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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 4, Pages 669–680 (Mi zvmmf10193)  

This article is cited in 9 scientific papers (total in 9 papers)

Generalized functions and additional boundary conditions in heat conduction problems for multilayered bodies

V. A. Kudinova, I. V. Kudinova, M. P. Skvortsova

a Samara State Technical University, ul. Molodogvardeiskaya 244, Samara, 443100, Russia

Abstract: The basic principles of a method for finding approximate analytical solutions of nonstationary heat conduction problems for multilayered structures are described. The method relies on determining a temperature perturbation front and introducing additional boundary conditions. An asymmetric unit step function is used to represent the original multilayered system as a single-layer one with piecewise homogeneous medium properties. Due to the splitting of the heat conduction process into two stages, the original partial differential equation is reduced at each stage to solving an ordinary differential equation. As a result, fairly simple (in form) analytical solutions are obtained with accuracy depending on the number of specified additional boundary conditions (on the number of approximations). It is shown that, as the number of approximations increases, same-type ordinary differential equations are obtained for the unknown time functions at the first and second stages of the process. As a result, analytical solutions can be found with a nearly prescribed degree of accuracy, including small and supersmall times.

Key words: multilayered structures, approximate analytical solution, heat balance integral method, temperature perturbation front, theory of generalized functions, additional boundary conditions.

DOI: https://doi.org/10.7868/S0044466915040080

Full text: PDF file (515 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:4, 666–676

Bibliographic databases:

UDC: 519.633
MSC: Primary 80M25; Secondary 65M99
Received: 31.07.2014

Citation: V. A. Kudinov, I. V. Kudinov, M. P. Skvortsova, “Generalized functions and additional boundary conditions in heat conduction problems for multilayered bodies”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 669–680; Comput. Math. Math. Phys., 55:4 (2015), 666–676

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Eremin, I. V. Kudinov, V. V. Zhukov, “Ob odnom metode resheniya zadach teploobmena pri techenii zhidkostei v ploskikh kanalakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:1 (2016), 109–120  mathnet  crossref  zmath  elib
    2. I. V. Kudinov, V. A. Kudinov, E. V. Kotova, “Analytic solutions to heat transfer problems on a basis of determination of a front of heat disturbance”, Russian Math. (Iz. VUZ), 60:11 (2016), 22–34  mathnet  crossref  isi
    3. I. V. Kudinov, E. V. Stefanyuk, M. P. Skvortsova, E. V. Kotova, G. M. Sinyaev, “Ob odnom metode resheniya nestatsionarnykh zadach teploprovodnosti s nesimmetrichnymi granichnymi usloviyami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:2 (2016), 342–353  mathnet  crossref  zmath  elib
    4. I. V. Kudinov, V. A. Kudinov, E. V. Kotova, “Additional boundary conditions in unsteady-state heat conduction problems”, High Temperature, 55:4 (2017), 541–548  mathnet  crossref  crossref  isi  elib
    5. I. V. Kudinov, V. A. Kudinov, E. V. Kotova, A. V. Eremin, “On one method of solving nonstationary boundary-value problems”, J. Eng. Phys. Thermophys., 90:6 (2017), 1317–1327  crossref  isi
    6. A. V. Eremin, I. V. Kudinov, A. I. Dovgyallo, V. A. Kudinov, “Heat exchange in a liquid with energy dissipation”, J. Eng. Phys. Thermophys., 90:5 (2017), 1234–1242  crossref  isi
    7. A. V. Eremin, E. V. Stefanyuk, O. Yu. Kurganova, V. K. Tkachev, M. P. Skvortsova, “A generalized function in heat conductivity problems for multilayer structures with heat sources”, J. Mach. Manuf. Reliab., 47:3 (2018), 249–255  crossref  isi
    8. I. V. Kudinov, O. Yu. Kurganova, V. K. Tkachev, “Poluchenie tochnogo analiticheskogo resheniya statsionarnoi dvumernoi zadachi teploprovodnosti s istochnikom teploty”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:1 (2019), 195–203  mathnet  crossref  zmath  elib
    9. I. V. Kudinov, E. V. Kotova, V. A. Kudinov, “A method of obtaining analytical solutions to boundary value problems based on defining additional boundary conditions and additional desired functions”, Num. Anal. Appl., 12:2 (2019), 126–136  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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