Heat conduction (as opposed to electrical conduction) is the flow of internal energy from a region of higher temperature to one of lower temperature by the interaction of the adjacent particles (atoms, molecules, ions, electrons, etc.) in the intervening space.

Note: it's the rate (Φ) at which heat is transferred, not the amount (Q) of heat transferred.

Φ̅ =  ΔQ
Φ =  dQ

W =  J

Factors affecting the rate of heat transfer by conduction.

  1. temperature difference
  2. length
  3. cross-sectional area
  4. material
Φ =  kAΔT

Fourier's law (compare to Ohm's law)

Φ =  P  =  ΔQ  = − k ∇T
A A Δt

Conductivities vary for material being greatest for metallic solids, lower for nonmetallic solids, very low for liquids, and extremely low for gases. The best ordinary metallic conductors are (in decreasing order) silver, copper, gold, aluminum, beryllium, and tungsten. Diamond beats them all, and graphite beats diamond only if the heat can be forced to conduct in a direction parallel to the crystal layers. The material with the greatest thermal conductivity is a superfluid form of liquid helium called helium II, which only exists at temperatures below 2.17 K. Since it is highly unlikely you will encounter this substance, it is really not worth thinking about except in the fact that it is an exceptional material.