A NUMERICAL STUDY FOR INWARD SOLIDIFICATION OF A LIQUID CONTAINED IN CYLINDRICAL AND SPHERICAL VESSEL

Abstract

This study presents a numerical solution of inward solidification of phase change material contained in cylinder/sphere. Here, constant thermal property is assumed throughout the analysis for the liquid, which is initially at fusion temperature. The governing dimensionless equations of the above problem and boundary conditions are converted to initial value problem of vector matrix form. The time function is approximated by Chebyshev series and the operational matrix of integration is applied. The solution is utilized iteratively in the interface condition to determine the time taken to attain a fixed interface position.

Keywords

Dates

  • Submission Date2009-05-24
  • Revision Date2009-12-03
  • Acceptance Date2009-12-12

DOI Reference

10.2298/TSCI1002365R

References

  1. Carslaw, H. S., Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, London, 1959
  2. Lunardini, V. J., Heat Transfer in Cold Climates, van Nostrand Reinhold Co., New York, USA, 1981
  3. Ozisik, M. N., Heat Conduction, 2nd ed., John Wiley and Sons, New York, USA, 1993
  4. Hill, J., One-Dimensional Stefan Problem, An Introduction, Longman Scientific and Technical, Essex, UK, 1987
  5. Shih, Y. P., Tsay, S. Y., Analytical Solution for Freezing a Saturated Liquid Inside and Outside Cylinder, Chem. Engg. Sci., 26 (1971), 6, pp. 809-816
  6. Prud'homme, M., Nguyen, T. H., Nguyen, D. L., A Heat Transfer Analysis for Solidification of Slabs, Cylinders and Sphere, Journal of Heat Transfer, 111 (1989), 3, pp. 699-705
  7. Feltham, D. L., Garside, J., Analytical and Numerical Solution Describing the Inward Solidification of a Binary Melt, Chem. Engg. Sci., 56 (2001), 7, pp. 2357-2370
  8. Lin, S., Jiang, Z., An Improved Quasi-Steady Analysis for Solving Freezing Problem in a Plate, a Cyllinder and a Sphere, J. Heat Transfer, 125 (2003), 6, pp. 1123-1128
  9. Tao, L. C., Generalized Numerical Solutions of Freezing a Saturated Liquid in Cylinders and Spheres, AIChE Journal, 13 (1967), 1, pp. 165-169
  10. Voller, V. R., Cross, M., Estimating the Solidification/Melting Times of Cylindrically Symmetric Regions, Int. J. Heat and Mass Transfer, 24 (1981), 9, pp. 1457-1462
  11. Voller, V. R., Fast Implicit Finite Difference Method for the Analysis of Phase Change Problems, Numerical Heat Transfer, B 17 (1990), 2, pp. 155-169
  12. Caldwell, J. D., Chan, C. C., Spherical Solidification by the Enthalpy Method and Heat Balance Integral Method, Applied Mathematical Modeling, 24 (2000), 1, pp. 45-53
  13. Ismail, K. A. R., Henriques, J. R., Solidification of PCM Inside a Spherical Capsule, Energy Conservation and Management, 41 (2000), 2 , pp. 173-187
  14. Ismail, K. A. R., Henriques, J. R., T. Da Silva, M., A Parametric Study on Ice Formation inside a Spherical Capsule, Int. J. Thermal Science, 42 (2003), 9, pp. 881-887
  15. Bilir, L., Ilken, Z., Total Solidification Time of a Liquid Phase Change Material Enclosed in Cylindrical/Spherical Containers, Applied Thermal Engineering, 25 (2005),10, pp. 1488-1502
  16. Assis, E., Ziskind, G., Letan, R., Numerical and Experimental Study of Solidification in a Spherical Shell, ASME J. Heat Transfer, 131 (2009), 2, pp. 1-5
  17. Liu, C. C., Shih, Y. P., Analysis and Parameter Identification of Linear Systems via Chebyshev Polynomials of Second Kind, Int. J. System Sci., 16 (1985), 6, pp. 753-759
  18. Parida, P. R., et al., Solidification of a Semitransparent Planar Layer Subjected to Radiative and Convective Cooling, J. Quantitative Spectroscopy & Radiative Transfer, 107 (2007), 2, pp. 226-235
Volume 14, Issue 2, Pages365 -372