Eddy thermal diffusivity

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. 

It has been shown that it is reasonable to assume that the eddy kinematic viscosity E and the eddy thermal diffusivity Eh are equal. The variation of E through the buffer zone is... 

In the buffer zone the value of d +/dy+ is twice this value. Obtain an expression for the eddy kinematic viscosity E in terms of the kinematic viscosity (pt/p) and y+. On the assumption that the eddy thermal diffusivity Eh and the eddy kinematic viscosity E are equal, calculate the value of the temperature gradient in a liquid flowing over the surface at y =15 (which lies within the buffer layer) for a surface heat flux of 1000 W/m The liquid has a Prandtl number of 7 and a thermal conductivity of 0.62 W/m K. 

It has been assumed that the density is constant in writing these equations, which are therefore strictly valid only for incompressible flow. ed is called the eddy diffusivity and eh the eddy thermal diffusivity. Although s can be interpreted as the eddy diffusivity of momentum, it is usually called the eddy viscosity and sometimes by the better name eddy kinematic viscosity. 

In the above equations, pi, Ejy, and v are eddy thermal diffusivity, eddy diffusivity, and eddy kinematic viscosity, respectively, all having the same dimensions (L- ). It should be noted that these are not properties of fluid or system, because... 

Ed, Eh, Ey Eddy diffusivity, Eddy thermal diffusivity, and Eddy kinematic viscosity, respectively (m2 h-1 or cm2 s-1)... 

C Prandtl Mixing Length and Eddy Thermal Diffusivity... 

The term L dvfldy by Eq. (3.10-29) is the momentum eddy diffusivity e,. When this term is in the turbulent heat-transfer equation (5.7-24), it is called a, eddy thermal diffusivity. Then Eq. (5.7-24) becomes... 

Similarities among momentum, heat, and mass transport. Equation (5.7-26) is similar to Eq. (5.7-20) for total momentum transport. The eddy thermal diffusivity a, and the eddy momentum diffusivity s, have been assumed equal in the derivations. Experimental data show that this equality is only approximate. An eddy mass diffusivity for mass transfer has also been defined in a similar manner using the Prandtl mixing length theory and is assumed equal to a, and e,. 

In these equations e, is the turbulent or eddy momentum diffusivity in mVs, a, the turbulent or eddy thermal diffusivity in mVs, and the turbulent or eddy mass diffusivity in mVs. Again, these equations are quite similar to each other. Many of the theoretical equations and empirical correlations for turbulent transport to various geometries are also quite similar. 

Introduction. In molecular transport of momentum, heat, or mass there are many similarities, which were pointed out in Chapters 2 to 6. The molecular diffusion equations of Newton for momentum, Fourier for heat, and Fick for mass are very similar and we can say that we have analogies among these three molecular transport processes. There are also similarities in turbulent transport, as discussed in Sections 5.7C and 6.1A, where the flux equations were written using the turbulent eddy momentum diffusivity e, the turbulent eddy thermal diffusivity a, and the turbulent eddy mass diffusivity. However, these similarities are not as well defined mathematically or physically and are more difficult to relate to each other. 

In many applications the flow in mass transfer is turbulent and not laminar. The turbulent flow of a fluid is quite complex and the fluid undergoes a series of random eddy movements throughout the turbulent core. When mass transfer is occurring, we refer to this as eddy mass diffusion. In Sections 3.10 and 5.7 we derived equations for turbulent eddy thermal diffusivity and momentum diffusivity using the Prandtl mixing length theory. 

A recent model (1988) was published by J. Guttierrez Gonzalez et al. According to the authors, although the liquid fiow is laminar, due to the high Schmidt number in the liquid phase, eddy mass transfer can be significant and eddy diffusion cannot be disregarded with respect to molecular diffusion. Eddy thermal diffusion in the liquid phase is much smaller than thermal diffusion, so that it is not introduced in the microscopic heat balance. The Spanish authors needed to validate their results on practical data. The pressure drop over the reactor, heat- and mass transfer were fitted. 

In similar fashion, an eddy thermal diffusivity //> length /time, can be used to describe the flux of heat as a result of a temperature gradient,... 

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