Thermal processes

The transferred heat per unity of surface and time depends on surface temperature, on external

temperature at large distance from the surface and on the convection coefficient h .

 Irradiation is the transfer related to EM emission and absorption. Exchanged heat quantity is

proportional to ΔT. The solution is thus complicated and cannot be solved analytically. Luckily, in

laser machining, this quantity is negligible with respect to conduction and convection.

Principle of energy conservation and Fourier equation

st

The 1 law assures that energy in an isolated volume must be conserved:

Sensible energy

Latent energy

Considering a homogeneous part characterized by:

- negligible mass motions

- no internal sources

- no phase changes

we obtain the Fourier equation, describing temperature

variation in time and space: 2

α is the thermal diffusivity [m /s] and it is the ration between the thermal conductivity and the volumetric

heat capacity.

If internal sources are present, we need to add the term relative to the source itself, which can depend on

space and time: 2

In case of laser machining, energy sorption is mostly on the surface so no internal sources are present. By the

way, this equation allows to make some considerations about superposition principle, valid also in case of

surface sources: →

Fourier equation requires boundary conditions, according to geometry and its

time evolution:

