Thermodynamics Analysis of the Distributed Parameter Model of Counterflow Heat Exchanger

Abstract

In this paper we are interested in the thermodynamic analysis of a counterflow heat exchanger, when the dynamics are described by two hyperbolic partial differential equations (PDEs). First from the first and second law of thermodynamics we derive the different models of the heat exchanger. Next we perform an analysis of the equilibrium profiles from a certain condition on the system parameters that guarantees the existence and uniqueness of the solution of the PDEs model. In this analysis we show the importance of the thermal pinch as an energy efficiency factor. Finally we study the passivity and the asymptotic stability of the considered heat exchanger essentially basing ourselves on the entropy as a storage function, entropy production as a dissipation function, and the thermodynamic availability function as a Lyapunov function.