Heat transfer and diffusion of particles
Fondamental : Definition 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
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 :
Attention : Definition of the thermal resistance
Exemple : Insulation 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.
Complément : Analogy 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.