Laminar flow mass transfer

Mass transfer for flow inside wetted-wall towers. When a gas is flowing inside the core of a wetted-wall tower the same correlations that are used for mass transfer of a gas in laminar or turbulent flow in a pipe are applicable. This means that Eqs. (7.3-24) and (7.3-25) can be used to predict mass transfer for the gas. For the mass transfer in the liquid film flowing down the wetted-wall tower, Eqs. (7.3-22) and (7.3-23) can be used for Reynolds numbers of 4T/p as defined by Eq. (2.9-29) up to about 1200, and the theoretically predicted values should be multiplied by about 1.5 because of ripples and other factors. These equations hold for short contact times or Reynolds numbers above about 100 (SI). 

Let us begin with the system of mass transfer for flow in a conduit Figure 11-2 illustrates the correlation for heat and mass transfer. Note that the additional parameter as L/D is used in the regimes of laminar and transition flow. Also note that the heat and mass transfer can be described by one correlation at high Reynolds numbers (i.e., 5000 or more). This means that the turbulent mass transfer Nusselt number (by analogy) to equation (6-21) is... 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

The rate of mass transfer in the liquid phase in wetted-waU columns is highly dependent on surface conditions. When laminar-flow conditions prevail without the presence of wave formation, the laminar-penetration theory prevails. When, however, ripples form at the surface, and they may occur at a Reynolds number exceeding 4, a significant rate of surface regeneration develops, resulting in an increase in mass-transfer rate. 

Because this mass-transfer step is so vital, conventional dead-end operation of ultrafilters is veiy rare. There are many ways to depolarize a membrane. Cross-flow is by far the most common. Turbulent flow is more common than laminar flow. 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

The preceding discussion has attempted to formulate the situation for laminar boundary layer flow as accurately as possible and to obtain precise correlation between the heat transfer and mass transfer factors. 

Tlie power for laminar flow is proportional to agitation rate, N2, and if the flow is turbulent the power is proportional to N3Dt2. Let us assume the mass transfer coefficients remain constant (Kha unchanged) ... 

When the flow in the boundary layer is turbulent, streamline flow persists in a thin region close to the surface called the laminar sub-layer. This region is of particular importance because, in heat or mass transfer, it is where the greater part of the resistance to transfer lies. High heat and mass transfer rates therefore depend on the laminar sublayer being thin. Separating the laminar sub-layer from the turbulent part of the boundary... 

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

Obtain the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer and write down the corresponding analogy for mass transfer. For a particular system, a mass transfer coefficient of 8,71 x 10 8 m/s and a heat transfer coefficient of 2730 W/m2 K were measured for similar flow conditions. Calculate the ratio of the velocity in the fluid where the laminar sub layer terminates, to the stream velocity. 

Celata GP, Cumo M, Marcom V, McPhail SJ, Zummo Z (2006) Micro-tube liquid single phase heat transfer in laminar flow. Int. J. Heat Mass Transfer 49 3538-3546... 

Davis EJ, Gill WN (1970) The effect of axial conduction in the waU on heat transfer with laminar flow. Int J Heat Mass Transfer 23 459 70... 

Gamart G, Favre-Marinet M, Asendrych D (2005) Conduction and entrance effects on laminar liquid flow and heat transfer in rectangular micro-channels. Int J Heat Mass Transfer 48 2943-2954... 

Kostic M (1994) On turbulent drag and heat transfer reduction phenomena and laminar heat transfer enhancement in non-circular duct flow of certain non-Newtonian fluid. Int J Heat Mass Transfer 37 133-147... 

Nguyen TV (1992) Laminar heat transfer for thermal developing flow in ducts. Int J Heat Mass Transfer 35 1733-1741... 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

Mass and heat transfer to the walls in turbulent flows is a complex mixture of molecular transport and transport by turbulent eddies. The generally assumed analogy between mass and heat transfer by assuming Sh = Nu, is not valid for turbulent flows [26]. Simulations and measurements have shown that there is a laminar film close to the surface where most of the mass transfer resistance for high Sc liquids is located. This fUm is located below y+ = 1 and for low Sc fluids, and for heat transfer the whole boundary layer is important [27]. 

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