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THERMAL CONDUCTIVITY
Thermal conduction is the phenomenon by which heat is transported from high to low-temperature regions of a substance. The property that characterizes the ability of a material to transfer
heat is the thermal conductivity. It is best defined in terms of the expression:
q = -k (ΔT/Δx)
where q denotes to the heat flux, or heat flow per unit time per unit area (area being taken as that perpendicular to the flow direction), k is the thermal conductivity, and ΔT/Δx is the temperature gradient through the conducting medium. The units of q and k are W/m2
and W/m. K, respectively. This equation is valid only for steady-state heat flow, that is, for situations in which the heat flux does not change with time. Also, the minus sign in the expression
indicates that the direction of heat flow is from hot to cold, or down the temperature gradient.
This equation is similar in form to Fick's first law:
J= -D (ΔC/Δx)
or atomic diffusion. For these expressions, k is analogous to the diffusion coefficient D, and the temperature gradient, ΔT/Δx parallels the concentration gradient, ΔC/
Δx.
MECHANISM OF HEAT CONDUCTION
Heat is transported in solid materials by both lattice vibration waves (phonons) and free electrons. A thermal conductivity is associated with each of these mechanisms, and the total
conductivity is the sum of the two contributions, or:
k = kl + ke
where kl and ke
represent the lattice vibration and electron thermal conductivities, respectively; usually one or the other predominates. The thermal energy associated with phonons or lattice waves is transported in the direction of their motion. The
kl contribution results from a net movement of phonons from high-to low-temperature regions of a body across which a temperature gradient exists.
Free or conducting electrons participate in electronic thermal conduction. To the free electrons in a hot region of the specimen is imparted a gain in kinetic energy. They then migrate to
colder areas, where some of this kinetic energy is transferred to the atoms themselves (as vibrational energy) as a consequence of collisions with phonons or other imperfections in the crystal. The relative
contribution of ke to the total thermal conductivity increases with increasing free electron concentrations, since more electrons are available to participate in this heat transference process.
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