In this presentation, we focus on the melting phenomenon during laser drilling. The governing equation is the transient three-dimensional heat conduction equation for the solid substrate and for the liquid molten part boundary layer approximations of the mass, momentum and energy equations are used. The melting interface is moving and therefore need to be determined as part of the solution. In this paper, coupled BEM-FDM formulation for the transient three-dimensional heat conduction equation with moving boundary and the boundary layer formulation will be presented. The moving boundary, solid-liquid interface, appears in the surface integral of the BEM formulation. Consequently, it is easy to track. The thin layer is coupled to the solid substrate at the solid-liquid interface by the interface velocity, energy flux and temperature. To increase the efficiency of the computation, we combine the BEM formulation with finite difference method, which models the region that is far away from the melting zone. We are working towards a coupled BEM-FDM-THINLAYER model, that would be effective in simulating the process of material removal in the laser drilling.

1.
Banerjee
,
P. K.
and
Butterfield
,
R.
, Boundary Element Methods in Engineering Science,
McGraw Hill
,
London
,
1981
.
2.
Beskos
,
D. E.
(ed.), Boundary Element Methods in Mechanics,
North-Holland Pub.
,
Amsterdam
,
1987
.
3.
Brebbia
,
C. A.
,
Telles
,
J. C. F.
and
Worbel
,
L. C.
, Boundary Element Techniques Theory and Applications in Engineering,
Springer-Verlag
,
Berlin
,
1984
.
4.
Chan
,
C. L.
,
1999
, “
Transient 1-D Laser Drilling Model with Variable Properties
,”
Proceeding of ICALEO 1999
, Vol.
87
, pp.
C21
C30
.
5.
Chan
,
C. L.
and
Mazumder
,
J.
,
1987
, “
One-dimensional Steady-State Model for Damage by Vaporization and Liquid Expulsion Due to Laser-Material Interaction
,”
Journal of Applied Physics
, Vol.
62
, No. 11, pp.
4579
4586
.
6.
Curran
,
D. A. S.
,
Lewis
,
B. A.
and
Cross
,
M.
, “
A Boundary Element Method for the Solutions of the Transient Diffusion Equation in Two Dimensions
,”
App. Math. Modelling
,
10
,
1986
, pp
107
113
.
7.
DeSilva
S.
and
C. L
Chan
, “
Coupled Boundary Element Method and Finite Diffenence Method for Laser Drilling
,”
Proceedings of Laser Institute of America
,
89
,
2000
, pp
193
201
8.
Fleuries
,
J.
and
Predeleanu
,
M.
, “
On the Use of Coupled Fundamental Solutions in BEM for Thermoelastic Problems
,”
Eng. Analysis
,
4
,
1987
, pp
70
7
.
9.
Mukherjee
,
S.
, Boundary Element Methods in Creep and Fracture,
Elsevier Applied Science Pub.
,
Barking, Essex
,
1982
.
10.
O’neill
,
K.
, “
Boundary Integral Equation Solution of Moving Boundary Phase Change Problems
,”
Int. J. Num. Meth. Eng.
,
19
,
1983
, pp
1825
1850
.
11.
Zabaras
,
N.
and
Mukherjee
,
S.
, “
An Analysis of Solidification Problems by the Boundary Element Method
,”
Int. J. Num. Meth. Eng.
,
24
,
1987
.
This content is only available via PDF.
You do not currently have access to this content.