# TWO PHASE SPHERICAL STEFAN INVERSE PROBLEM SOLUTION WITH LINEAR COMBINATION OF RADIAL HEAT POLYNOMIALS AND INTEGRAL ERROR FUNCTIONS IN ELECTRICAL CONTACT PROCESS

• S. N. Kharin Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
• T. A. Nauryz Kazakh-British Technical University, Almaty, Kazakhstan
• B. Miedzinski Wroclaw University, Wroclaw, Poland

### Abstract

Abstract. In this research the inverse Stefan problem in spherical model where heat flux has to be determined is considered. This work is continuing of our research in electrical engineering that when heat flux passes through one material to the another material at the point where they contact heat distribution process takes the place. At free boundary α (t) contact spot starts to boiling and at β (t) stars to melting and there appear two phase: liquid phase and solid phase. Our aim to calculate temperature in liquid and solid phase, then find heat flux entering into contact spot. The exact solution of problem represented in linear combination of series for radial heat polynomials and integral error functions. The recurrent formulas for determine unknown coefficients are represented. The effectiveness of method is checked by test problem and approximate problem in which exact solution and approximate solution of heat flux is compared. The coefficients of heat at liquid and solid phases and heat flux are found. The heat flux equation is checked by testing problem by using Mathcad program.Key words: Stefan problem, radial heat polynomials, Faa-di Bruno, collocation method.
Published
2020-12-31
How to Cite
KHARIN, S. N.; NAURYZ, T. A.; MIEDZINSKI, B.. TWO PHASE SPHERICAL STEFAN INVERSE PROBLEM SOLUTION WITH LINEAR COMBINATION OF RADIAL HEAT POLYNOMIALS AND INTEGRAL ERROR FUNCTIONS IN ELECTRICAL CONTACT PROCESS. International Journal of Mathematics and Physics, [S.l.], v. 11, n. 2, p. 4-13, dec. 2020. ISSN 2409-5508. Available at: <https://ijmph.kaznu.kz/index.php/kaznu/article/view/334>. Date accessed: 23 june 2021. doi: https://doi.org/10.26577/ijmph.2020.v11.i2.01.
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Section
MATHEMATICS