Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid
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 br...
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MDPI AG
2024-10-01
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| author | Sergey Sazhenkov Elena Sazhenkova |
| author_facet | Sergey Sazhenkov Elena Sazhenkova |
| author_sort | Sergey Sazhenkov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2a186ebc16bc4460b66848ecbe58f047 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-2a186ebc16bc4460b66848ecbe58f0472025-08-20T02:26:45ZengMDPI AGAxioms2075-16802024-10-01131173110.3390/axioms13110731Homogenization of a Thermoelastic Bristly Structure Immersed in a ThermofluidSergey Sazhenkov0Elena Sazhenkova1Laboratory for Mathematical and Computer Modeling in Natural and Industrial Systems, Altai State University, 656049 Barnaul, RussiaFaculty of Digital Technologies, Novosibirsk State University of Economics and Management, 630099 Novosibirsk, RussiaThe 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.https://www.mdpi.com/2075-1680/13/11/731compressible thermofluidthermoelastic solidStokes–Fourier equationslinear thermoelasticity equationshomogenizationperiodic structure |
| spellingShingle | Sergey Sazhenkov Elena Sazhenkova Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid Axioms compressible thermofluid thermoelastic solid Stokes–Fourier equations linear thermoelasticity equations homogenization periodic structure |
| title | Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid |
| title_full | Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid |
| title_fullStr | Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid |
| title_full_unstemmed | Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid |
| title_short | Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid |
| title_sort | homogenization of a thermoelastic bristly structure immersed in a thermofluid |
| topic | compressible thermofluid thermoelastic solid Stokes–Fourier equations linear thermoelasticity equations homogenization periodic structure |
| url | https://www.mdpi.com/2075-1680/13/11/731 |
| work_keys_str_mv | AT sergeysazhenkov homogenizationofathermoelasticbristlystructureimmersedinathermofluid AT elenasazhenkova homogenizationofathermoelasticbristlystructureimmersedinathermofluid |