### 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, T_{H} - T_{C}, 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:

P_{cond} | = |
Q | |
t | |
= |
Κ A (T_{H} - T_{C})
| |
L | |
≡ G (T_{H} - T_{C}) |

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