The fast and accurate modeling of phase change is of a significant importance in many processes from steel casting to latent heat thermal energy storage. The paper presents a numerical case study on the transient 3D heat diffusion problem with phase change. Three different approaches to modeling of the solid–liquid phase change in combination with four commonly used numerical schemes are compared for their efficiency, accuracy, applicability, simplicity of implementation, and robustness. The possibility of parallel decomposition of the approaches is also discussed. The results indicate that the best accuracy was achieved with the second-order implicit methods, and the best efficiency was reached with the simple explicit methods.

References

1.
Ockenden
,
J. R.
, and
Hodgkin
,
W. R.
,
1975
,
Moving Boundary Value Problems in Heat Flow and Diffusion
,
Oxford University Press
,
Oxford, UK
.
2.
Tavakoli
,
R.
, and
Davami
,
P.
,
2007
, “
Unconditionally Stable Fully Explicit Finite Difference Solution of Solidification Problems
,”
Metall. Mater. Trans. B
,
38
(
1
), pp.
121
142
.
3.
Douglas
,
J.
, and
Gunn
,
J. E.
,
1964
, “
A General Formulation of Alternating Direction Methods—Part I: Parabolic and Hyperbolic Problems
,”
Numer. Math.
,
6
(
1
), pp.
428
453
.
4.
Muhieddine
,
M.
,
Canot
,
É.
, and
March
,
R.
,
2009
, “
Various Approaches for Solving Problems in Heat Conduction With Phase Change
,”
Int. J. Finite
,
3
, pp.
1
20
.
5.
Liu
,
Y.-Ch.
, and
Chao
,
L.-S.
,
2006
, “
Modified Effective Specific Heat Method of Solidification Problems
,”
Mater. Trans. J.
,
47
(
11
), pp.
2737
2744
.
6.
Zhang
,
Y.
,
Du
,
K.
,
He
,
J. P.
,
Yang
,
L.
, and
Li
,
Y. J.
,
2014
, “
Impact Factors Analysis of the Enthalpy Method and the Effective Heat Capacity Method on the Transient Nonlinear Heat Transfer in Phase Change Materials (PCMs)
,”
Numer. Heat Transfer A
,
65
(
1
), pp.
66
83
.
7.
Li
,
Ch.-Y.
,
Garimella
,
S. V.
, and
Simpson
,
J. E.
,
2003
, “
Fixed-Grid Front-Tracking Algorithm for Solidification Problems—Part I: Method and Validation
,”
Numer. Heat Transfer, Part B
,
43
(
2
), pp.
117
141
.
8.
Voller
,
V.
,
1983
, “
An Explicit Numerical Method to Track a Moving Phase Change Front
,”
Int. J. Heat Mass Transfer
,
26
(
1
), pp.
147
150
.
9.
Hashemi
,
T. H.
, and
Sliepcevich
,
C. M.
,
1968
, “
A Numerical Method for Solving Two-Dimensional Problems of Heat Conduction With Change of Phase
,”
Chem. Eng. Prog. Symp. Ser.
,
63
, pp.
34
41
.
10.
Lewisa
,
R. W.
, and
Ravindran
,
K.
,
2000
, “
Finite Element Simulation of Metal Casting
,”
Int. J. Numer. Methods Eng.
,
47
(1–3), pp.
29
59
.
11.
Dusinberre
,
G. M.
,
1945
, “
Numerical Methods for Transient Heat Flows
,”
Trans. ASME
,
67
, pp.
703
712
.
12.
Mochnacki
,
B.
, and
Lara
,
S.
,
2003
, “
Application of Generalized Finite Difference Method in Numerical Modelling of Moving Boundary Problems
,”
Sci. Res. Inst. Math. Comput. Sci.
,
2
(1), pp.
129
143
.
13.
Minkowycz
,
W. J.
,
Sparrow
,
E. M.
,
Schneider
,
G. E.
, and
Pletcher
,
R. H.
,
1988
,
Handbook of Numerical Heat Transfer
,
Wiley
,
New York
.
14.
Voller
,
V. R.
,
1996
, “
An Overview of Numerical Methods for Solving Phase Change Problems
,”
Advances in Numerical Heat Transfer
, Vol.
1
,
W. J.
Minkowycz
and
E. M.
Sparrow
, eds.,
Taylor & Francis
,
London
, pp.
341
375
.
15.
Hahn
,
D. W.
, and
Ozisik
,
M. N.
,
2012
,
Heat Conduction
, 3rd ed.,
Wiley
,
Hoboken, NJ
.
16.
Yang
,
W. Y.
,
Cao
,
W.
,
Chung
,
T.-S.
, and
Morris
,
J.
,
2005
,
Applied Numerical Methods Using Matlab
,
Wiley
,
Hoboken, NJ
.
17.
Otto
,
S. R.
, and
Denier
,
J. P.
,
2005
,
An Introduction to Programming and Numerical Methods in MATLAB
,
Springer-Verlag
,
London
.
18.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
McGraw-Hill
,
New York
.
19.
Larkin
,
B. K.
,
1964
, “
Some Stable Explicit Difference Approximations to the Diffusion Equation
,”
Math. Comput.
,
18
(
86
), pp.
196
202
.
20.
Barakat
,
H. Z.
, and
Clark
,
J. A.
,
1966
, “
On the Solution of Diffusion Equation by Numerical Methods
,”
ASME J. Heat Transfer
,
88
(
4
), pp.
421
427
.
21.
Warming
,
R. F.
, and
Beam
,
R. M.
,
1979
, “
An Extension of A-Stability to Alternating Direction Implicit Methods
,”
BIT Numer. Math.
,
19
(
3
), pp.
395
417
.
22.
Wang
,
T.-Y.
, and
Chen
,
Ch. C.-P.
,
2002
, “
3-D Thermal-ADI: A Linear-Time Chip Level Transient Thermal Simulator
,”
IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.
,
21
(
12
), pp.
1434
1445
.
23.
Rubitherm Technologies GmbH, 2016, Data sheet RT28HC, Berlin, accessed Dec. 8, 2016, http://www.rubitherm.eu/
24.
Mauder
,
T.
,
Sandera
,
C.
, and
Stetina
,
J.
,
2015
, “
Optimal Control Algorithm for Continuous Casting Process by Using Fuzzy Logic
,”
Steel Res. Int.
,
86
(
7
), pp.
785
798
.
25.
Fu
,
W. S.
,
Wang
,
W. H.
, and
Huang
,
S. H.
,
2012
, “
An Investigation of Natural Convection of Three Dimensional Horizontal Parallel Plates From a Steady to an Unsteady Situation by a CUDA Computation Platform
,”
Int. J. Heat Mass Transfer
,
55
(17–18), pp.
4638
4650
.
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