Flow over a surface

When a gas or liquid flows over a surface, the pressure at the surface is reduced according to the formula shown in equation (1), in which d is the density and v is the linear flow velocity of the moving stream. 

The drop in pressure when a stream of gas or liquid flows over a surface can be estimated from the given approximate formula if viscosity effects are ignored. The example calculation reveals that, with the sorts of gas flows common in a concentric-tube nebulizer, the liquid (the sample solution) at the end of the innermost tube is subjected to a partial vacuum of about 0.3 atm. This vacuum causes the liquid to lift out of the capillary, where it meets the flowing gas stream and is broken into an aerosol. For cross-flow nebulizers, the vacuum created depends critically on the alignment of the gas and liquid flows but, as a maximum, it can be estimated from the given formula. 

Any of various types of heat transfer equipment, whereby relatively cold water flowing over a surface will, by conduction and convection means, transfer heat away from a process. The most common types of heat exchangers are plate and frame and shell and tube designs. A boiler is also a type of heat exchanger. 

When a fluid flows over a surface, that part of the stream which is close to the surface suffers a significant retardation, and a velocity profile develops in the fluid. The velocity gradients are steepest close to the surface and become progressively smaller with distance from the surface. Although theoretically there is no outer limit at which the velocity gradient becomes zero, it is convenient to divide the flow into two parts for practical purposes. 

When a viscous fluid flows over a surface it is retarded and the overall flowrate is therefore reduced. A non-viscous fluid, however, would not be retarded and therefore a boundary layer would not form. The displacement thickness 8 is defined as the distance the surface would have to be moved in the 7-direction in order to obtain the same rate of flow with this non-viscous fluid as would be obtained for the viscous fluid with the surface retained at x = 0. 

If a concentration gradient exists within a fluid flowing over a surface, mass transfer will take place, and the whole of the resistance to transfer can be regarded as lying within a diffusion boundary layer in the vicinity of the surface. If the concentration gradients, and hence the mass transfer rates, are small, variations in physical properties may be neglected and it can be shown that the velocity and thermal boundary layers are unaffected 55. For low concentrations of the diffusing component, the effects of bulk flow will be small and the mass balance equation for component A is ... 

Obtain the Taylor-Prandtl modification of the Reynolds Analogy between momentum transfer and mass transfer (equimolecular counterdiffusion) for the turbulent flow of a fluid over a surface. Write down the corresponding analogy for heat transfer. State clearly the assumptions which are made. For turbulent flow over a surface, the film heat transfer coefficient for the fluid is found to be 4 kW/m2 K. What would the corresponding value of the mass transfer coefficient be. given the following physical properties ... 

Annular flow, wavy interface (Henry, 1971) Under this condition the virtual mass of gas flowing over a wavy surface can be approximated by flow over a surface made of continuous rows of half-cylinders ... 

Borishansky, V. M., 1953, Heat Transfer to Liquid Freely Flowing over a Surface Heated to a Temperature above the Boiling Point, in Problems of Heat Transfer during a Change of State A Collection of Articles, S. S. Kutateladze, ed., Rep. AEC-tr-3405, p. 109. (2)... 

It is shown in Volume 1, Chapter 11 that, when a viscous fluid flows over a surface, the fluid is retarded in the boundary layer which is formed near the surface and that the boundary layer increases in thickness with increase in distance from the leading edge. If the pressure is falling in the direction of flow, the retardation of the fluid is less and the... 

Any of various types of heat-transfer equipment, whereby relatively cold water flowing over a surface will, by conduction and convection... 

An illustration of its application is where a very thin sheet of liquid flows over a surface. 

In some cases it is not possible to consider the modes separately. For example, if a gas, such as water vapor or carbon dioxide, which absorbs and generates thermal radiation, flows over a surface at a higher temperature, heat is transferred from the surface to the gas by both convection and radiation. In this case, the radiant heat exchange influences the temperature distribution in the fluid. Therefore, because the convective heat transfer rate depends on this temperature distribution in the fluid, the radiant and convective modes interact with each other and cannot be considered separately. However, even in cases such as this, the calculation procedures developed for convection by itself form the basis of the calculation of the convective part of the overall heat transfer rate. 

Consider a fluid flowing over a surface which is maintained at a temperature that is different from that of the bulk of the fluid as shown in Fig. 1.8. 

Attention will, lastly, be given to the Prandtl number. Consider a steady flow over a surface which is at a different temperature from the fluid flowing over the surface, the situation considered being shown in Fig. 1.20. 

