Buffer layers

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. 

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)]. 

That tire existence of the buffer layer may be neglected and that in turbulent flow the boundary layer may be considered as consisting of a turbulent region adjacent to a laminar sub-layer which separates it from the surface. 

Equation 11.12 does not fit velocity profiles measured in a turbulent boundary layer and an alternative approach must be used. In the simplified treatment of the flow conditions within the turbulent boundary layer the existence of the buffer layer, shown in Figure 11.1, is neglected and it is assumed that the boundary layer consists of a laminar sub-layer, in which momentum transfer is by molecular motion alone, outside which there is a turbulent region in which transfer is effected entirely by eddy motion (Figure 11.7). The approach is based on the assumption that the shear stress at a plane surface can be calculated from the simple power law developed by Blasius, already referred to in Chapter 3. 

Next, the buffer layer, in which molecular diffusion and eddy motion are of comparable magnitude. 

Equation 12.35 applies only in those regions where eddy transfer dominates, i.e. outside both the laminar sub-layer and the buffer layer (see below). 

The buffer layer covers the intermediate range 5 < >,+ < 30. A straight line may be drawn to connect the curve for the laminar sub-layer (equation 12.40) at y+ = 5 with the line... 

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 ... 

The equation should be compared with equation 11.49 obtained using PrandtTs simplified approach to boundary layer theory which also disregards the existence of the buffer layer ... 

Since the buffer layer is very close to the wall, Ry can be replaced by Rq. 

The original Reynolds analogy involves a number of simplifying assumptions which are justifiable only in a limited range of conditions. Thus it was assumed that fluid was transferred from outside the boundary layer to the surface without mixing with the intervening fluid, that it was brought to rest at the surface, and that thermal equilibrium was established. Various modifications have been made to this simple theory to take account of the existence of the laminar sub-layer and the buffer layer close to the surface. 

Taylor(4) and Prandtl(8 9) allowed for the existence of the laminar sub-layer but ignored the existence of the buffer layer in their treatment and assumed that the simple Reynolds analogy was applicable to the transfer of heal and momentum from the main stream to the edge of the laminar sub-layer of thickness <5. Transfer through the laminar sub-layer was then presumed to be attributable solely to molecular motion. 

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)... 

The method is based on the calculation of the total temperature difference between the fluid and the surface, by adding the components attributable to the laminar sub-layer, the buffer layer and the turbulent region. In the steady state, the heat flux (<70) normal to the surface will be constant if the effects of curvature are neglected. 

In the Universal Velocity Profile , the laminar sub-iayer extends to values of y+ = 5 and the turbulent zone starts at y+ = 30 and the range 5 < y+ < 30, the buffer layer, is covered by a second linear relation between and In, y+. What is the maximum difference between the values of u+, in the range 5 < y4 < 30, using the two methods of representation of the velocity profile ... 

In the buffer zone the value of d +/dy+ is twice this value. Obtain an expression for the eddy kinematic viscosity E in terms of the kinematic viscosity (pt/p) and y+. On the assumption that the eddy thermal diffusivity Eh and the eddy kinematic viscosity E are equal, calculate the value of the temperature gradient in a liquid flowing over the surface at y =15 (which lies within the buffer layer) for a surface heat flux of 1000 W/m The liquid has a Prandtl number of 7 and a thermal conductivity of 0.62 W/m K. 

A schematic of epitaxial growth is shown in Fig. 2.11. As an example, it is possible to grow gallium arsenide epitaxially on silicon since the lattice parameters of the two materials are similar. On the other hand, deposition of indium phosphide on silicon is not possible since the lattice mismatch is 8%, which is too high. A solution is to use an intermediate buffer layer of gallium arsenide between the silicon and the indium phosphide. The lattice parameters of common semiconductor materials are shown in Fig. 2.12. 

A SiC buffer layer was grown on a silicon wafer at 1150-1300°C from one to 45 minutes using C3Hg and H2 as reactant gases. The thickness of the film increased gradually by diffusion of Si into the deposit until a thickness controlled by temperature and silicon etching was reached. 

Ferro, G., et at, Infrared Kinetic Study of Ultrathin CiC Buffer Layers Grown by Reactive CVD, Thin Solid Films, 278(l-2) 22-27(1996)... 

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