Eddy defined

The value of the random number is applied for the characteristic lifetime of the eddy, defined as... 

At sufficiently high frequency, the electromagnetic skin depth is several times smaller than a typical defect and induced currents flow in a thin skin at the conductor surface and the crack faces. It is profitable to develop a theoretical model dedicated to this regime. Making certain assumptions, a boundary value problem can be defined and solved relatively simply leading to rapid numerical calculation of eddy-current probe impedance changes due to a variety of surface cracks. 

The Stsndard Depth of Penetration is defined as that depth at which the eddy current strength has dropped to 37% of that at the surface. 

L inductance of the solenoid in presence of eddy- current If we define the phases relative to the current then... 

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)]. 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

The difficulty with Eq, (26-58) is that it is impossible to determine the velocity at every point, since an adequate turbulence model does not currently exist, The solution is to rewrite the concentration and velocity in terms of an average and stochastic quantity C = (C) -t- C Uj = (uj) + Uj, where the brackets denote the average value and the prime denotes the stochastic, or deviation variable. It is also helpful to define an eddy diffusivity Kj (with units of area/time) as... 

If there is a temperature gradient within the fluid, the eddies will be responsible for heat transfer and an eddy thermal diffusivity Ep may be defined in a similar way. It is suggested that, since the mechanism of transfer of heat by eddies is essentially the same as that for transfer of momentum, Eh is related to mixing length and velocity gradient in a similar manner. 

On a similar basis an eddy diffusivity for mass transfer Er> can be defined for systems in which concentration gradients exist as ... 

The main reasons for the damage to cells in a reactor are the apparent shear forces and the collision of microcarriers with themselves and with turbulent eddies. In the literature studies are mainly focused on suspension cells and there again on hybridoma cells. The work reported in the hterature can be divided into two fields studies dealing with the influence of various stirrer speeds on cell viability and those investigating the influence of defined shear forces on cells with a viscosimeter. 

Cherry and Papoutsakis [33] refer to the exposure to the collision between microcarriers and influence of turbulent eddies. Three different flow regions were defined bulk turbulent flow, bulk laminar flow and boundary-layer flow. They postulate the primary mechanism coming from direct interactions between microcarriers and turbulent eddies. Microcarriers are small beads of several hundred micrometers diameter. Eddies of the size of the microcarrier or smaller may cause high shear stresses on the cells. The size of the smallest eddies can be estimated by the Kolmogorov length scale L, as given by... 

If a susceptor such as a metal crucible is placed within the coil. The R.F. power induces "eddy-currents" in the crucible, causing it to heat up. Eddy-currents are circular electrical currents induced within the metal by the R.F. field of the coil. It is essentially a "skin" effect, and the depth of penetration, l.e.- depth of eddy-current generation within the crucible is defined by ... 

The time-average velocity (u) obviously has zero components in the y and z directions, but the eddy velocity components are nonzero in all three directions. The time-average velocity is defined as... 

Carbon cpntent of reservoirs atmosphere (SJ, biosphere (Nb), mixed layer (N,J, and ocean (N0J. R is the t4C concentration of C in the reservoir and atmospheric concentration is defined as 100 percent. The I4C concentrations are corrected for isotopic fractionation to a common 8,3C = —25 per mil. K is the eddy diflusivity, and S,aC is the i3C concentration deviation from a standard. 

An additional equation is required to describe the turbulent flux. The usual approach is to define an eddy diffusivity Kj (with units of area/time) such that... 

An attempt has been made by Tsouris and Tavlarides[5611 to improve previous models for breakup and coalescence of droplets in turbulent dispersions based on existing frameworks and recent advances. In both the breakup and coalescence models, two-step mecha-nisms were considered. A droplet breakup function was introduced as a product of droplet-eddy collision frequency and breakup efficiency that reflect the energetics of turbulent liquid-liquid dispersions. Similarly, a coalescencefunction was defined as a product of droplet-droplet collision frequency and coalescence efficiency. The existing coalescence efficiency model was modified to account for the effects of film drainage on droplets with partially mobile interfaces. A probability density function for secondary droplets was also proposed on the basis of the energy requirements for the formation of secondary droplets. These models eliminated several inconsistencies in previous studies, and are applicable to dense dispersions. 

Note that at high Reynolds number Xg lies at scales between L and 77, and thus cannot be given a clear physical interpretation in terms of eddies in the flow. Nevertheless, the Taylor microscale is often used to define the Taylor-scale Reynolds number ... 

In a fully developed turbulent flow, the rate at which the size of a scalar eddy of length l,P decreases depends on its size relative to the turbulence integral scale L and the Kolmogorov scale ij. For scalar eddies in the inertial sub-range (ij < Ip, < Lu), the scalar mixing rate can be approximated by the inverse of the spectral transfer time scale defined in (2.68), p. 42 8... 

We note the similarity of Eqs. (3.27) and (3.15). In particular, if we define o- = 2X t, o-y = 2Kyyt, and = 2K t, the two expressions are identical when y = w = 0. Thus, we see that the mean concentration from an instantaneous point source in an infinite fluid with stationary, homogeneous turbulence has a Gaussian form, with the variances of the concentration distribution related to the variances of the wind velocity fluctuations or to constant eddy difihisivities. 

If we define AT as the eddy diffusivity for momentum, the vertictil eddy diffusion coefficient under unstable conditions can be expressed as... 

Convection-based systems fall into two fundamental classes, namely those using a moving electrode in a fixed bulk solution (such as the rotated disc electrode (RDE)) and fixed electrodes with a moving solution (such as flow cells and channel electrodes, and the wall-jet electrode). These convective systems can only be usefully employed if the movement of the analyte solution is reproducible over the face of the electrode. In practice, we define reproducible by ensuring that the flow is laminar. Turbulent flow leads to irreproducible conditions such as the production of eddy currents and vortices and should be avoided whenever possible. 

The thermal motion of molecules of a given substance in a solvent medium causes dispersion and migration. If dispersion takes place by intermolecular forces acting within a gas, fluid, or solid, molecular diffusion takes place. In a turbulent medium, the migration of matter within it is defined as turbulent diffusion or eddy diffusion. Diffusional flux J is the product of linear concentration gradient dCldX multiphed by a proportionality factor generally defined as diffusion coefficient (D) (see section 4.11) ... 

We shall define a closed vessel to be one for which fluid moves in and out by bulk flow alone. Plug flow exists in the entering and leaving streams. In a closed vessel diffusion and dispersion are absent at entrance and exit so that we do not, for example, have material moving upstream and out of the vessel entrance by swirls and eddies. 

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