Context. The non-linear boundary value problem of heat conduction for a thermosensitive non-homogeneous strip-shaped element<br />of a radio-electronic system with a through inclusion has been solved whose analytical-numerical solution enables us to analyze<br />temperature regimes in the element.<br />Objective. Is to develop such a method of linearization of mathematical model of heat conduction which enables us to obtain analytical<br />numerical solution of the corresponding non-linear boundary value problem for determination of temperature field in elements<br />of radio electronic devices, which are geometrically represented by a thermosensitive plate with a through inclusion.<br />Method. A linearizing function which enables us to partially linearize the initial non-linear mathematical model of heat conduction<br />for a thermosensitive non-homogeneous element of a radio electronic system in the form of “plate-inclusion” structure has been suggested. The introduced piece-wise linear approximation of temperature on plate-inclusion interfaces has enabled us to completely linearize the corresponding partially linearized boundary value problem relative to the linearizing function. After this, it became possible to apply Fourier’s integral transformation to the obtained linear problem with respect to one of the spatial coordinates, as well as to determine the linearizing function. The linear dependence of the coefficient of heat conductivity on temperature for structure materials with the use of the linearizing function has been considered. By solving the boundary value problem, the formulae for determination of temperature field in the “plate-inclusion” thermosensetive structure have been obtained.<br />Results. The obtained formulae for determination of temperature field in a thermosensitive non-homogeneous element of radio<br />electronic system were used to create the software which enables us to obtain distribution of value of temperature and to analyze<br />temperature regimes.<br />Conclusions. A mathematical model for the calculation for the temperature field in a “plate-inclusion” thermosensitive structure<br />is adequate to the actual physical process, because no jump of temperature at “plate-inclusion” interfaces is observed. The numerical<br />results for the chosen materials under linear dependence of the coefficient of thermoconductivity on temperature differ by 7% from<br />the results which are obtained for constant coefficient of heat conductivity. Prospect of further investigation will consider more complicated geometric representation of elements of radio electronic systems.
Науковий журнал «Радіоелектроніка, інформатика, управління»
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Havrysh, V. I.; Lviv Polytechnic National University, Lviv, Ukraine Baranetskij, Ya. O.; Lviv Polytechnic National University, Lviv, Ukraine. Kolyasa, L. I.; Lviv Polytechnic National University, Lviv, Ukraine. |
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Context. The non-linear boundary value problem of heat conduction for a thermosensitive non-homogeneous strip-shaped element<br />of a radio-electronic system with a through inclusion has been solved whose analytical-numerical solution enables us to analyze<br />temperature regimes in the element.<br />Objective. Is to develop such a method of linearization of mathematical model of heat conduction which enables us to obtain analytical<br />numerical solution of the corresponding non-linear boundary value problem for determination of temperature field in elements<br />of radio electronic devices, which are geometrically represented by a thermosensitive plate with a through inclusion.<br />Method. A linearizing function which enables us to partially linearize the initial non-linear mathematical model of heat conduction<br />for a thermosensitive non-homogeneous element of a radio electronic system in the form of “plate-inclusion” structure has been suggested. The introduced piece-wise linear approximation of temperature on plate-inclusion interfaces has enabled us to completely linearize the corresponding partially linearized boundary value problem relative to the linearizing function. After this, it became possible to apply Fourier’s integral transformation to the obtained linear problem with respect to one of the spatial coordinates, as well as to determine the linearizing function. The linear dependence of the coefficient of heat conductivity on temperature for structure materials with the use of the linearizing function has been considered. By solving the boundary value problem, the formulae for determination of temperature field in the “plate-inclusion” thermosensetive structure have been obtained.<br />Results. The obtained formulae for determination of temperature field in a thermosensitive non-homogeneous element of radio<br />electronic system were used to create the software which enables us to obtain distribution of value of temperature and to analyze<br />temperature regimes.<br />Conclusions. A mathematical model for the calculation for the temperature field in a “plate-inclusion” thermosensitive structure<br />is adequate to the actual physical process, because no jump of temperature at “plate-inclusion” interfaces is observed. The numerical<br />results for the chosen materials under linear dependence of the coefficient of thermoconductivity on temperature differ by 7% from<br />the results which are obtained for constant coefficient of heat conductivity. Prospect of further investigation will consider more complicated geometric representation of elements of radio electronic systems. |
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Zaporizhzhya National Technical University 2018-12-07 16:07:43 |
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application/pdf http://ric.zntu.edu.ua/article/view/148601 |
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Radio Electronics, Computer Science, Control; No 3 (2018): Radio Electronics, Computer Science, Control |
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Copyright (c) 2018 V. I. Havrysh |
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