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Numerical-Analytic Technique for the Solution of Nonstationary Problems of Heat Conduction in Locally Inhomogeneous Media

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We propose a procedure of simultaneous application of the splitting method, boundary-element method, step-by-step time scheme, and iterative FD (Finite-Discrete) procedure for the construction of the integral representation of the solution of a nonstationary problem of heat conduction for a closed domain with Dirichlet condition given on its boundary containing a locally inhomogeneous subdomain whose physical characteristics depend on the coordinates. We perform a comprehensive numerical analysis of this approach with regard for the fact that the heat field is affected by the dependences of the heatconduction coefficient and specific heat capacity of the material on the coordinates.

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References

  1. N. M. Belyaev and A. A. Ryadno, Mathematical Methods of Heat Conduction [in Russian], Vyshcha Shkola, Kiev (1993).

    MATH  Google Scholar 

  2. P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw-Hill, London (1981).

    MATH  Google Scholar 

  3. C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary Element Techniques: Theory and Applications in Engineering, Springer, Berlin–Heidelberg (1984).

    Book  MATH  Google Scholar 

  4. B. Hryts’ko, R. Gudz,’ and L. Zhuravchak, “Modeling of the distribution of temperature fields in inhomogeneous media with the help of boundary, near-boundary, and finite elements,” Visn. L’viv. Univ. Ser. Prykl. Mat. Informat., Issue 15, 208–223 (2009).

  5. R. V. Gudz’, L. M. Zhuravchak, and A. T. Petl’ovanyi, “Solution of the plane static thermoelasticity problem for locally inhomogeneous bodies by combining the methods of boundary, near-boundary, and finite elements,” Mat. Met. Fiz.-Mekh. Polya, 49, No. 2, 148–156 (2006).

  6. L. M. Zhuravchak, and E. H. Hryts’ko, Method of Near-Boundary Elements in Applied Problems of Mathematical Physics [in Ukrainian], Carpathian Branch of the Subbotin Institute of Geophysics, Ukrainian National Academy of Sciences, Lviv (1996).

    Google Scholar 

  7. L. M. Zhuravchak, R. V. Gudz’, and B. E. Hryts’ko, “Stationary temperature field in a piecewise homogeneous body with local inhomogeneities,” Prykl. Probl. Mekh. Mat., Issue 7, 111–120 (2009).

  8. Yu. M. Kolyano, Methods of Heat Conduction and Thermoelasticity for Inhomogeneous Bodies [in Russian], Naukova Dumka, Kiev (1992).

    MATH  Google Scholar 

  9. R. M. Kushnir and V. S. Popovych, Thermoelasticity of Thermosensitive Bodies, in: Ya. Yo. Burak and R. М. Kushnir (editors), Modeling and Optimization in Thermomechanics of Electroconductive Inhomogeneous Bodies [in Ukrainian], Vol. 3, Spolom, Lviv (2009).

  10. Ya. S. Podstrigach, V. А. Lomakin, and Yu. М. Kolyano, Thermoelasticity of Bodies with Inhomogeneous Structure [in Russian], Nauka, Moscow (1984).

  11. R. M. Kushnir, “Generalized conjugation problems in mechanics of piecewise–homogeneous elements of constructions,” Z. Angew. Math. Mech., 76, No. S5, 283–284 (1996).

    MATH  Google Scholar 

  12. R. M. Kushnir and V. S. Popovych, “Heat conduction problems of thermosensitive solids under complex heat exchange,” in: V. S. Vikhrenko (editor), Heat Conduction—Basic Research, Chapter 6, InTech, Rijeka (2011), pp. 131–154; http://www.intechopen.com/books/show/title/heat-conduction-basic-research

    Google Scholar 

  13. R. M. Kushnir, V. S. Popovych, and O. M. Vovk, “The thermoelastic state of a thermosensitive sphere and space with a spherical cavity subject to complex heat exchange,” J. Eng. Math., 61, No. 2-4, 357–369 (2008).

    Article  MATH  Google Scholar 

  14. R. Kushnir and B. Protsiuk, “Determination of the thermal fields and stresses in multilayer solids by means of the constructed Green functions,” in: R. B. Hetnarski (editor), Encyclopedia of Thermal Stresses, Vol. 2, Springer (2014), pp. 924–931.

  15. A. Sutradhar and G. H. Paulino, “The simple boundary element method for transient heat conduction in functionally graded materials,” Comput. Meth. Appl. Mech. Eng., 193, No. 42-44, 4511–4539 (2004).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Franko Lviv National University, Lviv, Ukraine

    B. Ye. Hryts’ko

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  1. B. Ye. Hryts’ko
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 3, pp. 35–42, July–September, 2015.

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Hryts’ko, B.Y. Numerical-Analytic Technique for the Solution of Nonstationary Problems of Heat Conduction in Locally Inhomogeneous Media . J Math Sci 226, 41–51 (2017). https://doi.org/10.1007/s10958-017-3517-y

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  • DOI: https://doi.org/10.1007/s10958-017-3517-y

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