Sublayer, laminar

As velocity continues to rise, the thicknesses of the laminar sublayer and buffer layers decrease, almost in inverse proportion to the velocity. The shear stress becomes almost proportional to the momentum flux (pk ) and is only a modest function of fluid viscosity. Heat and mass transfer (qv) to the wall, which formerly were limited by diffusion throughout the pipe, now are limited mostly by the thin layers at the wall. Both the heat- and mass-transfer rates are increased by the onset of turbulence and continue to rise almost in proportion to the velocity. 

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. 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

I0-38Z ) is solved to give the temperature distribution from which the heat-transfer coefficient may be determined. The major difficulties in solving Eq. (5-38Z ) are in accurately defining the thickness of the various flow layers (laminar sublayer and buffer layer) and in obtaining a suitable relationship for prediction of the eddy diffusivities. For assistance in predicting eddy diffusivities, see Reichardt (NACA Tech. Memo 1408, 1957) and Strunk and Chao [Am. ln.st. Chem. Eng. J., 10, 269(1964)]. 

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... 

If the buffer layer is neglected, it has been shown (Section 12.4.4) that the laminar sublayer will extend to y+ = 11.6 giving ... 

In the Taylor-Prandtl modification of the theory of heat transfer to a turbulent fluid, it was assumed that the heat passed directly from the turbulent fluid to the laminar sublayer and the existence of the buffer layer was neglected. It was therefore possible to apply the simple theory for the boundary layer in order to calculate the heat transfer. In most cases, the results so obtained are sufficiently accurate, but errors become significant when the relations are used to calculate heat transfer to liquids of high viscosities. A more accurate expression can be obtained if the temperature difference across the buffer layer is taken into account. The exact conditions in the buffer layer are difficult to define and any mathematical treatment of the problem involves a number of assumptions. However, the conditions close to the surface over which fluid is flowing can be calculated approximately using the universal velocity profile,(10)... 

Within the laminar sublayer the turbulent eddies are negligible, so... 

Equation (6-31) applies to the laminar sublayer region in a Newtonian fluid, which has been found to correspond to 0 < y+ < 5. The intermediate region, or buffer zone, between the laminar sublayer and the turbulent boundary layer can be represented by the empirical equation... 

However, the molecules percolating up into the boundary layer from beneath the soil surface tend to become trapped in the stagnant laminar sublayer of the boundary layer. This sublayer is usually much thinner than the overall turbulent boundary layer, since it is dominated by viscous and surface tension forces, rather than by velocity. Phelan and Webb call this the chemical boundary layer and state categorically that there will generally be no chemical signature above this chemical boundary layer [1, p. 52],... 

Further, if the concentration difference across the laminar sublayer does not vary appreciably with time, Eqs. (2) to (4) may be integrated directly to give linear relations between q and fciAc, between k and D, and between q and Dt( ic/ x). 

In the limit of extreme turbulence, when eddies of fresh solution are rapidly swept into the immediate vicinity of the interface, neither the laminar sublayer nor a stationary surface can exist the diffusion path may, according to Kishinevskii, become so short that diffusion is no longer rate-controlling, and consequently for such liquid-phase transfer (14)... 

Any consideration of mass transfer to or from drops must eventually refer to conditions in the layers (usually thin) of each phase adjacent to the interface. These boundary layers are envisioned as extending away from the interface to a location such that the velocity gradient normal to the general flow direction is substantially zero. In the model shown in Fig. 8, the continuous-phase equatorial boundary layer extends to infinity, but the drop-phase layer stops at the stagnation ring. At drop velocities well above the creeping flow region there is a thin laminar sublayer adjacent to the interface and a thicker turbulent boundary layer between this and the main body of the continuous phase. 

Very near a wall (approaching the laminar sublayer where the turbulence is so small that it is eliminated by the viscosity of the fluid) i.e., for zu v < 35, L (Reichardt, 1951). 

