Boundary conditions in the presence of internal variables.
A continuum theory for a rigid heat conductor is presented. Field gradients are included, and internal variables are introduced in order to deal with non-equilibrium complex material behavior. The physical nature of the internal variable is not specified. Since internal variables cannot be prescribed from outside, the problem of boundary conditions for them arises. The second law of thermodynamics in the form of the dissipation inequality is exploited according to the method of Coleman and Noll. The resulting restrictions on constitutive functions are interpreted as boundary conditions for the internal variables. Comparison is made with different approaches to the problem of boundary conditions in the recent literature.
scientific article; zbMATH DE number 1942717