Eucken factor

It turns out to be a surprisingly difficult task to determine accurately the thermal conductivity of polyatomic gases from the viscosity. Many of the approaches are motivated by the ideas of Eucken. The so-called Eucken factor is a nondimensional group determined by dividing the kinetic-theory expression for a monatomic gas by that for viscosity, yielding... 

As discussed, for example, in Reid et al. [332], there are many alternatives for representing the Eucken factor, as well as a variety of other approaches. 

In this equation the kinematic viscosity is v = fi/p, the thermal diffusivity is a = X/p-cp, and cp is the specific heat (per unit mass) at constant pressure. The Prandtl number is related to the Eucken factor as... 

Gases Methods for estimating low-pressure gas thermal conductivities are based on kinetic theory and generally correlate the dimensionless group kM/r C (M = molecular weight, T] = viscosity, C = isochoric heat capacity) known as the Eucken factor. The method of Stiel and Thodos is recommended for pure nonpolar compounds, and the method of Chung is recommended for pure polar compounds. 

Six methods are recommended by Reid et al. (1987) for the estimation of thermal conductivity of nonpolar compounds. These include the corresponding-states methods of Chung et al. (1984, 1988), Ely Hanley (1983) and Hanley (1976). The third method (Roy Thodos 1968, 1970) is recommended for polar as well as nonpolar compounds. Topical errors for nonpolar compounds are 5 to 7%, with higher errors expected for polar compounds. Both the Chung and Ely-Hanley methods correlate the Eucken factor, fy, = XMlriCv, with other variables such as C (heat capacity), Tr and 0) (acentric factor). Thus the viscosity is required to use these correlations. The Roy-Thodos correlation requires only the critical temperature and the pressure, and employs a group contribution method to account for the effect of internal degrees of freedom. 

The thickness 5 of the diffusion boundary layer depends on various factors. For cases where the liquid flows at 90° towards the edge of a plane electrode and parallel to the electrode surface, Vetter [6.5] gives, after Eucken and Levich, for laminar flow ... 

The Agari-Uno model (Agari and Uno 1986) shows that the thermal conductivity data are deviating from the Maxwell-Eucken equation at about a 10% volumetric fraction. At a high filler volume, the measured value was much higher than the prediction using existing correlations. This approach is based on series and parallel models and considers the crystaUmity of both phases and interfacial factor A, as shown in equation (11.5) ... 

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