Conduction and Thermal Resistance

Let us quantify the simplest transfer: conduction through a wall. The heat flow Φ (the energy crossing per second, in watts) depends on the area A, on the temperature difference ΔT between the two faces, on the thickness e, and on a property of the material, the thermal conductivity λ. This is Fourier's law:

   Φ = λ · A · ΔT / e        (Φ in watts)

How to read it: the flow increases with the area and the temperature difference, and decreases with the thickness. A thicker wall lets less heat through — hence the point of insulating. The conductivity λ sorts materials:

   material        λ (W/m·K)     role
   -------------   -----------   -------------------
   metal (copper)  ~ 400         excellent conductor
   glass           ~ 1           average
   wood            ~ 0.15        insulator
   glass wool      ~ 0.04        very good insulator
   still air       ~ 0.025       among the best

By analogy with electricity (where Φ plays the role of current and ΔT that of voltage), we define a thermal resistance:

   R = e / (λ · A)      and then   Φ = ΔT / R      (just like Ohm's law!)

The larger R is, the better the wall insulates. And like resistors in series, thermal resistances add up: that is why layers are stacked (wall + insulation + drywall). The secret of good insulators? They trap still air (glass wool, double glazing, feathers, wool): air conducts almost nothing, provided it is kept from moving — otherwise convection takes over.