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 deals with the study of this coupling.

In the paper the problem of initial - boundary of the continuous center, geometrically and physically linear, with moderate temperature change and moderate change in concentration of diffusion substance was considered. Such an issue can be written with conjugate differential equations, i.e., 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 actually leads to the generalized Hamilton’s principle (the original part of the work). The equation of a virtual power and Hamilton’s principle in the form shown in the work cannot be expressed as a minimum of a well-defined functional. It is known, however, that such formulation allows the use of direct methods. It is also easy to show that the elasticity, thermal conductivity and diffusion equations can be obtained from the presented variation principle.

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