Thermal Conductivity

In keeping with the theme of material properties from the last post, today we’ll talk about thermal conductivity which is a material property that relates to the conduction of heat.

We’ll use “k” to represent thermal conductivity, although that is by no means universal and a wide variety of symbols, including λ and κ, are commonly used.  Thermal conductivity is defined by:

where q” is the heat flux in the x-direction and T is the temperature.  In general, k could vary with direction, position, temperature, and time although it is a good approximation for many practical problems to consider the thermal conductivity isotropic and constant over a local region and constant in time and independent of temperature.  One notable exception to this is found in analyzing composite materials where it is common to have strong variations in k with direction and position.  Another occurs In situations where there are large temperature differences across a body and the temperature dependence of thermal conductivity becomes important.
In many cases, thermal conductivity exhibits general trends similar to electrical conductivity: metals tend to have high thermal conductivity, while ceramics and gases tend to act as thermal insulators with much lower thermal conductivity.  Sometimes these traits are at odds with each other.  For example, in some electronics applications, it would be desirable to have a material that would act as an electrical insulator while possessing a high thermal conductivity in order to conduct heat away and avoid high temperatures that can damage sensitive components.
The widely used thermal analogy to electrical resistance, discussed at some length here, uses a thermal resistance term which is inversely proportional to the thermal conductivity.  Thus, the thermal conductivity might be thought of as the material property relevant to how “easily” heat is conducted.
These figures supply a few examples of the value of thermal conductivity for purposes of garnering a rough sense of sizes.  The last figure provides a general comparison for the ranges of the first five figures.

 

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