INVESTIGATION OF TEMPERATURE MODES IN THERMOSENSITIVE NON-UNIFORM ELEMENTS OF RADIOELECTRONIC DEVICES
DOI:
https://doi.org/10.15588/1607-3274-2018-3-1Keywords:
temperature, heat conduction, nonlinear boundary-value problem, isotropic infinite thermosensitive plate with insulated faces, through inclusion, perfect thermal contact, heat flow.Abstract
Context. The non-linear boundary value problem of heat conduction for a thermosensitive non-homogeneous strip-shaped elementof a radio-electronic system with a through inclusion has been solved whose analytical-numerical solution enables us to analyze
temperature regimes in the element.
Objective. Is to develop such a method of linearization of mathematical model of heat conduction which enables us to obtain analytical
numerical solution of the corresponding non-linear boundary value problem for determination of temperature field in elements
of radio electronic devices, which are geometrically represented by a thermosensitive plate with a through inclusion.
Method. A linearizing function which enables us to partially linearize the initial non-linear mathematical model of heat conduction
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.
Results. The obtained formulae for determination of temperature field in a thermosensitive non-homogeneous element of radio
electronic system were used to create the software which enables us to obtain distribution of value of temperature and to analyze
temperature regimes.
Conclusions. A mathematical model for the calculation for the temperature field in a “plate-inclusion” thermosensitive structure
is adequate to the actual physical process, because no jump of temperature at “plate-inclusion” interfaces is observed. The numerical
results for the chosen materials under linear dependence of the coefficient of thermoconductivity on temperature differ by 7% from
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.
References
Savatorova V. L. Reshenie uravnenija teploprovodnosti v
neodnorodnoj srede s uchetom temperaturnoj zavisimosti
kojefficienta teploprovodnosti, Obozrenie prikladnoj i
promyshlennoj matematiki, 2009, 17, No. 1, pp. 135–137.
Kudinov V. A. Analiz nelinejnoj teploprovodnosti na
osnove opredelenija fronta temperaturnogo vozmushhenija,
Teplofizika vysokih temperatur, 2006, 44, No. 3, pp. 577–
Kudrjashov N. A. Priblizhennye reshenija odnomernyh
zadach nelinejnoj teploprovodnosti pri zadannom potoke,
Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki,
, 47, No. 1, pp. 110–120.
Carpinteri A., Paggi M. Thermoelastic mismatch in
nonhomogeneous beams, J. Eng. Math, 2008, 61, No. 2–4.
pp. 371–384.
Noda N. Thermal stresses in materials with temperaturedependent
properties, Appl. Mech. Rev,, 1991, 44, pp. 383–
Noda N. Thermal stresses in materials with temperaturedependent properties, Appl. Mech. Rev., 1991, 44, pp. 383– 397.
Otao Y. Tanigawa O., Ishimaru O. Optimization of
material composition of functionality graded plate for
thermal stress relaxation using a genetic algorithm, J.
Therm. Stresses, 2000, 23, pp. 257–271.
Tanigawa Y., Akai T., Kawamura R. Transient heat
conduction and thermal stress problems of a
nonhomogeneous plate with temperature-dependent
material properties, J. Therm. Stresses, 1996, 19, No. 1, pp.
–102.
Tanigawa Y., Otao Y. Transient thermoelastic analysis of
functionally graded plate with temperature-dependent
material properties taking into account the thermal
radiation, Nihon Kikai Gakkai Nenji Taikai Koen
Ronbunshu, 2002, 2, pp. 133–134.
Yangian Xu., Daihui Tu. Analysis of steady thermal stress
in a ZrO2/FGM/Ti-6Al-4V composite ECBF plate with
temperature-dependent material properties by NFEM,
-WASE Int. Conf. on Informa. Eng., Vol. 2–2, pp.
–436.
Golicyna E. V., Osipov Ju. R. Kvazistacionarnaja
trehmernaja zadacha teploprovodnosti vo vrashhajushhemsja sploshnom cilindre iz kompozicionnogo materiala s nelinejnymi granichnymi uslovijami, Konstrukcii iz kompozicionnyh materialov, 2007, No. 4, pp.
–58.