The gas film coefficient is dependent on turbulence in the boundary layer over the water body. Table 4.1 provides Schmidt and Prandtl numbers for air and water. In water, Schmidt and Prandtl numbers on the order of 1,000 and 10, respectively, results in the entire concentration boundary layer being inside of the laminar sublayer of the momentum boundary layer. In air, both the Schmidt and Prandtl numbers are on the order of 1. This means that the analogy between momentum, heat, and mass transport is more precise for air than for water, and the techniques apphed to determine momentum transport away from an interface may be more applicable to heat and mass transport in air than they are to the liquid side of the interface. 

Figure 2.4b shows, conceptually, the velocity distribution in steady turbulent flow through a straight round tube. The velocity at the tube wall is zero, and the fluid near the wall moves in laminar flow, even though the flow of the main body of fluid is turbulent. The thin layer near the wall in which the flow is laminar is called the laminar sublayer or laminar film, while the main body of fluid where turbulence always prevails is called the turbulent core. The intermediate zone between the laminar sublayer and the turbulent core is called the buffer layer, where the motion of fluid may be either laminar or turbulent at a given instant. With a relatively long tube, the above statement holds for most of the tube length, except for... 

Velocity distributions in turbulent flowthrough a straight, round tube vary with the flow rate or the Reynolds number. With increasing flow rates the velocity distribution becomes flatter and the laminar sublayer thinner. Dimensionless empirical equations involving viscosity and density are available that correlate the local fluid velocities in the turbulent core, buffer layer, and the laminar sublayer as functions of the distance from the tube axis. The ratio of the average velocity over the entire tube cross section to the maximum local velocity at the tube axis is approximately 0.7-0.85, and increases with the Reynolds number. 

The transfer of heat and/or mass in turbulent flow occurs mainly by eddy activity, namely the motion of gross fluid elements that carry heat and/or mass. Transfer by heat conduction and/or molecular diffusion is much smaller compared to that by eddy activity. In contrast, heat and/or mass transfer across the laminar sublayer near a wall, in which no velocity component normal to the wall exists, occurs solely by conduction and/or molecular diffusion. A similar statement holds for momentum transfer. Figure 2.5 shows the temperature profile for the case of heat transfer from a metal wall to a fluid flowing along the wall in turbulent flow. The temperature gradient in the laminar sublayer is linear and steep, because heat transfer across the laminar sublayer is solely by conduction and the thermal conductivities of fluids are much smaller those of metals. The temperature gradient in the turbulent core is much smaller, as heat transfer occurs mainly by convection - that is, by... 

If the temperature gradient across the laminar sublayer and the value of thermal conductivity were known, it would be possible to calculate the rate of heat transfer by Equation 2.1. This is usually impossible, however, because the thickness ofthe laminar sublayer and the temperature distribution, such as shown in Figure 2.5, are usually immeasurable and vary with fluid velocity and other factors. Thus, a common engineering practice is the use of the film (or individual) coefficient of heat transfer, h, which is defined by Equation 2.16 and based on the difference between the temperature at the interface, and the temperature of the bulk of fluid, f], ... 

Figure 5.2 shows the temperature gradients in the case of heat transfer from fluid 1 to fluid 2 through a flat metal wall. As the thermal conductivities of metals are greater than those of fluids, the temperature gradient across the metal wall is less steep than those in the fluid laminar sublayers, through which heat must be transferred also by conduction. Under steady-state conditions, the heat flux q (kcal In m 2 or W m ) through the two laminar sublayers and the metal wall should be equal. Thus,... 

The film model referred to in Chapters 2 and 5 provides, in fact, an oversimplified picture of what happens in the vicinity of interface. On the basis of the film model proposed by Nernst in 1904, Whitman [2] proposed in 1923 the two-film theory of gas absorption. Although this is a very useful concept, it is impossible to predict the individual (film) coefficient of mass transfer, unless the thickness of the laminar sublayer is known. According to this theory, the mass transfer rate should be proportional to the diffusivity, and inversely proportional to the thickness of the laminar film. However, as we usually do not know the thickness of the laminar film, a convenient concept of the effective film thickness has been assumed (as... 

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