High-performance numerical method for searching the effective thermal conductivity of media with inhomogeneous macrostructure

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Аннотация

When solving engineering problems, it is often necessary to know the physical properties of porous media with complex internal structure. In this paper we propose a technique for numerical modeling of heat conduction of this kind of bodies including non-conducting circular inclusions. This technique allows to calculate temperature fields and heat fluxes, as well as other parameters necessary for applications. One of such parameters demanded by practice is the effective thermal conductivity, which depends on the volume content of thermally insulated pores and their mutual location. The basis of the above studies is the indirect boundary element method proposed in this paper, based on pre-calculated analytical solutions, on which the decomposition is performed. In order to verify the developed methods, a comparison with the results of other authors is given in the paper. It showed a fairly good agreement.

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Авторлар туралы

A. Zvyagin

M.V. Lomonosov Moscow State University

Хат алмасуға жауапты Автор.
Email: zvsasha@rambler.ru
Ресей, Moscow

A. Udalov

M.V. Lomonosov Moscow State University; Scientific Research Institute for System Analysis RAS

Email: udalets@inbox.ru
Ресей, Moscow; Moscow

Әдебиет тізімі

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  9. Zvyagin A.V., Udalov A.S. A displacement discontinuity method of high-order accuracy in fracture mechanics // Moscow Univ. Mech. Bull., 2020, V. 75, pp. 153–159. https://doi.org/10.3103/S0027133020060060
  10. Zvyagin A.V., Udalov A.S., Shamina A.A. Boundary element method for investigating large systems of cracks using the Williams asymptotic series // Acta Astron., 2022, vol. 194, pp. 480–487.
  11. Zvyagin A.V., Udalov A.S., Shamina A.A. Numerical modeling of heat conduction in bodies with cracks // Acta Astron., 2023, vol. 214, pp. 196–201.
  12. Florence A.L., Goodier J.N. Thermal stresses due to disturbance of uniform heat flow by an insulated ovaloid hole // ASME. J. Appl. Mech., 1960, vol. 27(4), pp. 635–639.

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2. Fig. 1. The considered configuration of the medium

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3. Fig. 2. Analytical and numerical results of the temperature field of the verification problem

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4. Fig. 3. Dependence of the effective thermal conductivity coefficient on porosity

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