Heat Conduction

The following is my summary of relevant parts of a wikipedia article on Heat Conduction and other bits and pieces of information.

Conduction is one of the three ways in which heat can be transferred, the other ways being convection and radiation. Conduction can simply be thought of as heat transfer by “touch”, and only can occur in matter (solids, liquids and gases). Heat energy always flows from areas of higher to lower temperature, it therefore follows a negative temperature gradient. When the temperature has been equalised then a state of thermal equilibirum has been reached and no further heat transfer occurs. Heat transfer in solids is caused by vibration of neighbouring molecules and the movement of free electrons. In liquids and gases, molecules are in random motion and they transfer energy to each other by colliding, and when moving from areas of high to lower concentration (diffusion).

 

Heat transfer in metals is dominated by free electrons transferring heat energy. Because of this, thermal conductivity of metals is related to electrical conductivity. Metals are generally very good conductors, and usually non-metals are poor, the remarkable exception to this is diamond which has a thermal conductivity of up to 5 times greater than silver. This property can be used by gemologists to differentiate real from fake diamonds. In non-metals, phonons (quantised lattice vibrations in crystals) have a larger role in thermal conductivity. See phonon article if further information is desired.

 

Heat transfer in gases is generally low if convection is minimised, air for example is a good insulator when confined in small spaces, such as within animal fur like wool/feathers, or insulation foams used in building and other industries. The inert gas argon (1.8 kg/m³) is denser than air (1.2 kg/m³) and has a lower thermal conductivity, which is the reason it is used in double glazing (k of argon = 0.018 W/m.oC, k of air = 0.025). Lighter gases generally have higher thermal conductivites than heavier gases. Hydrogen is therefore used as a “coolant” in the steam driven rotors of large power stations, such as at Huntly thermal power station (k of hydrogen = 0.18).

 

The law of heat conduction is also called Fourier’s Law after the great French mathematician and physicist Joseph Fourier. It states that the flow rate of heat (measured in Watts) through a material depends on the temperature difference or gradient that exists between two surfaces (measured in degrees Celsius or Kelvin, per metre of thickness), and the thermal conductivity of the material. The thermal conductivity (symbol= k) can be thought of as the heat flow rate through a given square meter of surface area (ie. a flux), for each unit of temperature gradient. The units for thermal conductivity are therefore W/m² per K/m which equates to units of W/m.K or W.m^-1 K^-1.

 

Material	Thermal Conductivity(W/m.K)
Aerogels	0.01
Argon	0.018
Air	0.025
Building insulation	0.04
Water	0.6
Glass	1.1
Concrete	1.3
Sandstone	2.4
Steel	25- 50
Aluminium (pure)	220
Copper	380
Diamond	up to 2300 !

 

Thermal conductivity should not be confused with thermal conductance which is the heat flow through a surface of given area (A) and thickness (L), which equals kA/L and has units of W/K.

eg. A 50 m² concrete wall, of 150mm thickness with one degree celsius temperature will have thermal conductance (or heat flow) of: 1.3 x 50/0.15 = 430 W.

 

Generally, in the building industry one works with thermal resistance or “R-values”, which is the resistance to heat flow of a building component of given material and thickness. The R-value is calculated by the thickness of the wall/roof etc divided by the thermal conductivity. This then allows the various R-values to be added to give one overall R-value for a building element such as a wall, which is typically made of several layers of materials. The heat flow through the wall/roof is then given by the area divided by the thermal resistance ie. Heat Flow = Area/Resistance.

 

If the walls in a building are made up of different sections having differing construction and/or materials the heat flow calculation must be done for each section and added together to find the total heat flow. From this an average weighted R-value may be found R-weighted = total area / total heat flow.