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Minimum free energy in the frequency domain for a heat conductor with memory

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  • An explicit expression is given in the frequency domain for the minimum free energy related to a particular state of a linear rigid heat conductor with memory effects in the constitutive equations, using the fact that this quantity coincides with the maximum recoverable work obtainable from that state. The constitutive equations for the internal energy and the heat flux are expressed as linear functionals of the histories of temperature and its gradient, respectively, together with the present value of the latter quantity. Another equivalent expression for the minimum free energy is also deduced and used to derive explicit formulae for a discrete spectrum model.
    Mathematics Subject Classification: 80A20, 74F05.

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