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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. M. Belyaev and A. A. Ryadno, Mathematical Methods of Heat Conduction [in Russian], Vyshcha Shkola, Kiev (1993).
P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw-Hill, London (1981).
C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary Element Techniques: Theory and Applications in Engineering, Springer, Berlin–Heidelberg (1984).
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).
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).
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).
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).
Yu. M. Kolyano, Methods of Heat Conduction and Thermoelasticity for Inhomogeneous Bodies [in Russian], Naukova Dumka, Kiev (1992).
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).
Ya. S. Podstrigach, V. А. Lomakin, and Yu. М. Kolyano, Thermoelasticity of Bodies with Inhomogeneous Structure [in Russian], Nauka, Moscow (1984).
R. M. Kushnir, “Generalized conjugation problems in mechanics of piecewise–homogeneous elements of constructions,” Z. Angew. Math. Mech., 76, No. S5, 283–284 (1996).
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
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).
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.
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).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 3, pp. 35–42, July–September, 2015.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3517-y