2.2 Basic Models of Quasi-Steady Laser Welding
25
Ra =
gβ
λη
L
3
T − T re f
(2.14)
where: g—Gravitational acceleration;
β—Thermal expansion coefficient of material;
λ—Thermal diffusivity of material;
η—The kinematic viscosity of gas flow around workpiece.
For the definition of other parameters, refer to Eqs. (2.7), (2.10), and (2.12).
The convective heat transfer coefficient h c on the workpiece surface is calculated
by the following formula:
h c = N u
k air
L
(2.15)
In this equation:
k air —The heat conductivity of gas flow around workpiece.
The heat loss flow q r per unit area caused by radiation is calculated as follows:
q r = εσ
T
4
− T
4
amb
(2.16)
where: ε—The emissivity of materials on surface;
σ —The Stefan-Boltzmann constant, 5.6697 × 10
–8 .
The upper surface of weld pools:
μ
∂u
∂z
= −
∂γ
∂ T
∂ T
∂ x
(2.17)
In this equation:
∂γ
∂ T
—The temperature coefficient of surface tension of weld pool.
μ
∂v
∂z
= −
∂γ
∂ T
∂ T
∂ y
, w = 0
(2.18)
In solid zone:
u = v w , v = 0, w = 0
(2.19)
The lower surface of weld pools:
μ
∂u
∂z
= −
∂γ
∂ T
∂ T
∂ x
(2.20)
μ
∂v
∂z
= −
∂γ
∂ T
∂ T
∂ y
, w = 0
(2.21)