Transfer velocity Subject

Powder transfer velocity and mass flow rate are not subject to any maximum values,... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

The baffle cut determines the fluid velocity between the baffle and the shell wall, and the baffle spacing determines the parallel and cross-flow velocities that affect heat transfer and pressure drop. Often the shell side of an exchanger is subject to low-pressure drop limitations, and the baffle patterns must be arranged to meet these specified conditions and at the same time provide maximum effectiveness for heat transfer. The plate material used for these supports and baffles should not be too thin and is usually minimum thick-... 

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

Thus, a velocity boundary layer and a thermal boundary layer may develop simultaneously. If the physical properties of the fluid do not change significantly over the temperature range to which the fluid is subjected, the velocity boundary layer will not be affected by die heat transfer process. If physical properties are altered, there will be an interactive effect between the momentum and heat transfer processes, leading to a comparatively complex situation in which numerical methods of solution will be necessary. 

Macbeth (M5) has recently written a detailed review on the subject of burn-out. The review contains a number of correlations for predicting the maximum heat flux before burn-out occurs. These correlations include a dependence upon the tube geometry, the fluid being heated, the liquid velocity, and numerous other properties, as well as the method of heating. Sil-vestri (S6) has reviewed the fluid mechanics and heat transfer of two-phase annular dispersed flows with particular emphasis on the critical heat flux that leads to burn-out. Silvestri has stated that phenomena responsible for burn-out, due to the formation of a vapor film between the wall and the liquid, are believed to be substantially different from phenomena causing burn-out due to the formation of dry spots that produce the liquid-deficient heat transfer region. It is known that the value of the liquid holdup at which dry spots first appear is dependent on the heat flux qmi. The correlations presented by Silvestri and Macbeth (S6, M5) can be used to estimate the burn-out conditions. 

The second approach involves simultaneous variation of the weight of catalyst and the molal flow rate so as to maintain W/F constant. One then plots the conversion achieved versus linear velocity, as shown in Figures 6.4c and 6Ad. If the results are as indicated in Figure 6Ad, mass transfer limitations exist in the low-velocity regime. If the conversion is independent of velocity, there probably are no mass transfer limitations on the conversion rate. However, this test is also subject to the sensitivity limitations noted above. 

To determine the rate of transfer a large set of systems, each with an atom either to the left or near the saddle point is considered. Once an atom has moved to the right of LL the process is regarded as having occurred. The rate R is then defined as the net flux of atoms across LL, subject to several assumptions, introduced to ensure forward reaction. For n atoms in equilibrium near A, moving with mean Maxwell velocity v = y/2kT/irm towards the right, the required flux density is (1/2)vn, and the total flux is... 

Authors efforts in this part of the work have been concentrated on developing turbulence closures for the statistical description of two-phase turbulent flows. The primary emphasis is on development of models which are more rigorous, but can be more easily employed. The main subjects of the modeling are the Reynolds stresses (in both phases), the cross-correlation between the velocities of the two phases, and the turbulent fluxes of the void fraction. Transport of an incompressible fluid (the carrier gas) laden with monosize particles (the dispersed phase) is considered. The Stokes drag relation is used for phase interactions and there is no mass transfer between the two phases. The particle-particle interactions are neglected the dispersed phase viscosity and pressure do not appear in the particle momentum equation. 

The momentum equation (the Navier-Stokes equation) for fluid flow (De Groot and Mazur, 1962) is complicated and difficult to solve. It is the subject of fluid mechanics and dynamics and is not covered in this book. When fluid flow is discussed in this book, the focus is on the effect of the flow (such as a flow of constant velocity, or boundary flow) on mass transfer, not the dynamics of the flow itself. 

But suppose we are operating a heat exchanger subject to rapid rates of initial fouling. The start-of-run heat-transfer coefficient U is 120 Btu/[(h)(ft2(°F)]. Four months later, the U value has lined out at 38. The calculated clean tube-side velocity is lV2 ft/s. This is too low, but what can be done ... 

