Question

Value of thermal conductivity decreases with temperature

Answer 1

A material property denoted by λ and defined by Fourier's Law, which for one-dimensional conduction in an isotropic medium is:
(1)

The value of λ is temperature dependent and is usually determined experimentally by methods based on Fourier's Law, i.e.

(2)

where, for example,  is measured for an imposed value of dT/dx. Details of the range of methods used to determine λ for solids, liquids and gases are given by Tye (1969) and Maglic, Cezairliyan and Peletsky (1984, 1992). Values of λ are catalogued by Touloukian and Ho (1970 to 1977), an extensive data bank compiled by the Thermophysical Properties Research Center at Purdue University and continually extended and updated by CINDAS at the same university. Other readily available data books are those by Kaye and Laby (1986) and Perry and Green (1984).

Figure 1 illustrates the very wide range of values of λ for solids, liquids and gases at normal temperatures and pressures.

Figure 1. Spread of λ values for three states of matter.

The temperature dependence of λ values for the three states of matter is exemplified in Figures 2 and 3.

Figure 2. Variation of thermal conductivity of some metals with temperature.

Figure 3. Variation of thermal conductivity of some fluids with temperature.

The thermal conductivity of a metal can usually be correlated with temperature, over a restricted range, using an expression such as: λ = λ0(a + bθ + cθ2) where θ = T – Tref and λ0 is the thermal conductivity at a reference temperature Tref.

The thermal conductivity of a nonhomogeneous solid is usually dependent on the apparent bulk density and as a general rule increases with increasing temperature and increasing bulk density.

Figure 3 shows the temperature dependence of λ for some saturated liquids and vapors, and gases, of engineering importance. λ for most liquids decreases with increasing temperature. The exception is water, which exhibits increasing λ up to about 150°C and decreasing λ thereafter. Water has the highest thermal conductivity of all liquids except for liquid metals.

The thermal conductivity of gases increases with increasing temperature but is essentially independent of pressures for pressures close to atmospheric. λ values for steam exhibit strong pressure dependence.

Methods for the estimation of λ values outside the range of published values and for the λ values of liquid and gas mixtures are described by Reid et al. (1987).