Heat transfer

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.

Conduction

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, TH - TC, and the thermal conductivity k of the material.

The rate of energy transfer is power, so:

Pcond = Q/t = kA(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.

R = L/k

Convection

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).

The black can and the shiny can

Two cans, one black and one reflective, are at room temperature. They are then exposed to a heat lamp. Which one heats up fastest? The cans are identical except for their surfaces.

  1. the black can
  2. the shiny can
  3. they heat up at the same rate

We've probably all noticed, by leaving black objects out in the sun, that they heat up fastest. The black can absorbs radiation more efficiently than does the shiny can, which reflects most of the radiation away.

The same two cans are then filled with hot water. Which cools down fastest?

  1. the black can
  2. the shiny can
  3. they cool down at the same rate

Thermal Radiation

Energy transferred by thermal radiation is transferred in the form of 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.

We, and everything around us, are continually absorbing radiated energy, and radiating 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. Hotter objects emit more energy than they absorb, and colder objects absorb more than they emit.

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

Pnet = Prad - Pabs = σεA(T4 - Tenv4)

where Tenv 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, on the other hand, generally absorb and emit radiation very well, and 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.