Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Editorial staff
Guidelines for authors
License agreement
Editorial policy

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2016, Volume 20, Number 2, Pages 342–353
DOI: https://doi.org/10.14498/vsgtu1476
(Mi vsgtu1476)
 

Mathematical Modeling, Numerical Methods and Software Complexes

On one method for solving transient heat conduction problems with asymmetric boundary conditions

I. V. Kudinov, E. V. Stefanyuk, M. P. Skvortsova, E. V. Kotova, G. M. Sinyaev

Samara State Technical University, Samara, 443100, Russian Federation (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: Using additional boundary conditions and additional required function in integral method of heat-transfer we obtain approximate analytical solution of transient heat conduction problem for an infinite plate with asymmetric boundary conditions of the first kind. This solution has a simple form of trigonometric polynomial with coefficients exponentially stabilizing in time. With the increase in the count of terms of a polynomial the obtained solution is approaching the exact solution. The introduction of a time-dependent additional required function, setting in the one (point) of the boundary points, allows to reduce solving of differential equation in partial derivatives to integration of ordinary differential equation. The additional boundary conditions are found in the form that the required solution would implement the additional boundary conditions and that implementation would be equivalent to executing the original differential equation in boundary points. In this article it is noted that the execution of the original equation at the boundaries of the area only (via the implementation of the additional boundary conditions) leads to the execution of the original equation also inside that area. The absence of direct integration of the original equation on the spatial variable allows to apply this method to solving the nonlinear boundary value problems with variable initial conditions and variable physical properties of the environment, etc.
Keywords: transient heat conductivity, infinite speed of heat propagation, integral method of thermal balance, inhomogeneous boundary conditions, approximate analytical solution, additional required function, additional boundary conditions, trigonometric coordinate functions.
Funding agency Grant number
Russian Foundation for Basic Research 16-38-00059-мол_а
This work was supported by the Russian Foundation for Basic Research (project no. 16–38–00059-mol_a).
Original article submitted 12/II/2016
revision submitted – 29/III/2016
Bibliographic databases:
Document Type: Article
UDC: 517.958:536.2
MSC: 80A20
Language: Russian
Citation: I. V. Kudinov, E. V. Stefanyuk, M. P. Skvortsova, E. V. Kotova, G. M. Sinyaev, “On one method for solving transient heat conduction problems with asymmetric boundary conditions”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:2 (2016), 342–353
Citation in format AMSBIB
\Bibitem{KudSteSkv16}
\by I.~V.~Kudinov, E.~V.~Stefanyuk, M.~P.~Skvortsova, E.~V.~Kotova, G.~M.~Sinyaev
\paper On one method for solving transient heat conduction problems
with asymmetric boundary conditions
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 2
\pages 342--353
\mathnet{http://mi.mathnet.ru/vsgtu1476}
\crossref{https://doi.org/10.14498/vsgtu1476}
\zmath{https://zbmath.org/?q=an:06964491}
\elib{https://elibrary.ru/item.asp?id=27126251}
Linking options:
  • https://www.mathnet.ru/eng/vsgtu1476
  • https://www.mathnet.ru/eng/vsgtu/v220/i2/p342
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024