Conduction

Conduction is the transport of energy through a solid (or a still fluid), without any movement of matter. The mechanism is microscopic: molecules in the hot region oscillate more and, colliding with their neighbours, set them oscillating too. Thermal agitation thus propagates from molecule to molecule, from hot towards cold.

For a block of area $A$ and thickness $d$, with the two faces at temperatures $T_1$ and $T_2$ (with $T_1 > T_2$), the heat flow in steady state is given by Fourier’s law (in qualitative form):

Principle — Fourier's law (conduction)

$\ev{\frac{Q}{\Delta t} = k\,A\,\frac{T_1 - T_2}{d}}$ where $k$ is the material’s thermal conductivity (units W/(m·K)).

The flow therefore grows with area and with the temperature gap, and decreases with thickness: thick walls of small area lose less heat. The decisive parameter, though, is $k$, which spans four orders of magnitude between metals and insulators:

Material	$k$ (W/(m·K))
Silver	429
Copper	385
Aluminium	237
Steel	50
Glass	1.0
Liquid water	0.6
Glass wool	0.04
Air (still)	0.025

Metals versus insulators

The conductivity of a metal is about $10^4$ times that of a good insulator. That’s why a metal pan gets scorching hot in a few seconds while a wool blanket stays lukewarm. And note that still air is one of the best insulators: it’s the real secret of double glazing, where what insulates is not the glass but the air gap between the panes (see electric blanket versus window and double glazing with an air gap).

Links

Topics: Termologia Concepts: Trasmissione del calore

Related exercises: Problem — Single-pane window · Problem — From graph to conductivity · Problem — Two fabrics