Eucken formula

The translational part here is obtained from the dilute-gas viscosity according to the approximate Eucken formula... 

The simple Eucken formula leads to relatively good agreement only for low temperatures. The differences above 3(X) K are about 5%, increasing to about 8% at 1000 K. 

Fig. 14.13. Comparison of results for different approximations - Thermal conductivity (b) . Eucken formula,---modified Eucken expression,-Chapman-Cowling modified Eucken expression, van den Oord/Korving expression — via SCIOj ),-using Tj and K (1st approximation),-using rj and k (2nd approximation).

For polyatomic gases that have internal vibrational energy, Eucken has suggested a semiempirical formula for a which seems to fit the data fairly well ... 

As in the case of the diffusion coefficient, the thermal conductivity in fluids can be predicted with satisfactory accuracy using theoretical expressions, such as the formulas of Chapman and Enskog for monoatomic gases, of Eucken for polyatomic ones, or of Bridgman for pure liquids. The thermal conductivity of solids, however, has not yet been predicted using basic thermophysical or molecular properties, just like the analogous diffusion coefficient. Usually, the... 

Two frequently used estimation formulas are based on the original paper of Eucken (1913) and can be analyzed here in terms of the full theory. Starting from equations (4.26)-(4.28), that is, from the isotropic value for the thermal conductivity, it is assumed that there is no exchange of energy between translational and internal modes of motion. 

First, however, the contribution of vibration to the thermal conductivity, which is excluded from the simulation, has to be estimated. Following Evans Watts (1976), a dilute-gas vibrational contribution represented by a Eucken-type formula is considered... 

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