Multicomponent mixtures, thermal

The physical properties of the multicomponent mixture, such as viscosity, specific heats at constant volume and at constant pressure, and laminar thermal conductivity, are usually calculated under the assumption of an ideal mixture. Data and... 

Another class of separation problem attacked has been that of designing the most effective thermally coupled distillation column arrangement to separate a multicomponent mixture. Sargent and Gaxninibandara (1975) present a general column superstructure which they optimize. Imbedded in the superstructure are all the alternative thermally coupled and ordinary column sequences to be considered. The optimization eliminates those portions of the superstructure which are not economic leaving, hopefully, the optimal substructure. 

Thermally coupled systems can also be devised for multicomponent mixtures. Sargent and Gaminibandara (Optimization in Action, L. W. C. Dixon, ed.. Academic Press, London, 1976, p. 267) presented a natural extension of the Petlyuk column sequence to multi-component systems. Agrawal [Ind. Eng. Chem. Res., 35,1059 (1996) Trans. Inst. Chem. Eng., 78,454 (2000)] presented a method for generating an even more complete superstructure from which all the... 

For binary and multicomponent mixtures, the thermal conductivity depends on the concentrations as well as on temperature, and the formulas of the accurate kinetic theory are quite complicated [5]. Empirical expressions for X are therefore more useful for both binary [9] and ternary [6], [26] mixtures, although few data exist for ternary mixtures. Tabulations of available experimental and theoretical results for thermal conductivities may be found in [5], [6], [13], and [18]-[21], for example. The thermal diffusivity, defined as 2p/Cp, often arises in combustion problems its pressure and temperature dependences in gases are XjpCp T7p ( < a < 2), and its typical values in combustion lie between 10 cm /s and 1 cm s at atmospheric pressure. 

While equation (42) is valid for one-component systems without radiant transport, for binary and multicomponent mixtures there are other effects besides thermal conduction that contribute to the heat flux q. 

The identification of the chemical forms of an element has become an important and challenging research area in environmental and biomedical studies. Two complementary techniques are necessary for trace element speciation. One provides an efficient and reliable separation procedure, and the other provides adequate detection and quantitation [4]. In its various analytical manifestations, chromatography is a powerful tool for the separation of a vast variety of chemical species. Some popular chromatographic detectors, such flame ionization (FID) and thermal conductivity (TCD) detectors are bulk-property detectors, responding to changes produced by eluates in a characteristic mobile-phase physical property [5]. These detectors are effectively universal, but they provide little specific information about the nature of the separated chemical species. Atomic spectroscopy offers the possibility of selectively detecting a wide rang of metals and nonmetals. The use of detectors responsive only to selected elements in a multicomponent mixture drastically reduces the constraints placed on the separation step, as only those components in the mixture which contain the element of interest will be detected... 

Corresponding considerations are also valid for the thermal boundary layer in multicomponent mixtures. The energy transport through conduction and diffusion in the direction of the transverse coordinate x is negligible in comparison to that through the boundary layer. The energy equation for the boundary layer follows from (3.97), in which we will presuppose vanishing mass forces k Ki-... 

The equations (3.109), (3.117) or (3.118) and (3.120) for the velocity, thermal and concentration boundary layers show some noticeable similarities. On the left hand side they contain convective terms , which describe the momentum, heat or mass exchange by convection, whilst on the right hand side a diffusive term for the momentum, heat and mass exchange exists. In addition to this the energy equation for multicomponent mixtures (3.118) and the component continuity equation (3.25) also contain terms for the influence of chemical reactions. The remaining expressions for pressure drop in the momentum equation and mass transport in the energy equation for multicomponent mixtures cannot be compared with each other because they describe two completely different physical phenomena. 

Figure 4.3 Schematic diagram of a continuous flow apparatus capable of operating to 400°C and —350 bar with multicomponent mixtures that are thermally labile (adapted from Bolahos, Hoch-geschurtz, and Thies, 1991).

The differential form of the energy balance for a multicomponent mixture can be written In a variety of forms.1 6 It would contain terms reprenenting heat conduction and radiation, body forces, viscous dissipation, reversible work, kinetic energy, and the substantial derivative of the enthalpy of die mixture. Its formulation is beyond the scope of this chapter. Certain simplifled forms will be used in later chapters in problems such as simultaneous heal and mass transfer in air-water operations or thermal effects in gas absorbent. 

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). 

MOLECULAR FLUX OF THERMAL ENERGY IN BINARY AND MULTICOMPONENT MIXTURES VIA THE FORMALISM OF NONEQUILIBRIUM THERMODYNAMICS... 

ANALYSIS OF THE INTERDIFFUSIONAL FLUX OF THERMAL ENERGY IN BINARY MIXTURES AND GENERALIZATION TO MULTICOMPONENT MIXTURES... 

THERMAL ENERGY BALANCE IN MULTICOMPONENT MIXTURES AND NONISOTHERMAL EFFECTIVENESS FACTORS VIA COUPLED HEAT AND MASS TRANSFER IN POROUS CATALYSTS... 

THERMAL ENERGY BALANCE IN MULTICOMPONENT MIXTURES coordinates ... 

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