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Variational formulation of coupled of heat/mass transfer and thermoelasticity problem

Belov P.A., Lurie S.A.

#### Abstract:

A variational formulation of a coupled system of equations of thermoelasticity, heat and mass transfer is given. A special case of the gradient model of the Mindlin-Tupin medium is proposed, when the gradient component of the potential energy depends only on the gradients of the constrained dilation. In general, a generalized variational model is considered, in which the gradient variational model is expanded by taking into account the potential energy of defective media with dilatational damage, combining two types of free (incompatible) dilations: free dilations associated with a change in volume due to temperature effects, and free dilations associated with the concentration of impurities due to diffusion processes. As a result, the equations of motion included in the coupled system of equations are a special case of the gradient theory (dilation model) in the part of the differential operator over displacements. The heat and mass transfer equations have the same structure and reflect the diffusion-wave mechanism of evolution in a continuous medium of temperature and impurity. It was found that the coupled system of equations decomposes into three independent boundary value problems with respect to displacements, a free (incompatible) change in volume associated with temperature loading, and a free (incompatible) change in volume associated with the diffusion (concentration) process, when the tensors of physical properties are spherical and the corresponding connectivity coefficients are equal to zero. The consistency equations obtained from the generalized equations of Hooke’s law for force factors and their fluxes by eliminating kinematic variables give a whole spectrum of laws of heat conduction, diffusion and thermoelasticity, including the laws of Fourier, Maxwell-Cattaneo, Soret and Dufour.

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