Generalization of Hamilton’s principle for the problem of coupled thermodiffusion

openaccess, Vol. 618 (2) 2024 / piątek, 23 lutego, 2024

(Open Access)

DOI: 10.15199/33.2024.02.04

Sosnowska Magdalena, Lachowicz Magdalena, Podhorecki Adam. 2024. Generalization of Hamilton’s principle for the problem of coupled thermodiffusion. Volume 618. Issue 2. Pages 17-20. Article in PDF file

Accepted for publication: 24.01.2024 r.

Variables in time of temperature field and concentration of diffusion substance field cause deformation of the solid. There is also a reverse process, i.e., deformation of the solid causes thermal energy (and its conduction) and mass flow. The mentioned processes are coupled together and thermodiffusion dealswith the study of this coupling. In the paper the problem of initial – boundary of the continuous center with moderate temperature change and moderate change in concentration of diffusion substance was considered. Such an issue can be written with conjugate differential equations, extended thermal, diffusion and the theory of elasticity equations supplemented with boundary and initial conditions. It is possible to described such an issue by the integral form using for this purpose the above differential equations and the equation of a virtual power in the space–time domain. It has been shown in the work that the equation of a virtual power, derived from the above differential equations, actually leads to the generalized Hamilton’s principle. The equation of a virtual power and Hamilton’s principle in the form shown in the work cannot be expressed as aminimumof awell-defined functional. It is known, that such formulation allows the use of direct methods. It is easy to showthat the elasticity, thermal conductivity and diffusion equations can be obtained from the presented variation principle.
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dr inż. Magdalena Sosnowska, Politechnika Bydgoska, Wydział Budownictwa, Architektury i Inżynierii Środowiska ORCID: 0000-0002-1158-5943
dr inż. Magdalena Lachowicz, Politechnika Bydgoska, Wydział Budownictwa, Architektury i Inżynierii Środowiska ORCID: 0000-0003-4047-2769
prof. dr hab. inż. Adam Podhorecki, Politechnika Bydgoska, Wydział Budownictwa, Architektury i Inżynierii Środowiska ORCID: 0000-0002-9569-1769

dr inż. Magdalena Sosnowska, Politechnika Bydgoska, Wydział Budownictwa, Architektury i Inżynierii Środowiska ORCID: 0000-0002-1158-5943

magdalena.sosnowska@pbs.edu.pl

Full paper:

DOI: 10.15199/33.2024.02.04

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