Use of Lagrangian-Eulerian Computing Method for Systems with Phase Change at the Solution of Stefan Boundary Value Problem

Abstract:

The problem of a planar solidification of a material with an additional nonstationary radiant of heat on a semi-infinite plane has been solved. For a solution the condition of Stefan was used. Results have been compared with an analytical solution in case of the absence of an additional radiant of heat, as well as with a solution obtained by perturbations method. A more complicated two-dimensional nonstationary problem of a solidification of a liquid with interface free-boundary has been also solved. The purpose of this problem solution is to predict position of a material phase boundary, as well as the temperature distribution in a layer of PCM (Phase-Change Material) with boundary conditions of Dirichlet.

• Periodical: Key Engineering Materials (Volume 685)
• Pages: 177-180
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.685.177
• Online since: February 2016
• Authors: Alexander S. Ogorodnikov*, M.V. Troshin
• Keywords: Heat Transfer, Melting, PCM Storage, Solidification, Solid-Liquid Interface, Stefan Problem

References

[1] J. Fernandez-Diaz, W.O. Williams, A generalized Stefan condition, J. Applied Mathematics Physics (ZAMP), 30 (1979) 749–755.

DOI: 10.1007/bf01590684

[2] Zi-Tao Yu, Li-Wu Fan, Ya-Cai Hu, Ke-Fa Cen, Perturbation solution to heat conduction in melting or solidification with heat generation, Int. J. Heat Mass Transf., 46 (2010) 479-483.

DOI: 10.1007/s00231-010-0596-4

[3] David E. Glassa, M. Necati Ozisik, W. S. Kim, Hyperbolic Stefan Problem with Applied Surface Heat Flux and Temperature-Dependent Thermal Conductivity, Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, 18(4) (1991).

DOI: 10.1080/10407789008944805

[4] Jiji L.M., Gaye S. Analysis of solidification and melting of PCM with energy generation. Appl Therm Eng., 26 (2006) 568–575.

DOI: 10.1016/j.applthermaleng.2005.07.008

[5] C.W. Hirt, A.A. Amsden, and J.L. Cook. An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comp. Phys. 14 (1974), 227–253.

DOI: 10.1016/0021-9991(74)90051-5

[6] P. Lamberg , Approximate analytical model for two-phase solidification problem in a finned phase-change material storage, Applied Energy, 77(2004) 131–152.

DOI: 10.1016/s0306-2619(03)00106-5