Solving nonlinear nonstationary problem of heat-conductivity by finite element method
DOI:
https://doi.org/10.31498/2225-6733.32.2016.83945Keywords:
modelling of thermoelectric processes, finite elements method, Galerkin method, approximation, Mathcad, linearizationAbstract
Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM) and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular). Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditionsReferences
Моделирование термоэлектрической системы генерирования тепловой и электрической энергии / В.Я. Михайловский, Л.Т. Струтинская, Е.В. Чайковская // Технология и конструирование в электронной аппаратуре. – 2005. – № 4. – С. 27-30.
Ярымбаш Д.С. Идентификация электрических параметров печной петли мощных печей графитации / Д.С. Ярымбаш // Электротехника и электромеханика. – 2012. – № 1. – С. 49-54.
Yune Y.G. Transient Nonlinear Thermal Runaway Effects in Carbon Graphite Electrical Brushes / Y.G. Yune, M.D. Bryant // IEEE Transactions on Components Hybrids and Manufacturing Technology. – 1988. – Vol. 11, № 1. – P. 91-100.
Temperature evolution during field activated sintering / A. Zavaliangos, J. Zhang, M. Krammer, J.R. Groza // Materials Science and Engineering. – 2004. – Vol. 379, Iss. 1-2. – P. 218-228.
Кучерявая И.Н. Компьютерное моделирование электротепловых процессов в полимер-ной изоляции кабеля с воздушным включением при возникновении единичного частичного разряда / И.Н. Кучерявая // Технічна електродинаміка. – 2011. – № 5. – С. 18-24.
Study by simulation of the effect of temperature on the appearance of partial discharges in gaseous cavities contained in the insulator of high voltage cable / T. Seghir, A. Nouar, K. Lefkaier, D. Mahi // Power Tech Conference Proceedings. – Bologna, 2003. – Р. 718-721.
A numerical method for transient simulation of metallurgical compound electrodes / A. Bermudez, J. Bullon, F. Pena, P. Salgado // Finite Elements in Analysis and Design. – 2003. – Vol. 39, Iss. 4. – P. 283-299.
Зенкевич О. Метод конечных элементов в технике / О. Зенкевич ; пер. с англ. ; под ред. Б.Е. Победри. – М. : Мир, 1975. – 541 с.
Сегерлинд Л. Применение метода конечных элементов / Л. Сегерлинд ; пер. с англ. А.А. Шестакова ; под ред. Б.Е. Победри. – М. : Мир, 1979. – 392 с.
Карвацький А.Я. Метод скінченних елементів у задачах механіки суцільних середовищ. Програмна реалізація та візуалізація результатів : навчальний посібник. – К. : НТУУ «КПІ» ВПІ ВПК «Політехніка», 2015. – 392 c.
Самарский А.А. Разностные методы решения задач газовой динамики / А.А. Самарский, Ю.П. Попов. – М. : Наука, 1980. – 352 с.
Джордж А. Численное решение больших разреженных систем уравнений / А. Джордж, Дж. Лю ; пер. с англ. Х.Д. Икрамова. – М. : Мир, 1984. – 334 с.
Gmsh. a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities [Электронный ресурс]. – (http://geuz.org/gmsh/).
ParaView. An open-source, multi-platform data analysis and visualization application [Электронный ресурс]. – (http://www.paraview.org/).
Mathcad. Engineering math software that allows perform, analyze, and share your most vital calculations [Электронный ресурс]. – (http://www.ptc.com/engineering-math-software/mathcad/).
Исаченко В.П. Теплопередача : учебник для вузов / В.П. Исаченко, В.А. Осипова, А.С. Сукомел. – М. : Энергоиздат, 1981. – 416 с.
Matlab. The Language of Technical Computing [Электронный ресурс]. –(http://www.mathworks.com/products/matlab/).
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