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where m D viscosity of mixture,
m D density of mixture, CHEMICAL ENGINEERING
x 1 ,x 2 D mol fraction of components,
M 1 ,M 2 D molecular masses of components.
Bretsznajder (1971) gives a detailed review of the methods that have been developed
for estimating the viscosity of mixtures, including methods for aqueous solutions and
dispersions.
For heat-transfer calculations, Kern (1950) gives a rough rule of thumb for organic
liquid mixtures:

1 w 1 w 2
D C 8.11
m 1 2

where w 1 ,w 2 D mass fractions of the components 1 and 2,
1 , 2 D viscosities of components 1 and 2.

8.7.2 Gases
Reliable methods for the prediction of gas viscosities, and the effect of temperature and
pressure, are given by Bretsznajder (1971) and Reid et al. (1987).
Where an estimate of the viscosity is needed to calculate Prandtl numbers (see Volume 1,
Chapter 1) the methods developed for the direct estimation of Prandtl numbers should be
used.
For gases at low pressure Bromley (1952) has suggested the following values:

Prandtl number
Monatomic gases (e.g. Ar, He) 0.67 š 5 per cent
Non-polar, linear molecules (e.g. O 2 ,Cl 2 ) 0.73 š 15 per cent
Non-polar, non-linear molecules (e.g. CH 4 ,C 6 H 6 ) 0.79 š 15 per cent
Strongly polar molecules (e.g. CH 3 OH, SO 2 ,HCl) 0.86 š 8 per cent

The Prandtl number for gases varies only slightly with temperature.

8.8 THERMAL CONDUCTIVITY

The experimental methods used for the determination of thermal conductivity are
described by Tsederberg (1965), who also lists values for many substances. The four-
volume handbook by Yaws (1995 1999) is a useful source of thermal conductivity data
for hydrocarbons and inorganic compounds.

8.8.1. Solids
The thermal conductivity of a solid is determined by its form and structure, as well as
composition. Values for the commonly used engineering materials are given in various
handbooks.