The program, as available, will calculate flow over a surface with a varying free-stream velocity and varying surface temperature. These variations are both assumed to be described by a third-order polynomial, i.e., by ... 

If the Darcy assumptions are used then with forced convective flow over a surface in a porous medium, because the velocity is not assumed to be 0 at the surface, there is no velocity change induced by viscosity near the surface and there is therefore no velocity boundary layer in the flow over the surface. There will, however, be a region adjacent to the surface in which heat transfer is important and in which there are significant temperature changes in the direction normal to the surface. Under many circumstances, the normal distance over which such significant temperature changes occur is relatively small, i.e., a thermal boundary layer can be assumed to exist around the surface as shown in Fig. 10.9, the ratio of the boundary layer thickness, 67, to the size of the body as measured by some dimension, L, being small [15],[16]. 

Attention will be given to flow over a surface with a specified temperature and the following dimensionless variables are introduced for convenience ... 

With air flowing over a surface, the boundary layer thickness 8 increases along the surface in the direction of flow (Davies, 1966) ... 

In this section we shall consistently refer to resistivity, rather than to its reciprocal, conductivity. The choice is arbitrary, and commercial instruments are sometimes calibrated in units of resistance and sometimes in units of conductance.1 Unless otherwise stated, when we refer to resistivity we shall mean volume resistivity pv (Am), the resistance between opposite faces of a unit cube. A surface resistivity ps is often used to characterise current flow over a surface, as with an antistatic coating, and is defined as the resistance between opposite edges of a unit square. We note first that the resistance across a square is independent of the size of the square and that the unit of surface resistivity is simply the ohm (Q), occasionally written rather superfluously as ohm per square. Secondly, a conducting surface must in reality be a layer with a finite thickness t, and we have only an effective surface resistivity, which is related to the true volume resistivity of the layer by... 

Convection is classified as natural (or free) and forced convection, depend ing on how the fluid motion is initiated. In forced convection, the fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan. In natural convection, any fluid motion is caused by natural means such as the buoyancy effect, which manifests itself as the rise of warmer fluid and the fall of the cooler fluid. Convection is also classified a.s external and internal, depending on whether the fluid is forced to flow over a surface or in a pipe. 

We have seen that a velocity boundary layer develops when a fluid flows over a surface as a result of the fluid layer adjacent to the surface assuming the surface velocity (i.e., zero velocity relative to the surface). Also, we defined the velocity boundary layer as the region in which the fluid velocity varies from zero to 0.99V. Likewise, a thermal boundary layer develops when a fluid at a specified temperature flows over a surface that is at a different temperature, as shown in Fig. 6-15. 

Differential control volume used in the derivation of mass balance in velocity boundary layer in two-dimensional flow over a surface. 

These analogies are also applicable approximately for turbulent flow over a surface, even in the presence of pressure gradients. 

C Wilt a thermal boundary layer develop in flow over a surface even if both the fluid and the surface arc at the same temperature ... 

When a gas flows over a surface, the molecules leave some of their momentum and create shear stress on the wall. As shown in figure 2, specular reflections conserve the tangential momentum of molecules, and diffuse reflections results in vanishing tangential momentum. The fraction of the molecules that are diffusely reflected by the wall is defined as the tangential momentum... 

J An aerosol containing l- m particles with a density of 2 g/cm and a thermal conductivity of 3.5 X I0 cai/cm sec K flows over a surface. Calculate the minimum temperature gradient at the surface necessary to prevent particle depo.sLlion by sedimentation. Neglect diffusion and assume that the air flow is parallel to the surface, which is maintained at 20X. 

Similar results may be obtained for convective mass transfer. If a fluid of species concentration Ci, flows over a surface at which the species concentration is maintained at some value Clilv C, transfer of the species by convection will occur. Species 1 is typically a vapor that is transferred into a gas stream by evaporation or sublimation at a liquid or solid surface, and we are interested in determining the rate at which this transfer occurs. As for the case of heat transfer, such a calculation may be based on the use of a convection coefficient [3, 5]. In particular we may relate the mass flux of species 1 to the product of a transfer coefficient and a concentration difference... 

Because it pertains to the fluid velocity, the boundary layer described above may be referred to more specifically as the velocity boundary layer. Just as a velocity boundary layer develops when there is fluid flow over a surface, a thermal boundary layer must develop if the fluid free stream and surface temperatures differ. Similarly, a concentration boundary layer must develop if the fluid free stream and surface concentrations differ. Figure 2.1 illustrates how the thickness of the concentration boundary layer increases with distance x from the leading edge. 

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