Chapter 4

Heat transfer and diffusion of particles

Thermal resistance

FondamentalDefinition of the thermal resistance

Definition of the thermal resistance of an insulated cylindrical rod :

We want to determine, in stationnary mode, the temperature in a homogeneous cylindrical rod, with its length, its section and its edges are at temperatures and .

Let's suppose that the lateral surface is insulated.

The heat equation is simply

So :

The thermal flow through the rod is :

We can defined a thermal resistance such as :

That is to say :

We can also define thermal conductance :

AttentionDefinition of the thermal resistance

ExempleInsulation of the walls of a house

  • Blockworks, polystyrene, plasterboard and wallpapers : serial thermal resistances

  • Likewise with a window added : shunt thermal resistances.

Let's take the case of a double-glazing with a window (surface , its thickness and its conductivity), a gas layer with its conductivity, and second window similar to the first one.

It's the serial association of three heat resistances, hence the total resistance :

Where is the resistance of a window of thickness .

With , it appears that double-glazing allows us to multiply the thermal resistance by and thus to divide by the losses through the windows.

ComplémentAnalogy between Fourier's and Ohm's phenomenological laws

The classical Drude model affords to interpret local Ohm's law in the metals :

Let's remember that the expression of the heat resistance of a metal wire, with its length, its section and its conductivity ( its resistivity) :

Obviously, we can make the analogy with the thermal resistance of a one-dimensional straight-lined bar.

Heat transfers in a cylinder
Experimental measurement of a thermal conductivity