External flow defined

We assume the system under consideration to be a single domain. Then the orientational state of the system can be specified by the order parameter tensor S defined by Eq. (63), The time evolution of S is governed by the kinetic equation, Eq. (64), along with Eqs. (62) and (65). This kinetic equation tells us that the orientational state in the rodlike polymer system in an external flow field is determined by the term F related to the mean-field potential Vscf and by the term G arising from the external flow field. These two terms control the orientation state in a complex manner as explained below. 

The magnitude of the forced fluid velocity, U, relative to the body. The manner in which this is defined will depend on the nature of the problem as indicated in Fig. 1.14. In the case of external flows, the undisturbed ffeestream velocity is usually the most convenient to use for Uy whereas in the case of internal flows it is usually more convenient to take U as the mean or mass average velocity in the duct. 

Consideration will next be given to the determination of the conditions under which the temperature fields are similar. In order to define a dimensionless temper ature variable, a convenient reference fluid temperature, T, and some convenient measure of the wall temperature, 7wr, are introduced. In external flows, T is usu ally most conveniently taken as the freestream temperature while in internal flows it is usually taken as a convenient mean temperature. Using these the following dimensionless temperature is defined ... 

When external force is absent, and using the flows defined by N, = v,c we find... 

C What is the physical significance of the Reynolds number How is it defined for external flow over a plate of length L ... 

C Define frontal area of a body subjected to external flow. When is it appropriate to use the fronial area in drag and lift calculations ... 

Consider the flow of air over the free surface of a water body such as a lake under isothermal conditions. If the air is not saturated, the concentration of water vapor will vtsry from a maximum at the water surface where the air is always saturated to the free steam value far from the surface. In heat convection, we defined the region in which temperature gradients exist as the thermal boundary layer. Similarly, in mass convection, we define the region of the fluid in which concentration gradients exist as the conceniration boundary layer, as shown in Figure 14 -38. In external flow, the thickness of the concentration boundary layer S,. for a. species A at a. specified location on the surface is defined as the normal distance y from the surface at which... 

The temperature of the fluid t F far away from the wall, appears in (1.23), the definition of the local heat transfer coefficient. If a fluid flows around a body, so called external flow, the temperature t F is taken to be that of the fluid so far away from the surface of the body that it is hardly influenced by heat transfer, i) F is called the free flow temperature, and is often written as diDC. However, when a fluid flows in a channel, (internal flow), e.g. in a heated tube, the fluid temperature at each point in a cross-section of the channel will be influenced by the heat transfer from the wall. The temperature profile for this case is shown in Figure 1.8. i) F is defined here as a cross sectional average temperature in such a way that t F is also a characteristic temperature for energy transport in the fluid along the channel axis. This definition of F links the heat flow from the wall characterised by a and the energy transported by the flowing fluid. 

In external flow the free flow temperature SF = is normally constant. Therefore AS will be defined using and the characteristic wall temperature dtfl AS = Stfl — S. If the wall temperature of the body around which the fluid is flowing is constant, then At = Sw —S gives the following for the average heat transfer coefficient ... 

The steady drag is the component of the hydrod3mamic force acting on the particle surface in the continuous phase flow direction. One might, for example, imagine a uniform velocity in the z-direction as sketched in Fig 5.1, and describe the external flow using the Cartesian coordinate system, then the steady drag force is defined by [14, 30] ... 

For an external flow, it is as.sumed that the fluid has a uniform velocity, U, except in the region disturbed by the body. If the concentration in the mainstream of the fluid is a dimensionless concentration can be defined as follows ... 

In general, it is sufficient that the Rayleigh number is asymptotically small, where the Rayleigh number is defined in terms of the characteristic velocity of the external flow, uc, and the characteristic length scale of the flow, lc, as... 

The Reynolds analogy, defined as the ratio of the Stanton number to the local skin friction coefficient St/(c//2) is a function of the Prandtl number and is extremely useful for estimating heat transfer. Pressure drop can be used to predict heat transfer in pipes, and the skin friction can be used to predict Stanton number for external flows. 

The approximation just discussed is valid provided that the external flow rates P and W are small compared to the magnitude of the internal flow. The magnitude of the internal flow is measured by the integral of the axial velocity profile without regard to the sign of w(r), or a flow rate M is defined by... 

Newtonian behavior the rate of shear is small compared to the rate constant for the flow process. When molecular displacements occur very much faster than the rate of shear (7 < kj ), the molecules show maximum efficiency in dissipating the applied forces. When the molecules cannot move fast enough to keep pace with the external forces, they couple with and dissipate those forces to a lesser extent. Thus there is a decrease in viscosity from its upper, Newtonian limit with increasing 7/kj. The rate constant for the flow process is therefore seen to define a standard against which the rate of shear is to be judged large or small. In the next section we shall consider a molecular model in terms of which this rate constant can be analyzed. 

We defined the equation of motion as a general expression of Newton s second law applied to a volume element of fluid subject to forces arising from pressure, viscosity, and external mechanical sources. Although we shall not attempt to use this result in its most general sense, it is informative to consider the equation of motion as it applies to a specific problem the flow of liquid through a capillary. This consideration provides not only a better appreciation of the equation of... 

Figure 1.62b shows the result of raising the potential of a corroding metal. As the potential is raised above B, the current/potential relationship is defined by the line BD, the continuation of the local cell anodic polarisation curve, AB. The corrosion rate of an anodically polarised metal can very seldom be related quantitatively by Faraday s law to the external current flowing, Instead, the measured corrosion rate will usually exceed... 

F = (H+ cosor) (wVe/g) + (Pe-P0)Ae where oc = half of the divergence angle of the nozzle, w - weight rate of proplnt flow, g = acceleration of gravity, Ve = exit flow velocity, Pe = nozzle exit pressure, PQ = external atm pressure, and Ae = cross section at nozzle exit plane. An effective exhaust velocity is defined by... 

The bulk density of a powder is calculated by dividing its mass by the volume occupied by the powder (Abdullah Geldart, 1999). Tapped bulk density, or simply tapped density, is the maximum packing density of a powder achieved under the influence of well-defined, externally applied forces (Oliveira et al., 2010). Because the volume includes the spaces between particles as well as the envelope volumes of the particles themselves, the bulk and tapped density of a powder are highly dependent on how the particles are packed. This fact is related to the morphology of its particles and such parameters are able to predict the powder flow properties and its compressibility. 

Numbering-up can be performed in two ways (Figure 1.4). External numhering-up is referred to as the connection of many devices in a parallel fashion [8] (a similar, but less elaborate, definition was already provided in [9, 10] see also [11] for a realized industrial example). A device in the sense as it is used here is defined as a functional element, e.g. a micro-mixing flow configuration such as an interdigital... 

One method of characterising the residence time distribution is by means of the E-curve or external-age distribution function. This defines the fraction of material in the reactor exit which has spent time between t and t -i- dt in the reactor. The response to a pulse input of tracer in the inlet flow to the reactor gives rise to an outlet response in the form of an E-curve. This is shown below in Fig. 3.20. 

Rheological studies explore the flow of a material as an external force acts upon it. This flow depends not only on the magnitude and directionality of the external force, but also on the molecular composition and structure of the material that experiences the force. In this chapter, we will focus on the flow behavior of molten polymers, as it relates to their molecular structure. It is important to note that the molecular characteristics that determine a molten polymer s behavior also define the polymer s solid state behavior. Therefore, many of the concepts introduced in this chapter will reappear in Chapter 8, Solid State Properties of Polymers., ... 

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