Irreversible thermodynamics of thermoelectric devices: From local framework to global description

TL;DR

This paper extends the thermodynamics of thermoelectric devices from a local to a global framework, highlighting the quadratic flux-force dependence and clarifying differences with nonlinear models.

Contribution

It develops a global flux-force relation for thermoelectricity, incorporating Joule heating effects and linking local and global kinetic coefficients.

Findings

Global flux-force relations include quadratic terms due to Joule heating.

Global cross-coefficients are equal, derived from local properties.

Differences between global thermodynamics and minimally nonlinear models are clarified.

Abstract

Thermoelectricity is traditionally explained via Onsager's irreversible, flux-force framework. The coupled flows of heat and electric charge are modelled as steady-state flows, driven by the thermodynamic forces defined in terms of the gradients of local, intensive parameters like temperature and electrochemical potential. A thermoelectric generator is a device with a finite extension, and its performance is measured in terms of total power output and total entropy generation. These global quantities are naturally expressed in terms of discrete or global forces derived from their local counterparts. We analyze the thermodynamics of thermoelectricity in terms of global flux-force relations. These relations clearly show the additional quadratic dependence of the driver flux on global forces, corresponding to the process of Joule heating. We discuss the global kinetic coefficients defined by these flux-force relations and prove that the equality of the global cross-coefficients is derived from a similar property of the local coefficients. Finally, we clarify the differences between the global framework for thermoelectric energy conversion and the recently proposed minimally nonlinear irreversible thermodynamic model.