1.1 Conduction

Conduction is the transfer of energy due to either random molecular motion or due to the motion of free electrons.

  • In different phases of matter, the modes of conduction are slightly different:

    • Gases—conduction is due to collisions of randomly moving molecules.

    • Liquids—similar to gases, but with a much smaller “mean free path”.

    • Solids—conduction is due to lattice vibrations and/or motion of “free" electrons.

  • In solid bodies, conduction is the significant heat transfer mechanism because no material flows in the process. With flowing fluids, conduction dominates in the region very close to the solid boundary, where the flow is laminar and parallel to the surface where there is no eddy motion.

Fourier’s Law

\[\text{Rate of heat conduction} \propto \frac{\text{area}\times\text{temperature difference}}{\text{thickness}}\] i.e., \[Q = -kA\frac{dT}{dx} \tag*{(1)}\] Fourier’s law is a phenomenological law developed from observed phenomena rather than being derived from first principles.

Heat transfer rate in \(x\) direction is proportional to the temperature gradient, \(dT/dx\). The proportionality constant \(k\) is a transport property known as ‘thermal conductivity’ and is a characteristic of the material. The minus sign is a consequence of the fact that heat is transferred in the direction of decreasing temperature.