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Classical free energies of a heat conductor with memory and the minimum free energy for its discrete spectrum model. (English) Zbl 1216.35150

The first main result of the paper presents the expressions of free energies in the case of rigid heat conductors with memory. The second main result compares the minimum free energy for the discrete spectrum model with these free energies. The physical description of the model starts with Clausius-Duhem inequality which can be written as an equality introducing the internal dissipation term. The authors then derive the expression of the thermal work for any process with finite duration. When restricting to linear heat conductors, the authors recall the expressions of the free energies of viscoelastic materials and which are already available: Day, Dill, Fabrizio, Breuer-Onat, Graffi-Volterra and Golden. In each case, they draw computations which specialize these expressions in the current context. The last part of the paper introduces the discrete spectrum model for linear heat conductors. The authors here mainly compare the results with the expressions of some free energies which have been presented in the previous section. The authors mainly use Fourier’s transform and Plancherel formula.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
74D05 Linear constitutive equations for materials with memory
80A20 Heat and mass transfer, heat flow (MSC2010)
35Q79 PDEs in connection with classical thermodynamics and heat transfer
74F05 Thermal effects in solid mechanics
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