Heat and Mass Transfer Rates

Rate of cooling also is important in systems where crystallization is undesired. For amorphous products, cooling must be sufficiently rapid that the mass passes through the crystallization zone between the solubility curve and glass transition zone before nucleation occurs. In this case, heat transfer must occur more 

On the other hand, if few larger crystals are desired for efficient separation, then nucleation must occur at a point where fewer nuclei are formed. This point is at higher temperature (or lower concentration) than the maximum nucleation point. Nevertheless, it is still important that the nuclei are formed at the same time so that they ail grow to about the same product size for efficient filtration. 

TABLE 13.5 Effect of Crystallization Temperature on Crystal Size Distribution in Fondant Manufacture 

Fondant made with 90% sucrose and 10% corn syrup in dry matter and 90% total solids. (Data from Lees 1965.) 

If nucleation must be avoided in a product, agitation during processing must be kept to an absolute minimum. Sometimes even the shear forces that exist as a supersaturated fluid is passed through a pipe and fittings may be sufficient to initiate nucleation. 

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As velocity continues to rise, the thicknesses of the laminar sublayer and buffer layers decrease, almost in inverse proportion to the velocity. The shear stress becomes almost proportional to the momentum flux (pk ) and is only a modest function of fluid viscosity. Heat and mass transfer (qv) to the wall, which formerly were limited by diffusion throughout the pipe, now are limited mostly by the thin layers at the wall. Both the heat- and mass-transfer rates are increased by the onset of turbulence and continue to rise almost in proportion to the velocity. 

Combining equation 6 with the heat- and mass-transfer rate expressions gives... 

Product diameter is small and bulk density is low in most cases, except prilling. Feed hquids must be pumpable and capable of atomization or dispersion. Attrition is usually high, requiring fines recycle or recoveiy. Given the importance of the droplet-size distribution, nozzle design and an understanding of the fluid mechanics of drop formation are critical. In addition, heat and mass-transfer rates during... 

Correlations of heat and mass-transfer rates are fairly well developed and can be incorporated in models of a reaction process, but the chemical rate data must be determined individually. The most useful rate data are at constant temperature, under conditions where external mass transfer resistance has been avoided, and with small particles... 

The ROTOBERTY internal recycle laboratory reactor was designed to produce experimental results that can be used for developing reaction kinetics and to test catalysts. These results are valid at the conditions of large-scale plant operations. Since internal flow rates contacting the catalyst are known, heat and mass transfer rates can be calculated between the catalyst and the recycling fluid. With these known, their influence on catalyst performance can be evaluated in the experiments as well as in production units. Operating conditions, some construction features, and performance characteristics are given next. 

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. 

When the flow in the boundary layer is turbulent, streamline flow persists in a thin region close to the surface called the laminar sub-layer. This region is of particular importance because, in heat or mass transfer, it is where the greater part of the resistance to transfer lies. High heat and mass transfer rates therefore depend on the laminar sublayer being thin. Separating the laminar sub-layer from the turbulent part of the boundary... 

At high gas velocities in the bed, the stable bubbles break down into unstable voids that continuously disintegrate and reform. This type of bed is said to be operating in the turbulent fluidized-bed regime, and is characterized by higher heat- and mass-transfer rates than in the bubbling bed. As the gas velocity is increased further, the... 

Although the application of fluidisation techniques to sublimation-desublimation processes was first proposed by Matz" 11, the technique has not yet been widely adopted for large-scale commercial use, despite its obvious advantage of improving both heat and mass transfer rates. G aiko 112 1 has, however, reported on a fluidised-bed de-sublimation unit operating in the United States for the production of aluminum chloride at the rate of 3 kg/s (11 tonne/h). 

Sivasubramanian, M. S. and Boston, J. F., 1990, The heat and mass transfer rate-based approach for modelling multicomponent separation processes, in Computer Applications in Chemical Engineering, pp. 331-336. Elsevier, Amsterdam. 

The deposition of an inert porous diflfusion barrier on top of the catalyst layer can significantly hinder the rate of mass transfer of reactants to the catalyst surface, at the same time affecting only negligibly the rate of heat transfer to the gas phase. The effect is equivalent to that observed with fuels, like higher hydrocarbons, whose mass diffusi vity in air is considerably lower than thermal diffusivity of the fuel-air mixture (Lewis number >1). Such unbalancing of heat and mass transfer rates results in a significant decrease in the catalyst wall temperature. 

There is conflicting evidence regarding the extent to which imposed vibrations increase particle to fluid heat and mass transfer rates (G2), with some authors even claiming that transfer rates are decreased. For sinusoidal velocity variations superimposed on steady relative motion, enhancement of transfer depends on a scale ratio A/d and a velocity ratio Af /Uj (G3). These quantities are rather like the scale and intensity of turbulence (see Chapter 10). For Af /Uj < l/2n, the vibrations do not cause reversal in the relative motion and the enhancement of mass transfer has been correlated (G3) by... 

Tlie requirement for mechanical agitation can be avoided by using a fluidized bed reactor. In this type of reactor, the agitation and mixing are achieved by means of the moving liquid that carries the solids through the reactor or mixes with the particle phase. Thus, high heat and mass transfer rates are assured. 

C with a water content of 0.075 kg/kg. Although heat and mass transfer rates were relatively insensitive to the choice of the model, the amount of fog formation was not. The models neglect the effects of condensation within the boundary layer, thus underestimating fog formation by a factor of up to three. The amount of fog formed in flue-gas washing plants increased up to a maximum value with decreasing feed-water temperature over a narrow band of liquid-to-gas ratios. 

The overall specific resistance for heat or mass transfer is the reciprocal of the heat or mass transfer coefficient, U or K, where U and K are the common parameters characterizing heat and mass transfer rates, respectively, defined as... 

They represent heat and mass fluxes with unit gradients of temperature and concentration, respectively, and so can be considered as specific heat and mass transfer rates. 

Gas-continuous impinging streams with a liquid as the dispersed phase has wide application, such as in the combustion of liquid fuel droplets, absorption, water-spray cooling of air, etc. [9]. In such systems the dispersity of liquids plays a very important role affecting heat and mass transfer rates, because it influences both the interface area and the mean transfer coefficient. Wu et al. [68] investigated the influence of impinging streams on the dispersity of liquid. 

As will be seen throughout the rest of the text, typical examples include fast reactions and large heat and mass transfer rates. 

Internal recycle reactors are designed so that the relative velocity between the catalyst and the fluid phase is increased without increasing the overall feed and outlet flow rates. This facilitates the interphase heat and mass transfer rates. A typical internal flow recycle stirred reactor design proposed by Berty (1974, 1979) is shown in Fig. 18. This type of reactor is ideally suited for laboratory kinetic studies. The reactor, however, works better at higher pressure than at lower pressure. The other types of internal recycle reactors that can be effectively used for gas-liquid-solid reactions are those with a fixed bed of catalyst in a basket placed at the wall or at the center. Brown (1969) showed that imperfect mixing and heat and mass transfer effects are absent above a stirrer speed of about 2,000 rpm. Some important features of internal recycle reactors are listed in Table XII. The information on gas-liquid and liquid-solid mass transfer coefficients in these reactors is rather limited, and more work in this area is necessary. 

Heat- and mass-transfer rate correlations obtained in a fixed-bed reactor can be applied to this type of reactor. 

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