Abstract
A model is presented to simulate Ohno Continuous Casting (OCC) of cored rods. Equations describing the axisymmetric transport of heat in the mold and cored rod are discussed. Heat transfer between the system and the surrounding environment is assumed to take place via convection. If the velocity of casting, the external temperature profile, the mold temperature, and the mold-cooler distance are given, asymptotic solutions for the temperature profile in the rod are found and expressions for the solidifying interfacial shapes are developed in the limit of a small melt slenderness ratio (mold radius/mold length). The effect of process parameters on the shape of the cored rod system is investigated.
Similar content being viewed by others
References
H. Soda, F. Chabchoub, W. H. Lam, S. A. Argyroopoulos and A. McLean, The horizontal Ohno continuous casting process: Process variables and their effects on casting stability. Cast Metals 4 (1991) 12-19.
F. Chabchoub, J. Mostaghimi and S. A. Argyroopoulos, A three dimensional mathematical model for the horizontal Ohno continuous casting process. Transp. Phenom. Materials 169 (1992) 69-74.
H. Soda, F. Chabchoub, S. A. Argyroopoulos and A. McLean, Experimental study of the horizontal Ohno continuous casting system. Can. Metallurg. Quart. 31 (1992) 231-239.
H. Soda, A. Ichinose, G. Motoyasu, A. Ohno and A. McLean, A new fabrication method for the casting of cored materials. Cast Metals 5 (1992) 95-102.
F. Chabchoub, S. A. Argyroopoulos and J. Mostaghimi, Mathematical modeling and experimental measurements on the horizontal Ohno continuous casting process for pure tin. Can. Metallurg. Quart. 33 (1994) 73-88.
H. Soda, G. Motoyasu, A. McLean and A. Ohno, Effects of process variables on cast surface quality of alloy rod produced by the Ohno continuous casting (OCC) process. Can. Metallurg. Quart. 33 (1994) 89-98.
H. Soda, A. McLean, G. Motoyasu and A. Ohno, Ohno continuous casting. Adv. Mater. Proc. April (1995) 43-45.
H. Soda, A. McLean, Z. Wang and G. Motoyasu, Pilot-scale casting of single-crystal copper wires by the Ohno Continuous Casting process. J. Mat. Sci. 30 (1995) 5438-5448.
H. Soda, C. K. Jen, G. Motoyasu, S. Okumura, A. Ohno and A. McLean, Fabrication and characterization of aluminum clad aluminum-copper alloy cored rod. Mat. Sci. Tech. 11 (1995) 1174-1179.
H. Soda, G. Motoyasu, A. McLean, C.K. Jen and O. Lisboa, Method for continuous casting of metal wire and tube containing optical fibre. Mat. Sci. Tech. 11 (1995) 1169-1173.
V. Alexiades and A. D. Solomon, Mathematical Modeling of Melting and Freezing Processes (1st Edn.) Bristol: Hemisphere (1993) 323 pp.
A. A. Samarskii, P. N. Vabishchevich, O. P. Iliev and A. G. Churbanov, Numerical simulation of convection/diffusion phase change problems-a review. Int. J. Heat Mass Transfer 36 (1993) 4095-4106.
S. Weinbaum and L. M. Jiji, Singular perturbation theory for melting or freezing in finite domains initially not at the fusion temperature. J. Appl. Mech. 44 (1977) 25-30.
M. M. Yan and P. N. S. Huang, Perturbation solutions to phase change problem subject to convection and radiation. J. Heat Trans. 101 (1979) 96-100.
G. W. Barry and J. S. Goodling, A Stefan problem with contact resistance. J. Heat Transfer 109 (1987) 820-825.
Z. Dursunkaya and S. Nair, A moving boundary problem in a finite domain. J. Appl. Mech. 57 (1990) 50-56.
D. S. Cohen and T. Erneux, Changing time history in moving boundary problems, SIAM J. Appl. Math. 50 (1990) 483-489.
D. E. Glass, M. N. Ozisik and S. S. McRae, Formulation and solution of hyperbolic Stefan problem. J. Appl. Phys. 70 (1991) 1190-1197.
