External flow laminar forced convection

The /th species mass flux, j, and the total heat flux, q, can be expressed in terms of transfer coefficients. This is useful in situations where the liquid or gas phase is not completely resolved, or when the flow conditions are not exactly known. Often, these transfer coefficients are determined experimentally for a particular flow situation. For instance, different expressions are used, depending on whether the transfer is due to pure conduction or whether it is dominated by ccaivection. Also, the type of convection plays a role, that is, if the convection is forced or non-forced. A forced convection has a non-zero relative velocity between droplet and environment, whereas for a non-forced convection, the relative drop-gas velocity is zero and only the Stefan flow dominates. Note that the natural convection due to gravity is taken to be zero since gravity is an external force, and external forces are neglected in this article. In addition, in forced convection, the nature of the flow, that is, whether the flow is laminar or turbulent, plays an important role. These issues will be discussed in more detail in the following subsections. 

Acrivos, A. 1958. Combined laminar free and forced convection heat transfer in external flows. AIChE Journal. 4. 285-289. 

In electrochemical reactors, the externally imposed velocity is often low. Therefore, natural convection can exert a substantial influence. As an example, let us consider a vertical parallel plate reactor in which the electrodes are separated by a distance d and let us assume that the electrodes are sufficiently distant from the reactor inlet for the forced laminar flow to be fully developed. Since the reaction occurs only at the electrodes, the concentration profile begins to develop at the leading edges of the electrodes. The thickness of the concentration boundary layer along the length of the electrode is assumed to be much smaller than the distance d between the plates, a condition that is usually satisfied in practice. 

As with external mixed convection, the influence of buoyancy forces on the flow depends on the angle that the buoyancy forces makes to the direction of the forced flow. The heat transfer rate also, of course, depends on the duct cross-sectional shape as well as on whether the flow is laminar or turbulent. 

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