients are determined experimentally for a particular flow situation. For instance, different expressions are used, depending on whether the transfer is due to pure conduction or whether it is dominated by ccaivection. Also, the type of convection plays a role, that is, if the convection is forced or non-forced. A forced convection has a non-zero relative velocity between droplet and environment, whereas for a non-forced convection, the relative drop-gas velocity is zero and only the Stefan flow dominates. Note that the natural convection due to gravity is taken to be zero since gravity is an external force, and external forces are neglected in this article. In addition, in forced convection, the nature of the flow, that is, whether the flow is laminar or turbulent, plays an important role. These issues will be discussed in more detail in the following subsections. 

Electrochemical systems where the mass transport of chemical species is due to diffusion and electromigration were studied in previous chapters. In the present chapter, we are going to consider the occurrence of the third mechanism of mass transfer in solution convection. Although the modelling of natural convection has experienced some progress in recent years [1], this is usually avoided in electrochemical measurements. On the other hand, convection applied by an external source forced convection) is employed in valuable and popular electrochemical methods in order to enhance the mass transport of species towards the electrode surface. Some of these hydrodynamic methods are based on electrodes that move with respect to the electroljAic solution, as with rotating electrodes [2], whereas in other hydrodynamic systems the electrolytic solution flows over a static electrode, as in waU-jet [3] and channel electrodes [4]. 

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