More experimental work on this subject is needed. The above relation implies strong dependence of the heat transfer coefficient on the gas velocity and the liquid properties (pL, pL, AL, and CP). 

Water flows in a 2.5-cm-diameter pipe so that the Reynolds number based on diameter is 1500 (laminar flow is assumed). The average bulk temperature is 35°C. Calculate the maximum water velocity in the tube. (Recall that u, = 0.5wo.) What would the heat-transfer coefficient be for such a system if the tube wall was subjected to a constant heat flux and the velocity and temperature profiles were completely developed Evaluate properties at bulk temperature. 

A 3.0-cm-diameter cylinder is subjected to a cross flow of carbon dioxide at 200°C and a pressure of 1 atm. The cylinder is maintained at a constant temperature of 50°C and the carbon dioxide velocity is 40 m/s. Calculate the heat transfer to the cylinder per meter of length. 

Engineering systems mainly involve a single-phase fluid mixture with n components, subject to fluid friction, heat transfer, mass transfer, and a number of / chemical reactions. A local thermodynamic state of the fluid is specified by two intensive parameters, for example, velocity of the fluid and the chemical composition in terms of component mass fractions wr For a unique description of the system, balance equations must be derived for the mass, momentum, energy, and entropy. The balance equations, considered on a per unit volume basis, can be written in terms of the partial time derivative with an observer at rest, and in terms of the substantial derivative with an observer moving along with the fluid. Later, the balance equations are used in the Gibbs relation to determine the rate of entropy production. The balance equations allow us to clearly identify the importance of the local thermodynamic equilibrium postulate in deriving the relationships for entropy production. 

With the measurements subject to fluctuations of 20 or 30%, no accurate description of the profile is possible. All that can be said is that with moderate ratios of tube to particle diameter, the maximum velocity is about twice the minimum, and that when the particles are relatively small, the profile is relatively flat near the axis. It is fairly well established that the ratio of the velocity at a given radial position to the average velocity is independent of the average velocity over a wide range. Another observation that is not so easy to understand is that the velocity reaches a maximum one or two particle diameters from the wall. Since the wall does not contribute any more than the packing to the surface per unit volume in the region within one-half particle diameter from the wall, there is no obvious reason for the velocity to drop off farther than some small fraction of a particle diameter from the wall. In any case, all the variations that affect heat transfer close to the wall can be lumped together and accounted for by an effective heat-transfer coefficient. Material transport close to the wall is not very important, because the diffusion barrier at the wall makes the radial variation of concentration small. 

Constant Pattern Behavior. In a real system the finite resistance to mass transfer and axial mixing in the column lead to departures from the idealized response predicted by equilibrium theory. In the case of a favorable isotherm the shock wave solution is replaced by a constant pattern solution. The concentration profile spreads in the initial region until a stable situation is reached in which the mass transfer rate is the same at all points along the wave front and exactly matches the shock velocity. In this situation the fluid-phase and adsorbed-pliase profiles become coincident, as illustrated in Figure 13. This represents a stable situation and the profile propagates without further change in shape—lienee the term constant pattern. The form of the concentration profile under constant pattern conditions may be easily deduced by integrating the mass transfer rate expression subject to the condition c/c0 = q/qQy where qfj is the adsorbed phase concentration in equilibrium with c(y... 

A 2-m X 3-m flat plate is suspended in a room, and is subjected to air flow parallel to its surfaces along its 3-m-long side. The free stream temperature and velocity of air are 20°C and 7 m/s. The total drag force acting on the plate is measured to be 0.86 N. Determine the average convection heal transfer coefficient for the plate (Fig. 5-36). 

A 25-cm-diameter stainless steel ball (p = 8055 kg/m , Cp = 480 J/kg °C) is removed from the oven at a uniform temperature of 300 C (Fig. 7-24). The ball is then subjected to the flow of air at 1 atm pressure and 25°C with a velocity of 3 m/s. The surface temperature of the ball eventually drops to 200°C. Determine the average convection heat transfer coefficient during this cooling process and estimate hovr long the process will take. 

---