Numerical Simulation of Ice Melting Using the Finite Volume Method
Main Article Content
Abstract
The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen
to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one dimensional temperature
distribution with the analytical results.
Article Details
Section
How to Cite
References
Alexiades V. and Solomon A.D., Mathematical Modeling of Melting and Freezing Processes, Hemisphere Publishing Corporation, Washington, 1993.
Al-Zubaidy E.M., "A Computational and instructional study of the effect of natural convection on ice melting", M.Sc. Thesis, Department of Technical Education, University of Technology, Iraq, 2006.
Caldwell J. and Kwan Y.Y., "Numerical methods for one-dimensional Stefan problem", Communications in Numerical Methods in Engineering, Vol. 20, pp. 535-545,
John Wiley and Sons, 2004. Carslaw H.S. and Jaeger J.C., Conduction of Heat in Solids, Oxford University Press, London,
UK, 1959.
Chein-Shan Liu, "Solving two typical inverse Stefan problems by using the Lie-Group shooting method", International Journal of Heat and Mass Transfer, Vol. 54, pp. 1941- 1949, Elsevier, 2011.
Holman J.P., Heat Transfer, 7th ed in SI Units, McGraw-Hill , UK, 1992.
Myers T.G., Mitchell S.L., Muchatibaya G. and Myers M.Y., "A Cubic heat balance integral method for one-dimensional melting of a finite thickness layer", International journal of Heat and Mass Transfer, Vol. 50, pp.5305-5317, Elsevier, 2007.
Naaktgeboren C., "The zero-phase Stefan problem", International journal of Heat and Mass Transfer, Vol. 50, pp.4614-4622, Elsevier, 2007.
Ozisik M.N., Heat Conduction, John Wiley and Sons, New York, 1993.
Patrick K. et al., "Modeling and simulation of ice/snow melting", the 22nd ECMI Modeling Week Conference, Eindhoven, the Netherlands, 2008.
Prapainop R. and Maneeratana K., "Simulation of ice formation by the finite volume method", Songklanakarin J. Sci. Technol., Vol. 26,
No. 1, Jan.-Feb. 2004.
Rincon M.A. and Scardua A., "The Stefan problem with moving boundary", Bol. Soc. Paran. Mat., (3s) V.26, 1-2 , 2008.
Sadoun N., Si-Ahmed E.K. and Legrand J., "On Heat conduction with phase change: accurate explicit numerical method", Journal
of Applied Fluid Mechanics, Vol. 5, No. 1, pp- 105-112, 2012.
Savovic S. and Caldwell J., "Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions",
International journal of Heat and Mass Transfer, Vol. 46, pp. 2911-2916, Pergamon Press., 2003.
Sugawara M., Komatsu Y. and Beer H., "ThreeDimensional melting of ice around a liquidcarrying tube", Heat Mass Transfer, Vol. 47,
pp. 139-145, Springer, 2011.
Versteeg H.K. and Malalasekera W., An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Longman Scientific & Technical, England, 1995.
Witula R., Hetmaniok E., Slota, D. and Zielonka A., "Solution of the two-phase Stefan problem by using the Picards iterative method", Journal of Thermal Science, Vol. 15, Suppl. 1, pp. S21-S26, 2011.
Zhaochun WU, Jianping LUO and Jingmei FENG, "A Noval algorithm for solving the classical Stafan problem", Journal of Thermal Science, Vol. 15, Suppl. 1, pp. S39-S44,