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Abstrakty
The macroscopic equations describing the process of solidification in binary systems are usually introduced via the volume averaging technique. A different approach to obtain these equations, based on the ensemble averaging technique, is proposed in the paper. This technique was used to derive energy and solute conservation equations and the basic constitutive relations appearing in the macroscopic description of the solidification phenomena occurring in the mushy region. In general these relations are non-local and account for non-equilibrium processes. Problem of thermodynamic equilibrium (thermal and chemical) is also discussed. Formulae for enthalpy and porosity of the mushy zone, in the latter case, are given.
Rocznik
Tom
Strony
391--402
Opis fizyczny
Bibliogr. 24 poz., wykr.
Twórcy
autor
- Politechnika Warszawska, Instytut Techniki Cieplnej, ul. Nowowiejska 25, 00-665 Warszawa, Polska
Bibliografia
- [1] C. Beckermann, R. Viskanta. Mathematical modeling of transport phenomena during alloy solidification. Appl. Mech. Rev., 46: 1-27, 1993.
- [2] W. D. Bennon, F. P. Incropera. A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems - I and II. Int. J. Heat and Mass Transfer, 30: 2161-2187, 1987.
- [3] G. K. Batchelor. Transport properties of two-phase materials with random structure. Ann. Rev. Fluid Mech., 6: 227-255, 1974.
- [4] M. J. Beran, J. J. McCoy. Mean field variation in random media. Quarterly of Applied Mathematics, 245-258, July 1970.
- [5] Yu. A. Buyevich. Heat and mass transfer in disperse media. I. Averaged field equations. Int. J. Heat and Mass Transfer, 35: 2445-2452, 1992.
- [6] P. Furmański. A mixture theory for heat conduction in heterogeneous media. Int. J. Heat and Mass Transfer, 37: 2993-3002, 1994.
- [7] P. Furmański. Influence of laminar convection of fluid on effective thermal conductivity of some porous media. Advances in Engineering Heat Transfer, 513-524. Computational Mechanics Publications, Southampton, 1995.
- [8] P. Furmański. Heat conduction in composites. Homogenization and macroscopic behavior. Appl. Mech. Rev., 50: 327-356, 1997.
- [9] P. Furmański. Thermal properties and local heat sources in composite materials. Thermal Conductivity, 24: 581-594, 1999.
- [10] S. Ganesan, C. L. Chan, D.R. Poirier. Permeability for flow parallel to primary dendrite arms. Mater. Sci. and Eng., A151: 97-105, 1992.
- [11] R. Herczyński, I. Pieńkowska. Toward a statistical theory of suspensions. Ann. Rev. Fluid Mech., 12: 237-269, 1980.
- [12] R. N. Hills, D. E. Loper, P. H. Roberts. On continuum models for momentum, heat and species transport in solid-liquid phase change systems. Int. Comm. Heat and Mass Transfer, 19: 585-594, 1992.
- [13] E. J. Hinch. An averaged-equation approach to particle interactions in a fluid suspension. J. Fluid Mech., 83: 695-720, 1977.
- [14] D. L. Koch, J. F. Brady. A non-local description of advection-diffusion with application to dispersion in porous media. J. Fluid Mech., 180: 387-403, 1987.
- [15] I. A. Kunin. On foundations of the theory of elastic media with microstructure. Int. J. Engng Sci., 22: 969-978, 1984.
- [16] C. F. Naterer, G. E. Schneider. Phases model for binary-constituent solid-liquid phase transition. Part 1: Numerical method. Numerical Heat Transfer, Part B, 28: 111-126, 1995.
- [17] D. R. Poirier, P. J. Nandapurkar, S. Ganesan. The energy and solute conservation equations for dendritic solidification. Metadl. Trans., 22B: 889-900, 1991.
- [18] M. Quintard, S. Whitaker. One and two equations models for transient diffusion processes in two phase systems. Advances in Heat Transfer, 23: 369-464, 1993.
- [19] M. Rappaz, V. R. Voller. Modeling of micro-macrosegregation in solidification processes. Metali. Trans., 21A: 749-753, 1990.
- [20] A. Somoroff. Avariational approach to statistically nonhomogeneous fields. Quarterly of Applied Mathematics, 219-236, July 1970.
- [21] C. R. Swaminathan, V. R. Voller. General enthalpy method for modeling solidification processes. Metali. Trans., 23B: 651-665, 1992.
- [22] A. Tozeren, R. Skalak. Stress in a suspension near rigid boundaries. J. Fluid Mech., 82: 289-307, 1977.
- [23] V. R. Voller, A. D. Brent. The modeling of heat, mass and solute transport in solidification systems. Int. J. Heat and Mass Transfer, 32: 1719-1731, 1989.
- [24] V. Timchenko, P. Y. P. Chen, G. de Vahl Davies, E. Leonardi. Directional solidification in microgravity. Proceedings of 11th IHTC, August 23-28, 1998, Kyongju, Korea, 7: 241-246, 1998.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPB1-0005-0009