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Variational Method for Solving the Time-Fractal Heat Conduction Problem in the Claydite-Block Construction

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Advances in Computer Science for Engineering and Education (ICCSEEA 2022)

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 134))

Abstract

Mathematical models of the heat conduction problem in the claydite-block construction with taking into account the fractal structure of the material is constructed. Integro-differentiation apparatus of fractional order to take into account the fractal structure of the material was used. The variational formulation of the problem was constructed. The variational method for obtaining an approximate solution of the considered problem was proposed. The results of the numerical experiments of studying the thermal conductivity of claydite-block construction depending on the time, wall thickness and materials of different fractions were obtained. Analyzing the founded distributions of temperature fields allows us to more accurately reflect the real speed of the process.

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Author information

Authors and Affiliations

  1. Department of Artificial Intelligence, Lviv Polytechnic National University, Lviv, Ukraine

    Volodymyr Shymanskyi & Ivan Sokolovskyy

  2. Department of Computer-Aided Design Systems, Lviv Polytechnic National University, Lviv, Ukraine

    Yaroslav Sokolovskyy

  3. Department of Higher Mathematics, Lviv National Agrarian University, Lviv, Ukraine

    Taras Bubnyak

Authors
  1. Volodymyr Shymanskyi
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  2. Ivan Sokolovskyy
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  3. Yaroslav Sokolovskyy
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  4. Taras Bubnyak
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Corresponding author

Correspondence to Volodymyr Shymanskyi .

Editor information

Editors and Affiliations

  1. School of Computer Science, Hubei University of Technology, Wuhan, China

    Zhengbing Hu

  2. Faculty of Applied Mathematics, National Technical University of Ukraine “Igor Sikorsky Kiev Polytechnic Institute”, Kiev, Ukraine

    Ivan Dychka

  3. Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia

    Sergey Petoukhov

  4. Halmos College of Arts and Sciences, Nova Southeastern University, Ft. Lauderdale, FL, USA

    Matthew He

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Shymanskyi, V., Sokolovskyy, I., Sokolovskyy, Y., Bubnyak, T. (2022). Variational Method for Solving the Time-Fractal Heat Conduction Problem in the Claydite-Block Construction. In: Hu, Z., Dychka, I., Petoukhov, S., He, M. (eds) Advances in Computer Science for Engineering and Education. ICCSEEA 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-031-04812-8_9

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