Coupling between heat/mass transfer

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

The phenomenological coefficients are important in defining the coupled phenomena. For example, the coupled processes of heat and mass transport give rise to the Soret effect (which is the mass diffusion due to heat transfer), and the Dufour effect (which is the heat transport due to mass diffusion). We can identify the cross coefficients of the coupling between the mass diffusion (vectorial process) and chemical reaction (scalar process) in an anisotropic membrane wall. Therefore, the linear nonequilibrium thermodynamics theory provides a unifying approach to examining various processes usually studied under separate disciplines. 

In Equations [18.4] and [18.5] the resistivities are denoted by the symbol r, and the superscript denotes that these relate to the membrane, while the subscript identifies the type of resistivity. The diagonal resistivities, and can be related to the conductivity and diffusivity respectively, while the off-diagonal resistivities describe the coupling between heat and mass transfer. Also, the mass flux is denoted by J, and the sensible heat flux is denoted... 

Concentration and temperature profiles at 400 K (a) shows the temperature difference, while (b) shows the concentration profile across the membrane.The temperature difference between the two gas phases is kept at 0.8 K. In both cases, we considered the situations in which coupling between heat and mass transfer was included or excluded in the model.The effect of the coupling is negligible for this case. 

In most cases, however, heat transfer and mass transfer occur simultaneously, and the coupled equation (230) thus takes into account the most general case of the coupling effects between the various fluxes involved. To solve Eq (230) with the appropriate initial and boundary conditions one can decouple the equation by making the transformation (G3)... 

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 ... 

As can be seen from the expression for the driving force in terms of the chemical potential differences, which are related to the differences in temperature and concentration, the two transporting processes, heat transfer and mass transfer, are coupled in crystal growth. The degree of contribution from the respective transport process is determined by the degree of condensation of the environmental (ambient) phase. To grow crystals in a diluted ambient phase, a condensation process is required, and so mass transfer plays an essential role. The contribution of heat generated by crystallization in this case is small compared with that of the mass transfer. However, for crystallization in a condensed phase, such as a melt phase, heat transfer plays the essential role, and the contribution from the mass transfer will be very small, because the difference in concentration (density) between the solid and liquid phases is very small, smaller, say, than 1 or 2%. It is therefore necessary to classify the types of ambient phases and to be familiar with their respective characteristics from this standpoint. 

Therefore, the main source of multiplicity in fixed-bed catalytic reactors is through the coupling between the exothermic reaction and the catalyst pellet mass- and heat-transfer resistances. 

It should be understood that this rate expression may in fact represent a set of diffusion and mass transfer equations with their associated boundary conditions, rather than a simple explicit expression. In addition one may write a differential heat balance for a column element, which has the same general form as Eq. (17), and a heat balance for heat transfer between particle and fluid. In a nonisothermal system the heat and mass balance equations are therefore coupled through the temperature dependence of the rate of adsorption and the adsorption equilibrium, as expressed in Eq. (18). 

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. 

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. 

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. 

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