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

IF 0.2 Q4 MATHEMATICS
S. Kharin, T. Nauryz, B. Miedzinski
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引用次数: 4

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.
电接触过程中径向热多项式与误差积分函数线性组合的两相球面stefan反问题求解
摘要本文研究了球面模型中需要确定热流密度的反Stefan问题。这项工作是我们在电气工程方面的研究的继续,当热流通过一种材料到另一种材料时,在它们接触的地方,热量分布过程发生了变化。在自由边界α (t)处接触点开始沸腾,在β (t)处接触点开始熔化,出现液相和固相两相。我们的目的是计算液相和固相的温度,从而求出进入接触点的热流密度。径向热多项式与误差积分函数线性组合问题的精确解。给出了确定未知系数的递推公式。通过测试问题和近似问题,比较了热流密度的精确解和近似解,验证了方法的有效性。求得了液固两相的热系数和热流密度。利用Mathcad程序通过测试问题对热流方程进行了验证。关键词:Stefan问题,径向热多项式,Faa-di Bruno,配置法
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来源期刊
CiteScore
0.30
自引率
0.00%
发文量
11
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