Heat naturally flows from higher-temperature regions to lower-temperature regions. The three basic mechanisms by which heat is transferred are conduction, convection, and radiation. We'll look at each of these separately, but in a given situation more than one mechanism might be important.

Thermal conduction involves energy in the form of heat being transferred from a hot region to a cooler region through a material. At the hotter end the atoms, molecules, and electrons vibrate with more energy than they do at the cooler end. The atoms, molecules, and electrons generally don't flow from one place to the other - instead the energy flows through the material, 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.

The rate of energy transfer is power, so:

Pcond

=

Q t

=

k A (TH - TC) L

Metals generally have high thermal conductivities because of the free electrons that move around randomly. These are very efficient at transferring energy through the metal. Copper, for instance, has a thermal conductivity of 400 W/(m K), compared to 0.024 W/(m K) for foam insulation.

R values

Insulating materials are rated in terms of their R values, which measures their resistance to conduction. The higher the R, the lower the conductivity. In terms of the thickness L:

R

=

L k

Heat transfer in fluids generally takes place via convection, in which flowing fluid carries heat from one place to another. Convection currents are produced by temperature differences. Hotter (less dense) parts of the fluid rise, while cooler (more dense) areas sink. Birds and gliders make use of upward convection currents to rise, and we also rely on convection to remove ground-level pollution.

Forced convection, where the fluid does not flow of its own accord but is pushed, is often used for heating (e.g., forced-air furnaces) or cooling (e.g., fans, automobile cooling systems).

Thermal radiation involves energy transferred via electromagnetic waves. Often this is infrared radiation, but it can also be visible light or radiation of higher energy.

Thermal radiation is relatively safe, and is not the dangerous nuclear radiation associated with nuclear bombs, etc.

All objects continually absorb thermal energy and radiate it away again. When everything is at the same temperature, the amount of energy received is equal to the amount given off and no changes in temperature occur. If an object emits more than it absorbs, though, it cools down.

For an object with a temperature T (in Kelvin) and a surface area A, the net rate of radiated energy depends strongly on temperature:

P_net = P_rad - P_abs = σεA(T⁴ - T_env⁴)

where T_env is the temperature of the surrounding environment, and
the Stefan-Boltzmann constant σ = 5.67 x 10^-8 W/m²

ε is known as the emissivity. It is a measure of how efficiently an object absorbs and emits radiated energy. Highly reflective objects have emissivities close to zero. Black objects have emissivities close to 1. An object with ε = 1 is called a perfect blackbody,

The best absorbers are also the best emitters. Black objects heat up faster than shiny ones, but they cool down faster too.