Abstract
The main aim of this work is to study numerically the influence of an external magnetic field on the solidification processes of two-component materials. Based on the continuum model of two-phase flow a mathematical model for the directional solidification of a binary alloy in a magnetic field is presented. The model includes mass, momentum, energy and species mass conservation equations written in compressible form and additional relationships describing the temperature-solute coupling. The geometry under study is a cylindrical mold with adiabatic walls and cooled bottom. The macroscale transport in the solidification of alloys is governed by the progress of the two-phase mushy zone, which is treated by means of a porous medium approach. The volume fraction of liquid and solid phases, respectively, is calculated from a 2D approximation of the phase diagram. The results of calculation are compared with experimental data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Winter, J, Tyler, D E, Dantzig, J A. Method and Apparatus for Casting Metals and Alloys. US Patent No.4, 450, 893, 1984
Dantzig, J A, Tyler, D E. Mold for Use in Metal or Metal Alloy Casting Systems. US Patent No.4, 457, 354, 1984
Beckermann, C, Wang, C Y. Multiphase-multiscale Modeling of Alloy Solidification. Annual Review of Heat Transfer, 1995, 6: 115–119
Schneider, M C, Beckermann, C. A Numerical Study of the Combined Effects of Microsegregation, Mushy Zone Permeability and Flow, Caused by Volume Contraction and Thermosolutal Convection, on Macrosegregation and Eutectic Formation in Binary Alloy Solidification. Int. J. Heat Mass Transfer, 1995, 38(18): 3455–3473
Ni, J, Incropera, F P. Extension of the Continuum Model for Transport Phenomena Occurring During Metal Alloy Solidification - I. The Conservation Equations. Int. J. Heat Mass Transfer, 1995, 38(7): 1271–1284
Swaminathan, C R, Voller, V R. Towards a General Numerical Scheme for Solidification Systems. Int. J. Heat Mass Transfer, 1997, 40(12): 2859–2868
Swaminathan, C R, Voller, V R. On the Enthalpy Method. International Journal of Heat and Fluid Flow, 1993, 3: 233–234
Bennon, W D, Incropera, F P. Numerical Analysis of Binary Solid-liquid Phase Change Using a Continuum Model. Numerical Heat Transfer, 1988, 3: 277–296
Yoo, Hoseon, Viskanta, R. Effect of Anisotropic Permeability on the Transport Process During Solidification of a Binary Mixture. Int. J. Heat Mass Transfer, 1992, 35(10): 2335–2346
Neilson, D G, Incropera, F P. Three-dimensional Considerations of Unidirectional Solidification in a Binary Liquid. Numeraical Heat Transfer, Part A, 1993, 23: 1–20
Presscot, P J. Convection Transport Phenomena During Solidification of Binary Metal Alloys and the Effects of Magnetic Fields: [Ph.D. Thesis]. Purdue University, West Lafayatte, IN, 1992
Prescott, P J, Incropera, F P, Gaskell, D R. Influence of Electromagnetic Stirring on the Solidification of a Binary Metal Alloy. Exp. Heat Transfer, 1996, 9: 105–131
Prescot, P J, Incropera F P. Magnetically Damped Convection During Solidification of a Binary Metal Alloy. Journal of Heat Transfer, 1993, 115: 302–310
Prescott, P J, Incropera, F P. The Effect of Turbulence on Solidification of a Binary Metal Alloy With Electromagnetic Stirring. Journal of Heat Transfer, 1995, 117: 716–724
Karakaya, I, Thompson, W T. Binary Alloy Phase Diagrams. ASM International, Ohio, USA, 1988
Singh, A K, Basu, B. On Convection in Mushy Phase and Its Effect on Macrosegregation. Metallurgical and Material Transactions A, 2000, 31A: 1687–1692
Davidso, P A, Hunt, J C R. Swirling Recirculating Flow in a Liquid-metal Column Generated by a Rotating Magnetic Field. J. Fluid Mech., 1986, 185: 67–106
Patankar, S V. Numerical Heat Transfer and Fluids Flows. Hemisphere, Washington D.C., 1980
Ferziger, J H, Peric, M. Computational Methods for Fluid Dynamics. 3rd Edition. Springer-Verlag, 2002
Neilson, D G, Incropera, F P. Three-Dimensional Considerations of Unidirectional Solidification in a Binary Liquid. Numerical Heat Transfer, Part A, 1993, 23: 1–20
Neilson, D G. Unidirectional Solidification of a Binary Model Alloy and the Effect of Induced Fluid Motion. [Ph.D. Thesis]. Purdue University, West Lafayette, Ind., 1991
Chen, J H, Tsai, H L. Inverse Segregation for a Unidirectional Solidification of Aluminum-cooper Alloys. Int. J. Heat Mass Transfer, 1993, 36: 3069–3075
Krane, M, Incropera, F P. Analysis of the Effect of Shrinkage on Macrosegregation in Alloy Solidifcation. Metallurgical and Material Transactions A, 1995, 26A: 2329–2339
Moessner, R, Gerbeth, G. Buoyant Melt Flows Under the Influence of Steady and Rotation Magnetic Fields. Journal of Crystal Growth., 1999, 197: 341–354
Nikrityuk, A, Willers, B, Eckert, S, et al. The Influence of Rotating Magnetic Fields on the Solidification of PbSn-alloys: Experiment vs. Theory. In Preparation
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nikrityuk, P.A., Eckert, K., Grundmann, R. et al. Modeling and measurements of heat transfer phenomena in two-phase PbSn alloy solidification in an external magnetic field. J. of Therm. Sci. 12, 357–362 (2003). https://doi.org/10.1007/s11630-003-0044-6
Issue Date:
DOI: https://doi.org/10.1007/s11630-003-0044-6