Heat and mass transfer coupling

The equipartition principle is mainly used to investigate binary distillation columns, and should be extended to multicomponent and nonideal mixtures. One should also account for the coupling between driving forces since heat and mass transfer coupling may be considerable and should not be neglected especially in diabatic columns. 

Three different phenomena are considered to analyze the heat and mass transfers coupling (1) the different steps of the coupling of heat and mass transfers, (2) the impact of the heat flux density on drying time, and (3) the comparison between different THFs. 

Figure 19.18 Different steps of the heat and mass transfers coupling for the textile heat fluxmeter PES/CO3 with the heat flux density 464 W/m. ...

Dutour, S., Mazet, N., Joly, J.L. and Platel, V. (2005). Modeling of heat and mass transfer coupling with gas-solid reaction in a sorption heat pump cooled hy a two-phase closed thermosyphon. Chemical Engineering Science, Vol. 60, pp. 4093-4104. 

In this section, a general formulation will be given for the effect of bubble residence-time and bubble-size distributions on simultaneous and thermodynamically coupled heat- and mass-transfer in a multicomponent gas-liquid dispersion consisting of a large number of spherical bubbles. Here one can... 

The independent transport fluxes of simultaneous (coupled) heat- and mass-transfer in an n-component gas-liquid dispersion consisting of two phases (a = 1,2) can be written as (G3)... 

Curing of Polyimlde Resin. Thermoset processing involves a large number of simultaneous and interacting phenomena, notably transient and coupled heat and mass transfer. This makes an empirical approach to process optimization difficult. For instance, it is often difficult to ascertain the time at which pressure should be applied to consolidate the laminate. If the pressure is applied too early, the low resin viscosity will lead to excessive bleed and flash. But if the pressure is applied too late, the diluent vapor pressure will be too high or the resin molecular mobility too low to prevent void formation. This example will outline the utility of our finite element code in providing an analytical model for these cure processes. 

In addition to the effects of formulation factors on freeze-drying behavior, it is important for the pharmaceutical scientist to understand basic principles of heat and mass transfer in freeze-drying [29,30]. Because of the high heat input required for sublimation (670 cal/g), transfer of heat from the heated shelf to the sublimation front is often the rate-limiting step in the coupled heat... 

C. Coupling Between Heat and Mass Transfer Process Control... 

Heat and mass transfer are coupled by the constraint imposed by the conservation... 

Rapid evaporation introduces complications, for the heat and mass transfer processes are then coupled. The heat of vaporization must be supplied by conduction heat transfer from the gas and liquid phases, chiefly from the gas phase. Furthermore, convective flow associated with vapor transport from the surface, Stefan flow, occurs, and thermal diffusion and the thermal energy of the diffusing species must be taken into account. Wagner 1982) reviewed the theory and principles involved, and a higher-order quasisteady-state analysis leads to the following energy balance between the net heat transferred from the gas phase and the latent heat transferred by the diffusing species ... 

These ordered array materials find interest not only in catalysis, but in several other applications, from optical materials, sensors, low-k materials, ionic conductors, photonic crystals, and bio-mimetic materials.Flowever, with respect to these applications, catalysis requires additional specific characteristics, such as the presence of a thermally stable nanostructure, the minimization of grain boundaries where side reactions may occur, and the presence of a porous structure which guarantees a high surface area coupled to low heat and mass transfer limitations. An ordered assembly of ID nanostructures for oxide materials could, in principle, meet these different requirements. 

We will consider in this section how mass transfer proceeds, using crystal growth from a solution phase as a representative example of crystal growth in which heat and mass transfer are coupled. We will use the growth of ionic crystals in aqueous solution in a beaker as an example (Fig. 3.3). 

Trivic, D.N., O Brien, T.J., and Amon, C.H. Modeling the radiation of anisotropically scattering media by coupling Mie theory with Finite volume method. International Journal of Heat and Mass Transfer, 2004. 47, 5765-5780. 