C. Charach and I. Rubinstein, Pressure-temperature effects in planar Stefan problems with density change. J. Appl. Phys. 71 (1992) 1128-1137.
H. T. Chen and J. Y. Lin, Hybrid Laplace transform technique for Stefan problems with radiation-convection boundary condition. Int. J. Heat Mass Transfer 35 (1992) 3345-3351.
C. K. Hsieh and C. Y. Choi, Solution of one-and two-phase melting and solidification problems imposed with constant or time-variant temperature and flux boundary conditions. J. Heat Trans. 114 (1992) 524-528.
J. Y. Hsieh and C. C. Hwang, Nonlinear morphological instabilities in directional solidification-An integral approximation. J. Appl. Phys. 76 (1994) 2765-2772.
P. Tritscher and P. Broadbridge, A similarity solution of a multiphase Stefan problem incorporating general non-linear heat conduction. Int. J. Heat Mass Transfer 37 (1994) 2113-2121.
M. Conti, Planar solidification of a finite slab: effects of the pressure dependence of the freezing point. Int. J. Heat Transfer 38 (1995) 65-70.
C. K. Hsieh, Exact solutions of Stefan problems for a heat front moving at constant velocity in a quasi-steady state. Int. J. Heat Mass Transfer 38 (1995) 71-79.
R. H. Rangel and X. Bian, The inviscid stagnation-flow solidification problem. Int. J. Heat Mass Transfer 39 (1996) 1591-1602.
T. J. Fitzgerald and R. F. Singer, An analytical model for optimal directional solidification using liquid metal cooling. Met. Mat. Trans. A, Phys. Met Mat. Sci. 28A (1997) 1377-1383.
D. A. Tarzia and C. V. Turner, The one-phase supercooled Stefan problem with a convective boundary condition. Q. Appl. Math. 55 (1997) 41-50.
X. Bian and R. H. Rangel, Stagnation-flow solidification on a finite thickness substrate. Int. J. Heat Mass Transfer 41 (1998) 244-247.
I. Rubinstein and B. Zaltzman, Morphological instability of similarity solution to the Stefan problem with undercooling and surface tension. Q. Appl. Math. 56 (1998) 341-354.
L. H Ungar, M. J. Bennet and R. A. Brown, Cellular interface morphologies in directional solidification. III. The effects of heat transfer and solid diffusivity. Phys. Rev. B 31 (1985) 5923-5930.
L. H. Ungar and R. A. Brown, Cellular interface morphologies in directional solidification. IV. The formation of deep cells. Phys. Rev. B 31 (1985) 5931-5940.
K. Brattkus and S. H. Davis, Directional solidification with heat losses. J. Cryst. Growth. 91 (1988) 538-556.
R. A. Brown and D. H. Kim, Modelling of directional solidification: from Scheil to detailed numerical simulation. J. Cryst. Growth. 109 (1991) 50-65.
K. Tsiveriotis and R. A. Brown, Nonlinear local dynamics of the melt crystal interface of a binary alloy in directional solidification. Phys. rev. B-Condensed Matter 48 (1993) 13495-13501.
K. Tsiveriotis and R. A. Brown, Long-time scale dynamics observed in directional solidification of a binary alloy. Phys. Rev. B-Condensed Matter 49 (1994) 12724-12737.
K. Brattkus, Directional solidification into static stability. J. Fluid Mech. 304 (1995) 143-159.
G. W. Young and A. J. Chait, Steady State Thermal-Solutal Diffusion in a Float Zone. J. Cryst. Growth 96 (1989) 65-95.
G. W. Young and A. Chait, Surface tension driven heat, mass, and momentum transport in a two-dimensional float zone. J. Cryst. Growth 106 (1990) 445-466.
G. W. Young and J. A. Heminger, Modeling the time-dependent growth of single crystal fibers. J. Cryst. Growth 178 (1997) 410-421.
