296
L. V. Shmeleva et al.
surface waves and states, scattering, etc. [16, 17]. All these losses occur during the
transition q s → q 0s , and therefore they can be characterized by the coefficient of
not heat dissipative losses 0 ≤ L d ≤ 1. Then, the flow q 0s penetrating into the
solid medium can be associated with the flow q s , which reaches the surface, by the
relation: q 0s = (1 − L d )q s . Thus, the general equation of energy flow balance for a
non-destructive problem will have the form:
L d
n · q s
+ λ 0s (n · gradT 0 ) s = 0.
(12)
Two limiting cases are considered. The first, when the losses on the surface of the
substance affected by the energy flux are large, that is, L d ∼ 1 (the case of metals
and opaque materials). In this case, (12) takes the form:
n · q s
+ λ 0s (n · gradT 0 ) s = 0.
The second case, when the light flux nearly has no loss when passing through the
surface of the material, that is, L d → 0, leads (12) to the form:
λ 0s (n · gradT 0 ) s = 0.
When the surface is destroyed, due to local phase transitions, a strongly heated
plasma-gas medium is formed in the irradiated substance. In this case, the flux
Q s when passing through the “solid state–gas” interface will change, both due to
dissipative processes such as scattering, reflection, and transmission of the electromagnetic flux, and due to the properties of the substance associated with the
thermal characteristics of each of the two bordering environments. The heat flux
will undergo changes on the surface of the substance, for example, due to surface
atomic vibrations and radiation from a heated surface. It is convenient to take
these changes into account in the form of some loss coefficient 0 ≤ L ≤ 1.
That is, the transition λ 0s (n · gradT 0 ) s → λ s (n · gradT ) s can be defined as follows:
λ s (n · gradT ) s = (1 − L)λ s (n · gradT ) s . Thus, the energy flow balance (11) for
processes accompanied by destruction will have the form:
(n · v s )
ρ s U s + ρ s
i
v
i
s − v
i
0s
2
2
− ρ s U 0s +
1 −
ρ s
ρ 0s
P s
+
1 −
ρ s
ρ 0s
(n · v s )
c
n · q s
+ L d
n · q s
− Lλ s (n · gradT ) s = 0.
To estimate the value of the summand that determines the kinetic energy of
the process, we use the system of boundary conditions for the balance of the
momentum flux, written in explicit form. As a result, we obtain
i
v
i
s − v
i
0s
2 =
1 +
P
(0)s
ξζ
2 +
P
(0)s
ηζ
2
P s +q
(ζ )
s /c+P
(0)s
ζ ζ
2
v
(ζ )
s − v
(ζ )
0s
2
. Considering that the radiation flux is directed
L. V. Shmeleva et al.
surface waves and states, scattering, etc. [16, 17]. All these losses occur during the
transition q s → q 0s , and therefore they can be characterized by the coefficient of
not heat dissipative losses 0 ≤ L d ≤ 1. Then, the flow q 0s penetrating into the
solid medium can be associated with the flow q s , which reaches the surface, by the
relation: q 0s = (1 − L d )q s . Thus, the general equation of energy flow balance for a
non-destructive problem will have the form:
L d
n · q s
+ λ 0s (n · gradT 0 ) s = 0.
(12)
Two limiting cases are considered. The first, when the losses on the surface of the
substance affected by the energy flux are large, that is, L d ∼ 1 (the case of metals
and opaque materials). In this case, (12) takes the form:
n · q s
+ λ 0s (n · gradT 0 ) s = 0.
The second case, when the light flux nearly has no loss when passing through the
surface of the material, that is, L d → 0, leads (12) to the form:
λ 0s (n · gradT 0 ) s = 0.
When the surface is destroyed, due to local phase transitions, a strongly heated
plasma-gas medium is formed in the irradiated substance. In this case, the flux
Q s when passing through the “solid state–gas” interface will change, both due to
dissipative processes such as scattering, reflection, and transmission of the electromagnetic flux, and due to the properties of the substance associated with the
thermal characteristics of each of the two bordering environments. The heat flux
will undergo changes on the surface of the substance, for example, due to surface
atomic vibrations and radiation from a heated surface. It is convenient to take
these changes into account in the form of some loss coefficient 0 ≤ L ≤ 1.
That is, the transition λ 0s (n · gradT 0 ) s → λ s (n · gradT ) s can be defined as follows:
λ s (n · gradT ) s = (1 − L)λ s (n · gradT ) s . Thus, the energy flow balance (11) for
processes accompanied by destruction will have the form:
(n · v s )
ρ s U s + ρ s
i
v
i
s − v
i
0s
2
2
− ρ s U 0s +
1 −
ρ s
ρ 0s
P s
+
1 −
ρ s
ρ 0s
(n · v s )
c
n · q s
+ L d
n · q s
− Lλ s (n · gradT ) s = 0.
To estimate the value of the summand that determines the kinetic energy of
the process, we use the system of boundary conditions for the balance of the
momentum flux, written in explicit form. As a result, we obtain
i
v
i
s − v
i
0s
2 =
1 +
P
(0)s
ξζ
2 +
P
(0)s
ηζ
2
P s +q
(ζ )
s /c+P
(0)s
ζ ζ
2
v
(ζ )
s − v
(ζ )
0s
2
. Considering that the radiation flux is directed