Abstract
Phase transformations take place in familiar ways such as solidification, melting, vaporisation and condensation etc. A direct transformation from solid to vapour phase is called sublimation. From a thermodynamics point of view, when a system consists of more than one phase, each phase may be considered as a seperate system within the whole. The thermodynamic parameters of the whole system may then be constructed from those of the component phases. However, assuming thermodynamic equilibrium and restricting the interaction between the phases at the interface, solely to the flow of heat, no new complications arise and the two phase system can essentially be treated as a single system with anisotropic properties. This assumption has been used in this chapter to develop the algorithms for the numerical simulation of phase transformation processes. Furthermore, the processes considered here have been restricted to melting and solidification, involving only the solid and liquid phases of materials. The assumptions made above cease to remain valid, when the vapour phase is considered.
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References
S. DelGuidice, G. Comini, and R.W. Lewis. Finite element simulation of freezing processes in soils. International Journal of Numerical and Analytical Methods in Geomechanics, 2: 223–235, 1978.
P.E. Frivik, E. Thorbergsen, S. DelGuidice, and G. Comini. Thermal design of pavement structures in seasonal frost areas. Journal of Heat Transfer, 99: 533–540, 1977.
H.C.Huang and R.W.Lewis. Adaptive analysis for heat flow problems using error estimation techniques. In Sixth International Conference for Numerical Methods in Thermal Problems, Swansea, U.K., July 1989. Pineridge Press, Swansea.
J.Crank. Free and Moving Boundary Problems. Clarendon Press, Oxford, 1984.
M.T.Samonds. Finite Element Simulation of Solidification in Sand Mould and Gravity Die Castings - Ph.D. Thesis. University of Wales, Swansea, 1985.
R. J. Sarjant and M. R. Slack. Internal temperature distribution in the cooling and reheating of steel ingots. Journal of Iron and Steel Institute, 177: 428–444, 1954.
J.G. Henzel and J. Keverian. Predicting casting solidification patterns with a computer. Foundry, pages 50–53, 1964.
J.G. Henzel and J. Keverian. Predicting casting solidification patterns in a steel valve casting by means of a digital computer. Metals Eng. Quarterly, pages 39–44, 1965.
J.G. Henzel and J. Keverian. Comparison of calculated and measured solidification patterns in a variety of steel castings. AFS Cast Metals Research Journal, pages 19–36, 1965.
R. Weatherwax and O.K. Riegger. Computer-aided solidification study of a die cast aluminium piston. AFS Transactions, 85: 317–322, 1977.
P.N. Hansen. Numerical simulation of the solidification process. In Solidification and Casting of Metals, Sheffield, U. K., 1979. The Metals Society. Proceedings of the Conference.
J.I. Soliman and E.A. Fakhroo. Finite element solution of heat transmission in steel ingots. Journal of Mechanical Eng. Science, 14: 19 24, 1972.
K. Morgan, R.W. Lewis, and K.N.Seetharamu. Modelling of heat flow and thermal stress in ingot casting. Simulation, pages 55–63, 1981.
R.W. Lewis, K.N. Seetharamu, and K.Morgan. Application of the finite element method in the study of ingot castings. In Solidification Technology in the Foundry and Cast House, pages 40–43, Coventry, U.K., September 1983. The Metals Society. Proceedings of the Conference.
A.J. Dalhuijsen and A. Segal. Comparison of finite element techniques for solidification problems. International Journal for Numerical Methods in Engineering, 23: 1807–1829, 1986.
M. Salcudean and Z. Abdullah. On the numerical modelling of heat transfer during solidification processes. International Journal for Numerical Methods in Engineering, 25: 445–473, 1988.
V.R. Voller, C.R. Swaminathan, and B.G. Thomas. Fixed grid techniques for phase change problems: A review. International Journal for Numerical Methods in Engineering, 30:875–898, 1990. Special thermal issue.
J. Crank, How to deal with moving boundaries in thermal problems. In R.W. Lewis, K. Morgan, and O.C. Zienkiewicz, editors, Numerical Methods in Heat Trafsfer. Wiley, Chichester, 1981.
K. O’Neill and D.R. Lynch. A finite element solution of freezing problems using a continuously deforming coordinate system. In R.W. Lewis, K. Morgan, and O.C. Zienkiewicz, editors, Numerical Methods in Heat Trafsfer. Wiley, Chichester, 1981.
J. Yoo and B. Rubinsky. Numerical computation using finite elements for the moving interface in heat transfer problems with phase transformation. Numerical Heat Transfer, 6: 209–222, 1983.
R.W. Lewis K. Morgan and O.C. Zienkiewicz. An improved algorithm for heat conduction problems with phase change. International Journal for Numerical Methods in Engineering, 12: 1191–1195, 1978.
R.W. Lewis and H.C. Huang. A finite element analysis of fire resisting cabinets using an adaptive remeshing technique. Applied Mathematical Modelling, (to be published in 1991 ).
R.W. Lewis and P.M. Roberts. Finite element simulation of solidification problems. Applied Scientific Research, 44: 61–92, 1987.
E.C. Lemmon. Multidimensional integral phase change approxima-tions for finite element conduction codes. In R.W. Lewis, K. Morgan, and O.C. Zienkiewicz, editors, Numerical Methods in Heat Trafsfer. Wiley, Chichester, 1981.
R. Viskanta. Phase change heat transfer. In G.A.Lane, editor, Solar Heat Storage Latent Heat Materials. CRC Press, 1983.
V.R. Voller, M. Cross, and N.C. Markatos. An enthalpy method for convection/diffusion phase change. International Journal for Numerical Methods in Engineering, 24: 271–284, 1987.
W.D. Rolph and K.J. Bathe. An efficient algorithm for analysis of nonlinear heat transfer with phase changes. International Journal for Numerical Methods in Engineering, 18: 119–134, 1982.
J. Roose and O. Storrer. Modelization of phase changes by fictitious heat flow. International Journal for Numerical Methods in Engineering, 20: 217–225, 1984.
O.C. Zienkiewicz. The Finite Element Method. McGraw-Hill Book Company (UK) Limited, London, 1977.
H.S. Carslaw and J.C. Jaeger. Conduction of Heat in Solids. Clarendon Press, Oxford, 1959.
Jr. C. Hastings. Approximations for Digital Computers. Princeton University Press, Princeton,N.J., 1955.
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© 1994 Springer-Verlag London Limited
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Huang, HC., Usmani, A.S. (1994). Phase Transformation. In: Finite Element Analysis for Heat Transfer. Springer, London. https://doi.org/10.1007/978-1-4471-2091-9_5
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DOI: https://doi.org/10.1007/978-1-4471-2091-9_5
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