Indexing
All Issues
Submission
Author Guidelines
Reviewers
Editorial Members
Publication Fee
Vol.1 , No. 1, Publication Date: May 13, 2016, Page: 10-17
| [1] | Khujaev J. I., Center for the Development of Software and Hardware-Program Complexes, Tashkent University of Information Technologies, Tashkent, Uzbekistan. |
A mathematical model of Stefan problem considering the density change during the melting process is proposed. The task is complicated by the fact that the boundary of the computational area becomes variable within the time. We offer a combined method for solving the problem with the use of numerical methods of catching the front and straightening the front. The results of computational experiments on melting ice and copper are given as example. Algorithms and software can be used to study the melting process of other pure substances.
Keywords
Stefan Problem, Heat Transfer, the Front of the Phase Transition, Melting, Numerical Method, Catching the Front, Straightening the Front
Reference
| [01] | Back J. Stefan Problems for Melting Nanoscaled Particles // Thesis for the degree of Doctor of Philosophy, Queensland, Australia, 2014. – 199 p. |
| [02] | Shabnova M. P. Teploprovodnost v drobnom ischislenii: Prilozheniya v nestatsionarnym metodam opredeleniya teplofizicheskih harakteristik veshestv i k zadache Stefana // Avtoref. Dis. kand. tekh. nauk. – Mahachkala, 2011. – 24 pages. |
| [03] | Font F. M. Beyond the classical Stefan problem // PhD thesis, 2014, Barcelona, Spain. – 162 pages. |
| [04] | Sudakov I. A. Matematicheskoye modelirovaniye vzaimodeystviya kriolitozony i atmosfery // Avtoref. Dis. kand. f-m. nauk. – Velikiy Novgorod, 2011. – 20 pages. |
| [05] | Voller V. R., Swenson J. B., Paola C. An analytical solution for a Stefan problem with variable latent heat. Technical note // International Journal of Heat and Mass Transfer, Elsevier B.V., 2004, #47. – PP. 5387–5390. |
| [06] | Kim S. H. Two simple numerical methods for the free boundary in one-phase Stefan problem // Journal of Applied Mathematics. Volume 2014, Hindawi Publishing Corporation, Article ID 764532. – PP. 1-10. http://dx.doi.org/10.1155/2014/764532. |
| [07] | Escher J., Prüss J., Simonett G. Analytic solutions for a Stefan problem with Gibbs-Thomson correction // Journal für die reine und angewandte Mathematik // Walter de Gruyter, Berlin, New York, 2003, #563. – PP. 1-52. |
| [08] | Tarzia D. A. Determination of one unknown thermal coefficient through the one-phase fractional Lamé-Clapeyron-Stefan problem // Applied Mathematics, Scientific research publishing. 2015, #6. – PP. 2182-2191. http://www.scirp.org/journal/am, http://dx.doi.org/10.4236/am.2015.613191. |
| [09] | Rubtsov N. A., Sleptsov S. D., Savvinova N. A. Chislennoye modelirovaniye odnofaznoy zadachi Stefana v sloye s prozrachnymi i poluprozrachnymi granitsami // Prikladnaya mehanika i tehnicheskaya fizika. Novosibirsk. 2006. T. 47, #3. PP. 84-91. |
| [10] | Hu H., Argyropoulos S. A. Mathematical modelling of solidification and melting: a review // Modelling and simulation in materials science and engineering, IOP publishing UK, 1996, #4. – PP. 371-396. |
| [11] | Javierre E., Vuik C., Vermolen F. J., van der Zwaag S. A comparison of numerical models for one-dimensional Stefan problems // Journal of Computational and Applied Mathematics, Elsevier, 2006, #192. – PP. 445–459. |
| [12] | Lukyanov A. A. Realna li ekologicheskaya katastrofa, svyazannaya s tayaniyem ledovogo pokrytiya Zemli? O vozmozhnoy skorosti tayaniya aysbergov // Uchyoniye zapiski, #5, 2009. – PP. 154-163. |
| [13] | Salva N. N., Tarzia D. A. Explicit solution for a Stefan problem with variable latent heat and constant heat flux boundary conditions // Journal of Mathematical Analysis and Applications, 379, Elsevier, 2011. – PP. 240–244. |
| [14] | Heim D. Two solution methods of heat transfer with phase change within whole building dynamic simulation // Ninth International IBPSA Conference, Montreal, Canada August 15-18, 2005. – PP. 397-402. |
| [15] | Tihonov A. M., Samarskiy A. A. Uravneniya matematicheskoy fiziki. – M.: Nauka, 1977. – 736 pages. |
| [16] | Budak B. M., Vasilyev F. P., Uspenskiy A. B. Raznostniye metody resheniya nekotoryh krayevyh zadach tipa Stefana // Sbornik VTs MGU, v VI, Chislenniye metody v gazovoy dinamike, 1965, PP. 139-183. |
| [17] | Budak B. M., Goldman N. L., Uspenskiy A. B. Raznostniye shemy s vypryamleniyem frontov dlya resheniya mnogofrontovyh zadach tipa Stefana // DAN SSSR, 1966, Tom 167, #4. – PP. 735-738. |
| [18] | Samarskiy A. A., Vabishevich P. N. Vychislitelnaya teploperedacha // M.: Editorial URSS, 2003. – 784 pages. |
| [19] | Kalitkin N. N. Chislenniye metody // M.: Nauka, 1978. 512 pages. |
