Least-entropy generation: Variational principle of Onsager’s type for transient hyperbolic heat and mass transfer

For coupled transfer of the energy and mass in a multicomponent system at mechanical equilibrium a simple thermodynamic theory is developed, and the damped wave equations of change are derived. We show that under nonstationary conditions, where relaxation of diffusive fluxes is essential, the evolution of the distributed coupled transfer of the energy and mass follows the path that minimizes the difference between the total entropy generated within the system and that exchanged by the system. The principle is also valid in the limit in which flux relaxation effects are negligible and the heat and mass transfer, whether steady or not, obeys Onsager's generalization of the Fourier and Fick laws. For coupled steady-state processes the principle goes into that of Onsager, yielding his phenomenological equations. In contrast to the local steady-state nature of Onsager's principle the new principle is global, valid for both stationary and transient situations, and requires no frozen fields. For an isolated, distributed system, in which transient relaxation to equilibrium is the only possible process, the principle implies the least possible increase of the system entropy between any two successive configurations.