Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T07:24:24.143Z Has data issue: false hasContentIssue false
  • English
  • Français

Solidification of a Liquid Metal with Natural Convection in a Thick-Walled Container

Published online by Cambridge University Press:  05 May 2011

H. C. Tien  and
C.C. Wang
H. C. Tien*
Affiliation:
Department of Mechanical and Marine Engineering, National Taiwan Ocean University, Keelung, Taiwan 202, R.O.C.
C.C. Wang*
Affiliation:
Department of Mechanical and Marine Engineering, National Taiwan Ocean University, Keelung, Taiwan 202, R.O.C.
*
*Associate Professor
**Graduate student
Get access

Abstract

The solidification of a phase change material (PCM), exemplified by a molten metal, in a thick-walled container is analyzed in this paper. The effects of natural convection and several important controlling parameters are investigated extensively. These parameters include the initial temperature of the PCM, external cooling conditions, thickness and thermal properties of the wall, and the thermal contact resistance at the PCM/wall interface. Two representative configurations are examined in this study. A modified version of the enthalpy formulation in which the sensible heat is separated from the latent heat, is employed to construct the energy equation for the PCM. Vorticity-stream-function approach is adopted for solving the flow field. The governing equations pertinent to the problem are discretized by the weighting function scheme and finally solved by the SIS (Strongly Implicit Solver) algorithm. It is demonstrated that for both configurations natural convection has prominent effect on the temperature distribution of the liquid phase of the PCM; however, the effect of natural convection on the shape of the solid/liquid interface and the overall solid fraction is case dependent. It is also shown that the above-mentioned controlling parameters have a direct impact on the solidification process. Specifically, an increase in the Biot number (from 1 to infinity) and the thermal diffusivity of the mold (from 0.8 to 5) enhances the solidification rate. Reverse effect was found for the other controlling parameters.

Keywords

Phase changeFree convectionMold effect
Type
Articles
Information
Journal of Mechanics , Volume 15 , Issue 2 , June 1999 , pp. 47 - 55
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Schneider, G. E., “A Numerical Study of Phase Change Energy Transport in Two-Dimensional Rectangular Enclosures,” J. Energy, Vol. 7, pp. 652–659 (1982).Google Scholar
2.Smith, R. N., Pike, R. L. and Bergs, C. M., “Numerical Analysis of Solidification in a Thick-Walled Cylindrical Container,” J. Thermophysics, Vol. 1, pp. 90–96(1987).Google Scholar
3.Tzong, R. Y. and Lee, S. L., “Solidification of Arbitrarily Shaped Casting in Mold-Casting System,” Int. J. Heat Mass Transfer, Vol. 35, pp. 2795–2803 (1992).Google Scholar
4.Viskanta, R.“Heat Transfer during Melting and Solidification of Metals,” J. Heat Transfer, Vol. 110, pp. 1205–1219 (1988).CrossRefGoogle Scholar
5.Raw, W. Y. and Lee, S. L., “Application of Weighting Function Scheme on Convection-Conduction Phase Change Problem,” Int. J. Heat Mass Transfer, Vol. 34, pp. 1503–1513 (1991).CrossRefGoogle Scholar
6.Ramachandran, N, Jaluria, Y. and Gupta, J. P., “Thermal and Fluid Flow Characteristics in One-Dimensional Solidification,” Let. Heat Mass Transfer, Vol. 8, pp. 69–77 (1981).CrossRefGoogle Scholar
7.Ramachandran, N., Gupta, J. P. and Jaluria, Y, “Thermal and Fluid Flow Effects during Solidification in a Rectangular Enclosure,” Int. J.Heat Mass Transfer, Vol. 25, pp. 187–194 (1982).Google Scholar
8.Sparrow, E. M. and Ohkubo, Y., “Numerical Analysis of Two-Dimensional Transient Freezing Including Solid-Phase and Tube-Wall Conduction and Liquid-Phase Natural Convection,” Num. Heat Transfer, Vol. 9, pp. 59–77 (1986).Google Scholar
9.Sparrow, E. M. and Ohkubo, Y., “Numerical Predictions on Freezing in a Vertical Tube,” Num. Heat Transfer, Vol. 9, pp. 79–95 (1986).Google Scholar
10.Lee, S. L. and Tzong, R. Y, “A Numerical Technique for Phase Change Problems with Large Thermal Conductivity Jump across the Interface,” Int. J. Heat Mass Transfer, Vol. 34, pp. 1491–1502 (1991).CrossRefGoogle Scholar
11.Lee, S. L., “A Strongly Implicit Solve for Two-Dimensional Elliptic Differential Equations,” Num.Heat Transfer, Vol. 16, pp. 161–178 (1989).CrossRefGoogle Scholar
12.Cubberly, W. H, “Metal Handbook, Properties and Selection: Nonferrous Alloys and Pure Metals,” 9th ed., ASM, Metal Park, Ohio (1979).Google Scholar
13.Wolff, F. and Viskanta, R., “Solidification of a Pure Metal at a Vertical Wall in the Presence of Liquid Superheat,” Int. J. Heat Mass Transfer, Vol. 31, pp. 1735–1744(1988).Google Scholar
14.Rappaz, M., “Modelling of Microstructure Formation in Solidification Process,” Int. Mat. Rev., Vol. 34, pp. 93–123(1989).Google Scholar
15.Flach, G. P. and Ozisik, M. N., “Periodic B-Spline Basic for Quasi-Steady Periodic Inverse Heat Conduction,” Int. J. Heat Mass Transfer, Vol. 30, pp. 869–880 (1987).CrossRefGoogle Scholar
16.Flach, G. P. and Ozisik, M. N., “Inverse Heat Conduction Problem for Periodically Contacting Surfaces,” J Heat Transfer, Vol. 110, pp. 821–829 (1988).Google Scholar