ASM Handbook Volume 15 Casting. United States: ASM International (1992) 937 pp.
J. Campbell, Castings. Oxford: Butterworth-Heinemann Ltd (1991) 288 pp.
J. Szekely, J. W. Evans and J. K. Brimacombe, The Mathematical and Physical Modeling of Primary Metals Processing Operations. New York: John Wiley & Sons, Inc. (1988) 261 pp.
E. Takeuchi and J. K. Brimacombe, The formation of oscillation marks in the continuous casting of steel slabs. Metallurg. Trans. B 15B (1984) 493-509.
G. J. Kor, An analysis of the fluid flow of liquid mold powder in the space between the continuous casting mold and the steel shell. Proceedings: 2nd Processing Technical Conference 2 (1981) 124-132.
R. Bommaraju and E. Saad, Mathematical modelling of lubrication capacity of mold fluxes. Steelmaking Conf. Proc. (1990) 281-296.
I. B. Risteski, A mathematical model of the conduct of the molten powder in the gap between the mold and the slab in the vicinity of the meniscus. Steel and Metals Mag. 28 (1990) 661-665.
E. Anzai, T. Ando, T. Shigezumi, M. Ikeda and T. Nakano, Hydrodynamic behavior of molten powder in meniscus zone of continuous casting Mold. Nippon Steel tech. Rep. 34 (1987) 31-40.
J. K. Brimacombe, Design of continuous casting machines based on a heat flow analysis: State of the art review. Can. Metallurg. Quart. 15 (1976) 163-175.
A. A. Sfeir and J. A. Clumpner, Continuous casting of cylindrical ingots. J. Heat Trans (1977) 29-34.
I. V. Samarasekera and J. K. Brimacombe, Application of mathematical models for the improvement of billet quality. Steelmaking Conf. Proc. (1991) 91-103.
D. Mazumdar, A consideration about the concept of effective thermal conductivity in continuous casting. ISIJ (1989) 524-528.
D. Mazumdar and R. Verma, A predictive mathematical model for analysis of continuous casting of steel. Trans. Indian Inst. Metals 42 (1989) 447-459.
A. Moitra and B. G. Thomas, Application of a thermo-mechanical finite element model of steel shell behavior in the continuous slab casting mold. 76th Steelmaking Conference, Dallas, TX, Iron and Steel Society, Warrendale, PA 76 (1993) 657-667.
P. J. Flint, A three-dimensional finite difference model of heat transfer, fluid flow, and solidification in the continuous slab caster. Steelmaking Conf. Proc. (1990) 481-490.
B. G. Thomas, Mathematical modelling of the continuous slab casting mold: A state of the art review. Steelmaking Conf. Proc. (1991) 105-118.
J. DiLellio and G. W. Young, An asymptotic model of the mold region in a continuous steel caster. Metallurg. Trans. (1995) 1225-1241.
H. K. Kuiken, The cooling of low-heat-resistance cylinders by radiation. J. Engng. Math. 13 (1979) 97-106.
H. K. Kuiken and P. J. Roksnoer, Analysis of the temperature distribution in FZ silicon crystals. J. Cryst. Growth 47 (1979) 29-42.
S. A. Morman, An asymptotic approach to mathematically modeling the Ohno continuous casting process. Masters Thesis, The University of Akron. May (1997).
Metals Handbook. Properties and selection: Nonferrous alloys and special-purpose materials. United States: ASM International 2(ed. 10) (1990) 1328 pp.
Metals Handbook. Properties and selection: Nonferrous alloys and special-purpose materials. United States: ASM International 2(ed. 9) (1979) 855 pp.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Morman, S., Young, G. An asymptotic approach to the mathematical modeling of Ohno continuous casting of cored rods. Journal of Engineering Mathematics 38, 51–76 (2000). https://doi.org/10.1023/A:1004630731573
Issue Date:
DOI: https://doi.org/10.1023/A:1004630731573