Kudrjashov N. A., Chmyhov M. A. Priblizhennye reshenija
pervoj i vtoroj kraevyh zadach nelinejnoj teploprovodnosti
na polubeskonechnoj prjamoj, Inzhenernaja fizika, 2007,
No. 3, pp. 12–15.
Kudinov V. A., Averin B. V., Stefanyuk E. V.,
Nazarenko S. A. Analysis of nonlinear heat conduction
based on determining the front of temperature perturbation,
High Temperature, 2006, 44, № 4, pp. 574–583.
Popovich V. S., Іvankіv K. S. Nelіnіjna zadacha
teploprovіdnostі dlja kulі z teploobmіnom, Vіsnik L'vіv. untu.
Ser. Prikl. matematika ta іnformatika, 2002, No. 5,
pp. 136–144.
Savula Ja. G., Djakonjuk L. M. Doslіdzhennja varіacіjnoї
zadachі teploprovіdnostі u bagatosharovih seredovishhah z
tonkimi vkljuchennjami, Vіsnik LNU іm. І. Franka, Ser.
prikl. matem. ta іnformat, 2000, No. 3, pp. 125–130.
Gavrish V. І., Fedasjuk D. V. Modeljuvannja temperaturnih
rezhimіv u kuskovo-odnorіdnih strukturah. L'vіv: V-vo
Nac. un-tu «L'vіvs'ka polіtehnіka», 2012, 176 p.
Gavrysh V. I. Chislenno-analiticheskoe reshenie nelinejnoj
stacionarnoj zadachi teploprovodnosti dlja beskonechnoj
termochuvstvitel'noj mnogoslojnoj plastiny, Jelektronnoe
modelirovanie, 2014, 36, No. 3, pp. 59–70.
Gavrish V. І. Doslіdzhennja temperaturnih rezhimіv u
termochutlivіj plastinі z chuzhorіdnim naskrіznim
vkljuchennjam, Fіziko-matematichne modeljuvannja ta
іnformacіjnі tehnologії. Naukovij zbіrnik, 2013, Vipusk 18,
pp. 43–50.
Gavrish V. І. Nelіnіjna krajova zadacha teploprovіdnostі
dlja sharuvatoї plastinі z vkljuchennjam, Fіziko-hіmіchna
mehanіka, 2015, 51, No. 3, pp. 32–38.
Bayat A., Moosavi H., Bayat Y. Thermo-mechanical
analysis of functionally graded thick spheres with linearly
time-dependent temperature [Text], Scientia Iranica, 2015,
Vol. 22, Issue 5, pp. 1801–1812.
Mohazzab A. H., Jabbari M. Two-Dimensional Stresses in
a Hollow FG Sphere with Heat Source [Text], Advanced
Materials Research, 2011, Vol. 264–265, pp. 700–705.
DOI: 10.4028/www.scientific.net/amr.264-265.700
Ghannad M., Yaghoobi M. P. A thermoelasticity solution
for thick cylinders subjected to thermo-mechanical loads
under various boundary conditions, International Journal
of Advanced Design & Manufacturing Technology, 2015,
Vol. 8, No. 4, pp. 1–12.
Jabbari M., Karampour S., Eslami M. R. Radially
symmetric steady state thermal and mechanical stresses of
a poro FGM hollow sphere, International Scholarly
Research Network ISRN Mechanical Engineering, 2011,
Vol. 2011, pp. 1–7. Article ID 305402. DOI:
5402/2011/305402 24.
Podstrigach Ja. S., Lomakin V. A., Koljano Ju. M.
Termouprugost' tel neodnorodnoj struktury. Moscow,
Nauka, 1984, 368 p.
Koljano Ju. M. Metody teploprovodnosti i termouprugosti
neodnorodnogo tela. Kiev, Naukova dumka, 1992, 280 p.
Korn G., Korn T. Spravochnik po matematike dlja
nauchnyh rabotnikov i inzhenerov. Moscow, Nauka, 1977,
p.
Lomakin V. A. Teorija uprugosti neodnorodnyh tel.
Moscow, Izd-vo Mosk. un-ta, 1976, 376 p.
Berman R. Teploprovodnost' tverdyh tel. Moscow, Mir,
, 288 p.
Downloads
How to Cite
Issue
Section
License
Copyright (c) 2018 V. I. Havrysh
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
-
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
-
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
-
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
