Heat transfer multicomponent liquid

The general case of coupled heat-transfer and multicomponent mass-transfer in swarms of bubbles with residence-time and size distributions is treated in Section IV, L. In previous sections simplified cases of uncoupled mass transfer are considered starting from the most simplified models available for gas-liquid dispersions. 

The proposed technique will be used here to illustrate the case of interfacial heat and multicomponent mass transfer in a perfectly mixed gas-liquid disperser. Since in this case the holding time is also the average residence time, the gas and liquid phases spend the same time on the average. If xc = zd = f, then for small values of t, the local residence times tc and td of adjacent elements of the continuous and dispersed phases are nearly of the same order of magnitude, and hence these two elements remain in the disperser for nearly equal times. One may conclude from this that the local relative velocity between them is negligibly small, at least for small average residence times. Gal-Or and Walatka (G9) have recently shown that this is justified especially in dispersions of high <6 values and relatively small bubbles in actual practice where surfactants are present. Under this domain, Eqs. (66), (68), (69) show that as the bubble size decreases, the quantity of surfactants necessary to make a bubble behave like a solid particle becomes smaller. Under these circumstances (pd + y) - oo and Eq. (69) reduces to... 

Examples chosen for this category include the operations of vapor/liquid separation, heat transfer, and fluid flow. The Underwood method of estimating the minimum reflux ratio for a fractionation column multicomponent... 

The material balance relations presented above are valid for any number of components. We shall discuss solutions to this system of equations for binary mixtures in the remainder of this section of Chapter 12 before moving on to obtain generalized results for multicomponent systems in Section 12.2. In the analyses that follow we shall ignore the effects of heat transfer between the vapor and liquid phases. 

Simultaneous Mass and Heat Transfer Between the Vapor and Liquid Phases where the Phases are Composed of Multicomponent Mixtures... 

Effect of Multicomponent Mixtures in Nucleate Pool Boiling. For a binary liquid mixture of composition xu we may define a heat transfer coefficient h as... 

In processes where a condensing vapor or vapor from a liquid phase moves through an inert gas, eg, condensation in the presence of air, drying, humidification, crystallization (qv), and boiling of a multicomponent liquid, mass-transfer as well as heat-transfer effects are important (see Air conditioning Distillation Evaporation). Such processes are discussed elsewhere in the Encyclopedia, but the primary emphasis is on either the heat transfer or the mass transfer taking place. Herein the interactions between heat and mass transfer in such processes are discussed, and applications to humidification, dehumidification, and water cooling are developed. These same principles are applicable to other operations. 

The transfer of heat in a fluid may be brought about by conduction, convection, diffusion, and radiation. In this section we shall consider the transfer of heat in fluids by conduction alone. The transfer of heat by convection does not give rise to any new transport property. It is discussed in Section 3.2 in connection with the equations of change and, in particular, in connection with the energy transport in a system resulting from work and heat added to the fluid system. Heat transfer can also take place because of the interdiffusion of various species. As with convection this phenomenon does not introduce any new transport property. It is present only in mixtures of fluids and is therefore properly discussed in connection with mass diffusion in multicomponent mixtures. The transport of heat by radiation may be ascribed to a photon gas, and a close analogy exists between such radiative transfer processes and molecular transport of heat, particularly in optically dense media. However, our primary concern is with liquid flows, so we do not consider radiative transfer because of its limited role in such systems. 

In some services (e.g., refinery fractionators), vapor approaching the chimney tray is hotter than the chimney tray liquid. Heat will be transferred from the vapor to the liquid. If the vapor is condensable, some will condense on the bottom face of the chimney tray. The net result is analogous to leakage. The author is familiar with situations where refractory was installed on the bottom face of the chimney tray. In all these cases, steps were also taken to minimize leakage, making it difficult to independently assess the effectiveness of the refractory. For multicomponent, partially condensable vapor condensing on an uninsulated bottom face of a chimney tray (e.g., in a refinery fractionator), a typical heat transfer coefficient is 15 Btu/(h ft °F) (237). 

Liquid distribution. Liquid needs to be uniformly distributed to the shell, particularly when boiling a multicomponent mixture. Uneven distribution may locally deplete the lighter component and result in localized pinching and loss of heat transfer. Uneven distribution can also promote uneven heating, resulting in further loss of heat transfer. In extreme cases, maldistribution can lead to stratified flow, local mist flow, excessive thermal stresses, and accelerated corrosion (430). 

Multicomponent condensation. In multicomponent condensation, the heavier components are preferentially condensed first. As these are removed from the vapor, the dew point and condensation temperature of the remaining vapor decrease. Equilibrium occurs at the vapor-liquid interface, and the remaining vapor must be cooled down to stay in equilibrium at the interface. Sensible heat removal from the vapor becomes important and has a low heat transfer coefficient. In such cases, there is a resistance in the vapor phase as well as in the condensate film (Fig. 15.126). 

A somewhat ainilar tqiproach has been proposed by Feintuch and Tribal for the design of complex multicomponent adiabatic systems. This is an extension of a previously developed mediod of estimating beat effects for simple three-component systems and takes into account the mass and heat transfer resistances of bodi the liquid and gas plmses. ... 

To resolve such problems, rigorous mass-transfer theory has been applied to a distillation stage in combination with the required heat transfer models (Krishna and Standart, 1979 Taylor and Krishna, 1993). Based on such theories, numerical models have been developed wherein correlations of mass-transfer and heat-transfer coefficients for the distillation device, of packed or plate type, are incorporated (Krishnamurthy and Taylor, 1985 Taylor etoL, 1994). For multicomponent systems, Maxwell-Stefan formalism (Section 3.1.5.1) provided a structural framework for such models. Such theories are known as a rate based approach for modding distillation where equilibrium between phases is nonexistent except at the vapor-liquid interfeice. 

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