In this paper, we present a one-dimensional (1D) melting, evaporating, and resolidifying model describing the interaction of a scanning laser beam with a metal surface wherein the continuous and stepwise heat flux is applied. One set of 1D conduction equations, which is valid in all phases including solid, liquid, and vapor, has been developed along with two phase boundary conditions between the solid/liquid and liquid/air using an appropriate scaling law. The 1D heat equation has been solved separately in each phase using a sharp interface temperature technique based on the front tracking method. The generalized relations of nondimensional maximum melting depth, final evaporation depth, and maximum melting time related to nondimensional interaction time and heat flux factor are established.

1.
Deckard
,
C. R.
, 1988, “
Selective Laser Sintering
,” Ph.D. thesis, University of Texas, Austin, TX.
2.
Khan Malek
,
C. G.
, 2006, “
Laser Processing for Bio-Microfluidics Applications (Part I)
,”
Anal. Bioanal. Chem.
1618-2642,
385
, pp.
1351
1361
.
3.
Khan Malek
,
C. G.
, 2006, “
Laser Processing for Bio-Microfluidics Applications (Part II)
,”
Anal. Bioanal. Chem.
1618-2642,
385
, pp.
1362
1369
.
4.
Bertolotti
,
M.
, and
Sibilia
,
C.
, 1981, “
Depth and Velocity of the Laser Melted Front From an Analytical Solution of the Heat Conduction Equation
,”
IEEE J. Quantum Electron.
0018-9197,
17
, pp.
1980
1989
.
5.
Chung
,
H.
, and
Das
,
S.
, 2002, “
Scaling Laws for Melting and Resolidification in Direct Selective Laser Sintering of Metals
,”
Solid Freeform Fabrication Symposium 2002
, The University of Texas at Austin, pp.
322
330
.
6.
Cline
,
H. E.
, and
Anthony
,
T. R.
, 1977, “
Heat Treating and Melting Material With a Scanning Laser or Electron Beam
,”
J. Appl. Phys.
0021-8979,
48
, pp.
3895
3900
.
7.
Cohen
,
M. I.
, 1967, “
Melting of a Half-Space Subjected to a Constant Heat Input
,”
J. Franklin Inst.
0016-0032,
283
, pp.
271
285
.
8.
Wood
,
R. F.
, and
Geist
,
G. A.
, 1986, “
Modeling of Nonequilibrium Melting and Solidification in Laser-Irradiated Materials
,”
Phys. Rev. B
0163-1829,
34
, pp.
2606
2620
.
9.
Xu
,
X.
,
Grigoropoulos
,
C. P.
, and
Russo
,
R. E.
, 1995, “
Heat Transfer in Excimer Laser Melting of Thin Polysilicon Layers
,”
ASME J. Heat Transfer
0022-1481,
117
, pp.
708
715
.
10.
Zhang
,
Y.
, and
Faghri
,
A.
, 1999, “
Vaporization, Melting and Heat Conduction in the Laser Drilling Process
,”
Int. J. Heat Mass Transfer
0017-9310,
42
, pp.
1775
1790
.
11.
Chung
,
H.
, and
Das
,
S.
, 2004, “
Numerical Modeling of Scanning Laser-Induced Melting, Vaporization and Resolidification in Metals Subjected to Step Heat Flux Input
,”
Int. J. Heat Mass Transfer
,
47
, pp.
4153
4164
. 0017-9310
12.
Chung
,
H.
, and
Das
,
S.
, 2004, “
Numerical Modeling of Scanning Laser-Induced Melting, Vaporization and Resolidification in Metals Subjected to Time-Dependent Heat Flux Inputs
,”
Int. J. Heat Mass Transfer
,
47
, pp.
4165
4175
. 0017-9310
13.
Kelly
,
R.
, and
Miotello
,
A.
, 1999, “
Contribution of Vaporization and Boiling to Thermal-Spike Sputtering by Ions or Laser Pulses
,”
Phys. Rev. E
1063-651X,
60
(
3
), pp.
2616
2625
.
14.
Juric
,
D.
, and
Tryggvason
,
G.
, 1998, “
Computations of Boiling Flows
,”
Int. J. Multiphase Flow
0301-9322,
24
(
3
), pp.
387
410
.
15.
Tryggvason
,
G.
,
Bunner
,
B.
,
Esmaeeli
,
A.
,
Juric
,
D.
,
Al-Rawahi
,
N.
,
Tauber
,
W.
,
Han
,
J.
,
Nas
,
S.
, and
Jan
,
Y. -J.
, 2001, “
A Front Tracking Method for the Computations of Multiphase Flow
,”
J. Comput. Phys.
0021-9991,
169
, pp.
708
759
.
16.
Udaykumar
,
H. S.
,
Mittal
,
R.
, and
Shyy
,
W.
, 1999, “
Computation of Solid-Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids
,”
J. Comput. Phys.
0021-9991,
153
, pp.
535
574
.
17.
Shin
,
S.
, and
Abel-Khalik
,
S. I.
, 2007, “
Numerical Modeling of Evaporating Thin Liquid Film Instability on a Heated Cylindrical Rod With Parallel and Cross Vapor Flow
,”
Nucl. Sci. Eng.
,
156
, pp.
24
39
. 0029-5639
18.
Fedkiw
,
R. P.
,
Aslam
,
T.
,
Merriman
,
B.
, and
Osher
,
S.
, 1999, “
A Non-Oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)
,”
J. Comput. Phys.
0021-9991,
152
, pp.
457
492
.
19.
Ye
,
T.
,
Shyy
,
W.
,
Tai
,
C. -F.
, and
Chung
,
J. N.
, 2004, “
Assessment of Sharp- and Continuous-Interface Methods for Drop in Static Equilibrium
,”
Comput. Fluids
0045-7930,
33
, pp.
917
926
.
You do not currently have access to this content.