### Thermal Conduction

In thermal conduction, heat is transferred from a hot region to a cooler region through a material. At the hotter end, atoms vibrate more energetically than at the cooler end. The atoms don't flow---instead the energy flow through the material is passed along by the vibrations.

The rate at which heat is conducted along a bar of length L depends on the length, the cross-sectional area A, the temperature difference between the hot and cold ends, TH - TC, and the thermal conductivity k of the material.

There is a one-to-one correspondence between electrical and thermal conduction.

The rate of energy transfer has units of power. If an amount of heat is transferred at a constant rate in a time t, then:

Pcond   =
 Q t
=
 Κ A (TH - TC) L
≡   G (TH - TC)

Here the thermal conductivity Κ is an intrinsic material property, while the thermal conductance G involves both material properties and geometry.

Units of Κ:   power/(length∗degrees K).

Important:

• Thermal conductivity is an instrinsic material property.
• Thermal conductance includes geometrical effects. For a fixed temperature difference:
• wider system → more heat flow;
• longer system → less heat flow.

Metals generally have high thermal conductivities because they contain freely moving electrons that are efficient at transferring energy. Copper, for example, has a thermal conductivity of 400 W/(m K), compared to 0.024 W/(m K) for foam insulation.

Note: thermal resistance and thermal conductance are completely analagous to electrical resistance and electrical conductance.

#### R values

Insulating materials are rated in terms of their R values, which is proportional to (but not exactly equal to) their thermal resistance. Higher R means lower conductivity. In terms of the thickness L of the material, R ≡ L/Κ.

Some typical R values (per inch):

• metal 0
• wood 0.91
• fiberboard 2.78
• fiberglass 3.90
• sprayed polyurethane foam 6.9