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Fortunately, there is just a small difference between the thermal conductivities of water vapor and air. Thus, it is reasonable to take on the gas mixture in the pores as one component.

Owing to the contribution of both evaporation and conduction, the total heat flux transferred through the membrane can be written as

Within the thermal boundary layer at the permeate side, heat flux is produced in the similar manner as at the feed side, i.e.

where hp (W m"2 K"1) is the film heat transfer coefficient in the boundary layer.

In summary, the heat transfer process in MD includes three steps, and the corresponding regions are the thermal boundary layer of the feed side, the membrane itself and the thermal boundary layer of the permeate side. The heat fluxes for these regions are schematically represented in Fig. 11 in an electrical analog.

3.2. Mass transfer

In general, the mass transfer in MD consists of two steps: one is across the boundary layer at the feed side; the other is across the membrane. The latter is somewhat complicated and includes several basic mechanisms. Fig. 12 illustrates the relationship of all the possible basic mass transfer mechanisms in an electrical analogy. Note that the surface diffusion mechanism, which occurs in the process of gas mass transfer through porous medium, isn't included because it has little influence on the whole process due to the weak molecule-membrane interaction. Herein, it should be mentioned that the occurrence and the weight of a mechanism in mass transfer process rest on many factors, such as the composition of the feed, the fluid dynamics, the operation temperature and pressure, the membrane characteristics, the structure of the membrane module, etc.

If pure water (or other pure volatile solvent) is used as the feed in MD, the concentration of volatile component at the membrane surface is equal to that of the bulk fluid, i.e., no concentration profile exists at the feed side. In this case no mass transfer resistance is associated with the feed, and all mass transfer resistance is concentrated on the membrane itself.

heat conduction through the membrane

If thermal boundary of the feed side thermal boundary of the permeate side vaporation

Fig. 11. Schematic representation of heat transfer in MD.

Poiseuille Flow

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