Boundary layer concept

Figure 3.26 Velocity and temperature distribution in a subcooled boiling flow (bubble boundary-layer concept). (From Larson and Tong, 1969. Copyright 1969 by American Society of Mechanical Engineers, New York. Reprinted with permission.)...

Boundary layer concept, 11 751-753 Boundary lubricity additives, 15 213, 224-225... 

The Schmidt number is the ratio of kinematic viscosity to molecular diffusivity. Considering liquids in general and dissolution media in particular, the values for the kinematic viscosity usually exceed those for diffusion coefficients by a factor of 103 to 104. Thus, Prandtl or Schmidt numbers of about 103 are usually obtained. Subsequently, and in contrast to the classical concept of the boundary layer, Re numbers of magnitude of about Re > 0.01 are sufficient to generate Peclet numbers greater than 1 and to justify the hydrodynamic boundary layer concept for particle-liquid dissolution systems (Re Pr = Pe). It can be shown that [(9), term 10.15, nomenclature adapted]... 

The diameter of drug particles and hence the surface specific length L is much smaller than the pipe diameter. For this reason, particle-liquid Reynolds numbers characterizing the flow at the particle surface are considerably lower than the corresponding bulk Reynolds numbers. Particle-liquid Reynolds numbers for particle sizes below 250 pm were calculated to be below Re 1 for flow rates up to 100 mL/min. However, this circumstance does not limit the applicability of the boundary layer concept, since in aqueous hydrodynamic... 

In developing the boundary layer concept, Prandtl suggested an order-of-magnitude evaluation of the terms in the Navier-Stokes equations, which provides an expression (with an unknown proportionality constant) for the... 

Keulegan (K13) applied the semiempirical boundary-layer concepts of Prandtl and von K arm an to the case of turbulent flow in open channels, taking into account the effects of channel cross-sectional shape, roughness of the wetted walls, and the free surface. Most of the results are applicable mainly to deep rough channels and bear little relation to the flow of thin films. 

Figure 9.1 Boundary layer concept for free convection.

Mndhoo, A. and Mohee, R. 2008. Modeling heat loss during self-healing composting based on combined fluid film theory and boundary layer concepts. Journal of Environmental Informatics, 11 74—89. 

The velocity boundary layer concept can be extended to define the temperature and concentration of a fluid. The temperature boundary layer thickness is the distance from the body to a layer at which the temperature is 99% of the temperature from an inviscid solution. The boundary layer thickness for the fluid concentration has the same definition. Their relationships are expressed by [29]... 

The boundary layer concept is attributed to Ludwig Prandtl (1874—1953). His manuscript, published in 1904, formed the basis for the future work on skin friction, heat transfer, and fluid separation. He later made original contributions to finite wing theory and compressibility effects. Theodore von Karman and Max Munk were among his many famous students. 

BOUNDARY-LAYER CONCEPT. LAMINAR FORCED CONVECTION O... 

Sec. 5.1 Boundary-Layer Concept. Laminar Forced Convection O 245... 

Boundary Layer Concept. The transfer of heat between a solid body and a liquid or gas flow is a problem whose consideration involves the science of fluid motion. On the physical motion of the fluid there is superimposed a flow of heat, and the two fields interact. In order to determine the temperature distribution and then the heat transfer coefficient (Eq. 1.14) it is necessary to combine the equations of motion with the energy conservation equation. However, a complete solution for the flow of a viscous fluid about a body poses considerable mathematical difficulty for all but the most simple flow geometries. A great practical breakthrough was made when Prandtl discovered that for most applications the influence of viscosity is confined to an extremely thin region very close to the body and that the remainder of the flow field could to a good approximation be treated as inviscid, i.e., could be calculated by the method of potential flow theory. 

Clearly, as time proceeds, this ratio continues to grow, so that the region of applicability of the zero-order solution, based on the thin thermal boundary layer concept, cannot be extended very far into the collapse phase. This is in accord with the physical facts, since the thermal boundary layer thickness is monotonically increasing, while the bubble radius is shrinking. 

C. Theory of Weak Boundary Layers Concept of Interphase... 

Heat transfer by convection is a complex process but the analysis is simplified by the boundary layer concept. All resistance to heat transfer on the fluid side of a hot surface is supposed to be concentrated in a thin film of fluid close to the solid surface. Transfer within the film is by conduction. The temperature profile for such a process is shown in Figure 7.27. The thickness of the thermal boundary layer is not generally equal to that of the hydrodynamic boundary layer. The heat flux could be expressed as... 

The solutions to Navier-Stokes equations are typically very difficult to arrive at. This fact is attested to by the extraordinary development of numerical computation in fluid mechanics. Only a few exact analytical solutions are known for Navier-Stokes equations. We present in this chapter some laminar flow solutions whose interpretation per se is essential in this regard. We then introduce the boundary layer concept. We conclude the chapter with a discussion on the uniqueness of solutions to Navier-Stokes equations, with special reference to the phenomenon of turbulence. 

The boundary layer concept is introduced when dealing with a flow where the effect of viscosity is confined to the vicinity of solid walls. Such case is obtained when the flow s Reynolds number (introduced in Chapter 3) is sufficiently large. 

The boundary layer concept is formalized when the thickness 5 of the boundary layer is small compared to the geometrical dimensions of the zone of the flow that lies outside the boundary layer. Apart from the case (Figure 1.6(d)) where the boundary layer separates from the wall, the drawings of Figure 1.6 are distorted representations where the boundary layer thickness is exaggerated to show the inside of the boundary layer. The actual boundary layer thickness is very small compared... 

The boundary layer concept is needed to explain the following paradoxes associated with fluid flow ... 

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