Simultaneous Mass and Heat Transfer

Heat transfer and mass transfer occur simultaneously whenever a transfer operation involves a change in phase or a chemical reaction. Of these two situations, only the first is considered herein because in reacting systems the complications of chemical reaction mechanisms and pathways are usually primary (see HeaT-EXCHANGETECHNOLOGy). Even in processes involving phase changes, design is frequendy based on the heat-transfer process alone mass transfer is presumed to add no compHcations. But in fact mass transfer effects do influence and can even limit the process rate. 

Condensation and Vaporization as Effected by Simultaneous Heat and Mass Transfer 

This process has been used for various situations (1—14). Eor the condensation of a single component from a binary gas mixture, the gas-stream sensible heat and mass-transfer equations for a differential condenser section take the following forms  

No condensation is taking place here in the bulk gas phase. If condensation does take place so that fogging occurs, these equations become 

The term e/(e — 1), which appears in equations 1 and 2, was first developed to account for the sensible heat transferred by the diffusing vapor (1). The quantity S represents the group ratio of total transported energy to convective heat transfer. Thus it may be thought of as the fractional 

Processes involving coupled heat and mass transfer occur frequently in nature. They are central to the formation of fog, to cooling towers, and to the wet-bulb thermometer. They are important in the separation of uranium isotopes and in the respiration of water lilies. This chapter analyzes a few of these processes. Not unexpectedly, such processes are complex, for they involve equations for both diffusion and heat conduction. These equations are coupled, often in a nonlinear way. As a result, our descriptions will contain approximations to reduce the complexities involved. 

We begin this chapter with a comparison of the mechanisms responsible for mass and heat transfer. The mathematical similarities suggested by these mechanisms are discussed in Section 21.1, and the physical parallels are explored in Section 21.2. The similar mechanisms of mass and heat transfer are the basis for the analysis of drying, both of solids and of sprayed suspensions. However, the detailed models differ, as shown by the examples in Section 21.3. In Section 21.4, we outline cooling-tower design as an example based on mass and heat transfer coefficients. Finally, in Section 21.5, we describe thermal diffusion and effusion. 

We now turn our attention to processes where heat and mass transfer occur in unison. This is far from being an unusual event, but it raises the complexity of the underlying model, a fact that persuaded us to defer its consideration to the last chapter. 

Mass Transfer and Separation Processes Principles and Applications 

Simultaneous heat and mass transfer also occur in exothermic or endothermic heterogeneous reacting systems and in the absorption or adsorption from concentrated gas streams. Some of these topics are addressed in separate illustrations, but we retain the air-water system as the central theme of this chapter. 

Because evaporation is an endothermic process, heat must be delivered to the system, either through convection, conduction, radiation, or a combination of these methods. The solvents are evaporated from the coating surface and at the same time the latent heat of solvent cool 

Assuming that the heat is supplied only by convection of hot air and the substrate is impermeable. Further if we neglect the internal resistance of solvent transport to the coating surface, the heat and mass balance consist a lumped parameter system. 

Subscript f and C mean the substrate and coating layer respectively. Equation 7.3.1 and 

The equilibrium saturated solvent concentration is related to the concentration of solvent at the coating surface by thermodynamic equilibrium relations, such as Henry s law, Raoult s law and the Flory-Huggins equation. The Raoult s law is 

The saturated vapor pressure is calculated from the Antoine equation at the specific temperature. 

Our treatment so far has made occasional reference to heat transfer, primarily to draw the reader s attention to tiie analogies that exist between the transport of heat and mass. For example, in Chapter 1 we highlighted the similarities between the rate laws governing convective and diffusive heat and mass transfer. The analogy between tiie two phenomena when dealing witii co-current or countercurrent operations has been brought out on several occasions, notably Illustration 8.7. 

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Humidification. For wiater operation, or for special process requirements, humidification maybe required (see Simultaneous HEAT and mass transfer). Humidification can be effected by an air washer which employs direct water sprays (see Evaporation). Regulation is maintained by cycling the water sprays or by temperature control of the air or water. Where a large humidification capacity is required, an ejector which direcdy mixes air and water in a no22le may be employed. Steam may be used to power the no22le. Live low pressure steam can also be released directly into the air stream. Capillary-type humidifiers employ wetted porous media to provide extended air and water contact. Pan-type humidifiers are employed where the required capacity is small. A water filled pan is located on one side of the air duct. The water is heated electrically or by steam. The use of steam, however, necessitates additional boiler feed water treatment and may add odors to the air stream. Direct use of steam for humidification also requires careful attention to indoor air quahty. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the stmcture and properties of a soHd phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particularly active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust control, industrial). Eor these kinds of appHcations psychrometric charts for systems other than air—water would be useful. The constmction of such has been considered (54). 

Simultaneous heat and mass transfer also occurs in drying processes, chemical reaction steps, evaporation, crystallisation, and distillation. In all of these operations transfer rates are usually fixed empirically. The process can be evaluated using either the heat- or mass-transfer equations. However, if the process mechanism is to be fully understood, both the heat and mass transfer must be described. Where that has been done, improvements in the engineering of the process usually result (see Process energy conservation). 

ABM AbdulHye, Simultaneous Heat and Mass Transfer from a Vertical, Isothermal Suface, Ph.D. dissertation. University ofWindsor, Canada, 1979. 

I.e Lewis Sc-Pr k Dh CppD I) Simultaneous heat and mass transfer... 

In the processing of materials it is often necessary either to increase the amount of vapour present in a gas stream, an operation known as humidification or to reduce the vapour present, a process referred to as dehumidification. In humidification, the vapour content may be increased by passing the gas over a liquid which then evaporates into the gas stream. This transfer into the main stream takes place by diffusion, and at the interface simultaneous heat and mass transfer take place according to the relations considered in previous chapters. In the reverse operation, that is dehumidification, partial condensation must be effected and the condensed vapour removed. 

Thomas, W.,1. and Houston, P. Brit. Chem. Eng. 4 (1959) 160, 217. Simultaneous heat and mass transfer in cooling towers. 

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