Eddy diffusivity of heat

B Eddy diffusivity 8 for eddy diffusivity of momentum 8 for eddy diffusivity of heat mVs fft/h... 

THE/EDDy DIFFUSIVITY OF HEAT. When there is no temperature gradient across the isothermal surface, all eddies have the same temperature independent of the point of origin, dT/dy = 0, and no net heat flow occurs. If a temperature gradient exists, an analysis equivalent to that leading to Eq. (3.17) shows that the eddies carry a net heat flux from the higher temperature to the lower, in accordance with the equation... 

Eddy Diffusivity Models. The mean velocity data described in the previous section provide the bases for evaluating the eddy diffusivity for momentum (eddy viscosity) in heat transfer analyses of turbulent boundary layers. These analyses also require values of the turbulent Prandtl number for use with the eddy viscosity to define the eddy diffusivity of heat. The turbulent Prandtl number is usually treated as a constant that is determined from comparisons of predicted results with experimental heat transfer data. 

Cho and Hartnett [108,109] calculated the eddy diffusivity of heat for drag-reducing viscoelastic fluids using a successive approximation technique. The result for the minimum asymptotic case can be expressed in the following polynomial equation with respect to y ... 

Heat and mass eddy diffusivity The evidence is that with Prandtl and Schmidt numbers close to unity, as for most gases, the eddy diffusivities of heat and mass are equal to the momentum eddy diffusivity for all regions of turbulence [15], For turbulent fluids where Prandtl and Schmidt numbers exceed unity, the ratios E jand E /E will vary with location relative to the wall and in the turbulent core will lie generally in the range 1,2 to 1.3, with E and essentially equal [44, 62], For = 0 to 45, with Pr and Sc > 1, a critical analysis of the theoretical and experimental evidence [44] led to... 

Noncatalytic gas-solid reactions in mixed bed systems usually involve the movement of a reaction front in the direction of the flow and radial gradients of concentration are usually not very signfiicant. It follows that radial dispersion usually plays an insignificant role in mass transfer problems. However, radial eddy diffusion of heat (eddy thermal conductivity) may play an important role in reactors that are heated or cooled through the bounding walls. An interesting example of this type has been presented by Amundson [20]. 

A closer look at the Lewis relation requires an examination of the heat- and mass-transfer mechanisms active in the entire path from the hquid—vapor interface into the bulk of the vapor phase. Such an examination yields the conclusion that, in order for the Lewis relation to hold, eddy diffusivities for heat- and mass-transfer must be equal, as must the thermal and mass diffusivities themselves. This equahty may be expected for simple monatomic and diatomic gases and vapors. Air having small concentrations of water vapor fits these criteria closely. 

Time of Mixing The Dead Sea. Although it has been stressed earlier that the relationship between N and K established for one lake may not hold for another lake, in the present case the relationship between N and K derived for the thermocline of Lake Tiberias is the only one available and the only one which may be applied to estimate the eddy diffusion coefficients in the pycnocline of the Dead Sea. Implicit is an assumption that the eddy diffusivity of dissolved salts is equal to that of heat. 

To further verify the above conclusion on the failure of the analogy between momentum and heat transfer in the case of viscoelastic fluids, the approximate values of the eddy diffu-sivities of momentum and heat transfer corresponding to the minimum asymptotic cases will be compared. The eddy diffusivity of momentum corresponding to the minimum asymptotic case was calculated by Kale [84] directly from Deissler s continuous eddy diffusivity model ... 

We can extend the mixing-length concept to the turbulent heat flux. We consider the same shear flow as above, in which buoyancy effects are, for the moment, neglected. The mean vertical turbulent heat flux is pcpu O. By analogy to the definition of the eddy viscosity, we can define an eddy diffusivity for heat transfer by... 

The three eddy diffusivities of momentum, heat, and mass can be computed from measured velocity, temperature, and concentration gradients, respectively, in that order of increasing difficulty. 

In the case of turbulent flow, the differential equations will contain time-averaged velocities and in addition the eddy diffusivities of momentum, mass, and heat transfer. The resulting equations cannot be solved for lack of information about the eddy diffusivities, but one might expect results of the form... 

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)]. 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

The energy of large and medium-size eddies can be characterized by the turbulent diffusion coefficient. A, m-/s. This parameter is similar to the parameter used by Richardson to describe turbulent diffusion of clouds in the atmosphere. Turbulent diffusion affects heat and mass transfer between different zones in the room, and thus affects temperature and contaminant distribution in the room (e.g., temperature and contaminant stratification along the room height—see Chapter 8). Also, the turbulent diffusion coefficient is used in local exhaust design (Section 7.6). 

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

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. 

Conduction of heat Highest of all liquids Although important on small scale, as in living cells, the molecular processes are far outweighed by eddy diffusion... 

Diffusion The transfer of matter or heat as a result of molecular motion. This motion causes net transport from regions of high concentration (or heat) to regions of lower concentration. In the absence of gradients, this motion is random and causes no net transport. Also see Eddy diffusion. 

The radial dispersion coefficient for this case is, of course, the average eddy diffusivity as discussed in works on turbulence (H9). If the various analogies between momentum, heat, and mass transport are used. 

The relative importance of gas-phase and surface resistances depends on the nature of the pollutant and the surface as well as the meteorology (Shaw, 1984 Unsworth et al., 1984 Chameides, 1987 Wesely and Hicks, 1999). The gas-phase resistance (rgas) is determined by the vertical eddy diffusivity, which depends on the evenness of the surface and the meteorology, for example, wind speed, solar surface heating, and so on. The surface resistance (rsur[) depends on the detailed characteristics of the surface (e.g., type, whether... 

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