This chapter is concerned with the mathematical modeling of coupled chemical reaction and heat and mass transfer processes occurring in porous catalysts. It focuses primarily on steady state catalyst operation which is the preferred industrial practice. Stationary operation may be important for the startup and shutdown of an industrial reactor, or with respect to dynamic process control. However, these effects are not discussed here in great detail because of the limited space available. Instead, the interested reader is referred to the various related monographs and articles available in the literature [6, 31, 46-49]. 

The contents of the present contribution may be outlined as follows. Section 6.2.2 introduces the basic principles of coupled heat and mass transfer and chemical reaction. Section 6.2.3 covers the classical mathematical treatment of the problem by example of simple reactions and some of the analytical solutions which can be derived for different experimental situations. Section 6.2.4 is devoted to the point that heat and mass transfer may alter the characteristic dependence of the overall reaction rate on the operating conditions. Section 6.2.S contains a collection of useful diagnostic criteria available to estimate the influence of transport effects on the apparent kinetics of single reactions. Section 6.2.6 deals with the effects of heat and mass transfer on the selectivity of basic types of multiple reactions. Finally, Section 6.2.7 focuses on a practical example, namely the control of selectivity by utilizing mass transfer effects in zeolite catalyzed reactions. 

In the general case, eqs 4 and 5 constitute a system of nonlinear coupled second-order partial differential equations. To specify the boundary conditions for this problem, it is necessary to include the external (interphase) heat and mass transfer, as both the concentration and the temperature at the external surface of the catalyst pellet may differ from the corresponding values in the bulk of the surrounding fluid phase. 

The optimal Reynolds number defines the operating conditions at which the cylindrical system performs a required heat and mass transport, and generates the minimum entropy. These expressions offer a thermodynamically optimum design. Some expressions for the entropy production in a multicomponent fluid take into account the coupling effects between heat and mass transfers. The resulting diffusion fluxes obey generalized Stefan-Maxwell relations including the effects of ordinary, forced, pressure, and thermal diffusion. 

Heat and mass transfer in a distillation column are coupled, and if the temperature field or chemical force is specified in the column, the other force would be defined. Maximum second law efficiency results from minimizing the entropy production rate with respect to one of the forces. For example, if the contribution of mass transfer is dominant, we should try to minimize the change of the entropy production with respect to the chemical force. 

Simultaneous heat and mass transfer plays an important role in various physical, chemical, and biological processes hence, a vast amount of published research is available in the literature. Heat and mass transfer occurs in absorption, distillation extraction, drying, melting and crystallization, evaporation, and condensation. Mass flow due to the temperature gradient is known as the thermal diffusion or Soret effect. Heat flow due to the isothermal chemical potential gradient is known as the diffusion thermoeffect or the Dufour effect. The Dufour effect is characterized by the heat of transport, which represents the heat flow due to the diffusion of component / under isothermal conditions. Soret effect and Dufour effect represent the coupled phenomena between the vectorial flows of heat and mass. Since many chemical reactions within a biological cell produce or consume heat, local temperature gradients may contribute in the transport of materials across biomembranes. 

Various formulations and methodologies have been suggested for describing combined heat and mass transfer problems, such as the integral transform technique, in the development of general solutions. In this chapter, cross phenomena or coupled heat and mass transfer are discussed using the linear nonequilibrium thermodynamics theory. 

Example 7.4 Modified Graetz problem with coupled heat and mass flows The Graetz problem originally addressed heat transfer to a pure fluid without the axial conduction with various boundary conditions. However, later the Graetz problem was transformed to describe various heat and mass transfer problems, where mostly heat and mass flows are uncoupled. In drying processes, however, some researchers have considered the thermal diffusion flow of moisture caused by a temperature gradient. 

Equations (9.69) and (9.70) represent the modeling of reaction-diffusion systems with the thermodynamically coupled heat and mass flows excluding the coupling effects due to reaction. After combining Eqs. (9.64), (9.69), and (9.70) steady-state balance equations with the coupled heat and mass transfer become... 

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