Thermal processes

Thermal processes

Index

• Heat exchange .............................................................................................................................................. 1
• Principle of energy conservation and Fourier equation ............................................................................... 2
• Motionless extended planar heat source ..................................................................................................... 3
• Heating phase ........................................................................................................................................... 3
• Cooling phase ........................................................................................................................................... 4
• Moving linear heat source ............................................................................................................................ 4
• 1D source.................................................................................................................................................. 5
• 2D linear ................................................................................................................................................... 5

Heat exchange

Heat is a form of energy that propagates through system boundaries due to a ΔT. There are three mechanisms:

• Conduction is short-range energy transfer through particles collision (vibrational motion and free electrons). It is the mechanism related to solids. Considering two points along x-axis, at a distance dx and with dT we have: Thermal conductivity k (W/mK) depends on material, position, heat flux direction and temperature, but for the sake of simplicity, it is assumed as constant. Furthermore, if k is independent on position (homogeneous piece), on flux direction (isotropic) and on T, it is equal in all directions and this equation is obtained: In general, k depends on temperature, so we can use this approach as a first approximation, to be improved then with FEM.
• Convection is long-range transfer, associated with a macroscopic mass transfer (movement of molecules within a fluid). It can be natural if the fluid motion is due to different densities (because of different temperatures), or forced if the fluid motion is imposed (pumps, …). In laser machining, forced convection prevails: a shielding gas is used in the beam/surface contact zone. Convection is governed by Newton’s law: The transferred heat per unit 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.