THE THERMODYNAMIC DESCRIPTION OF HETEROGENEOUS DISSIPATIVE SYSTEMS BY VARIATIONAL METHODS: I. A FORMULATION OF THE PRINCIPLE OF MINIMUM RATE OF ENTROPY PRODUCTION WITH APPLICATION TO CERTAIN STATIONARY HETEROGENEOUS CONVECTIVE SYSTEMS

Abstract

The variational principle[Formula: see text]where, in terms of the system's independent thermodynamic forces, Xi, the rate of entropy production per unit volume is[Formula: see text]is known to describe the integral behavior of certain non-convective, steady (constrained) dissipative processes since the Euler–Lagrange equations corresponding to each degree of freedom define just sufficient steady state conditions to uniquely specify the configuration. It is herein demonstrated that this principle generates the Le Chatelier principle in the presence of constraints which are more general than previously considered. This has made possible the description of certain heterogeneous convective systems which were not previously amenable to unique thermodynamic analysis. In particular, the principle has been used to rationalize cellular or dendritic growth from the melt in alloys. The supporting observation is cited that the non-planar morphology, as compared to a planar one, leads to the maximum rate of conservation of available energy as solute segregation.