Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid

Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid Full article

Journal

Axioms
ISSN: 2075-1680

Output data

Year: 2024, Volume: 13, Number: 11, Article number : 731, Pages count : DOI: 10.3390/axioms13110731

Tags

compressible thermofluid; thermoelastic solid; Stokes–Fourier equations; linear thermoelasticity equations; homogenization; periodic structure; biotechnology; bionics

Authors

Sazhenkov Sergey ^1,2 , Sazhenkova Elena ³

Affiliations

1	Laboratory for Mathematical and Computer Modeling in Natural and Industrial Systems, Altai State University, 656049 Barnaul, Russia
2	Theoretical Department, Lavrentyev Institute of Hydrodynamics SB RAS, 630090 Novosibirsk, Russia
3	Faculty of Digital Technologies, Novosibirsk State University of Economics and Management, 630099 Novosibirsk, Russia

Funding (1)

Министерство науки и высшего образования Российской Федерации

FWGG-2021-0010

The article considers the mathematical model describing the joint motion of a viscous compressible heat-conducting fluid and a thermoelastic plate with a fine two-level thermoelastic bristly microstructure attached to it. The bristly microstructure consists of a great amount of taller and shorter bristles, which are periodically located on the surface of the plate, and the model under consideration incorporates a small parameter, which is the ratio of the characteristic lengths of the microstructure and the entire plate. Using classical methods in the theory of partial differential equations, we prove that the initial-boundary value problem for the considered model is well-posed. After this, we fulfill the homogenization procedure, i.e., we pass to the limit as the small parameter tends to zero, and, as a result, we derive the effective macroscopic model in which the dynamics of the interaction of the ‘liquid–bristly structure’ is described by equations of two homogeneous thermoviscoelastic layers with memory effects. The homogenization procedure is rigorously justified by means of the Allaire–Briane three-scale convergence method. The developed effective macroscopic model can potentially find application in further mathematical modeling in biotechnology and bionics taking account of heat transfer.

Sazhenkov S. , Sazhenkova E.
Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid
Axioms. 2024. V.13. N11. 731 . DOI: 10.3390/axioms13110731 WOS РИНЦ OpenAlex

Submitted:	Sep 11, 2024
Accepted:	Oct 20, 2024
Published print:	Oct 22, 2024

Web of science:	WOS:001366831700001
Elibrary:	74024687
OpenAlex:	W4403691386

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