Eddy diffusivity for heat

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. 

It is at = At/gc with the turbulent thermal conductivity or eddy diffusivity for heat transfer1 At (SI units W/K m). The total heat flux is... 

On page 55 an eddy diffusivity for momentum transfer was defined. A corresponding eddy diffusivity for heat transfer can be defined by... 

Similarly, eddy diffusivities for heat and mass transfer, eH and em, respectively, may be defined by the relations... 

The quantity is called the eddy diffusivity for momentum, and ew is the eddy diffusivity for heat. They are related through the turbulent Prandtl number Pr, = eM/eH. 

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... 

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)]. 

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

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 ... 

Mizushina, T., and H. Usui, "Reduction of Eddy Diffusivity for Momentum and Heat in Viscoelastic Fluid Flow in a Circular Tube", Phys. Fluids Suppl., S 100 (1977)... 

Mizushina, T. Usui, H. Reduction of eddy diffusion for momentum and heat in viscoelastic fluid flow in a circular tube. Phys. Fluids 20 (1977) S100-S108. 

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... 

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. 

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... 

The balance between conduction and diffusion still operates for a much larger isolated wet object, provided radiation is excluded. This is the basis of the wet bulb thermometer method for measuring humidity. The actual rate of evaporation now is not as simply determined and is influenced by wind. The wet bulb temperature is almost independent of wind condition, owing to a convenient accident. Heat conduction is a diffusion process, and the diffusion coefficient for water vapor in air (0.24 sq. cm./sec.) is numerically close to the diffusion coefficient of temperature in air (thermal conductivity/specific heat = 0.20 sq. cm./sec.). Hence, the exact way in which each molecular diffusion process merges into the more rapid eddy diffusion process is not important because no matter how complex the transition is, it must be quantitatively similar for the two processes. 

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