Gradient Thermodynamics & Heat Equations
Résumé
In this paper, a thermodynamic description is proposed to include the gradient of the temperature in the set of state variables. It is based upon an original expression of the entropy and of the internal energy taking account of the presence of the temperature gradient by Legendre transform with respect to the variable (T, grad T ). The proposed description can be justified in a homogenization process. In particular, the associated heat equations is derived and discussed in comparison with the existing results of the literature. It is shown that this equation removes the paradox of instantaneous propagation.