“GENERALIZED” ENTROPY PRODUCTION RATE ASSOCIATED TO ONE-DIMENSIONAL HEAT CONDUCTION- EXTREMUM POINTS AND APPLICATIONS

Abstract

In previous papers, the author considered the critical or the extremum points of the entropy production rate in insulations with one-dimensional heat conduction, either alone or associated with other refrigerating systems necessary to maintain the steady state.

The aim of this paper is to obtain a general formulation for the presence of critical or extremum points of the (generalized) entropy production rate in a more ample domain that includes the previous cases as particular ones.

Homogeneous and more than one component systems are considered; for homogeneous systems, the necessary and sufficient condition for the minimum of the (generalized) entropy production rate in the system is obtained, while for two or more component systems only the necessary condition for a relative extremum is stated. In the latter case one can have also a particular state which is not an extremum and can be known as a “saddle point” state from analogy.

This general formulation can be used for the thermodynamic optimization of cryogenic plants, extensively used in large-scale superconducting plants operating at liquid helium temperatures.

KEYWORDS:

• Entropy production
• Heat conduction