Local-stability analysis of a low-dissipation heat engine working at maximum power output

I. Reyes-Ramírez, J. Gonzalez-Ayala, A. Calvo Hernández, and M. Santillán
Phys. Rev. E 96, 042128 – Published 16 October 2017

Abstract

In this paper we address the stability of a low-dissipation (LD) heat engine (HE) under maximum power conditions. The LD system dynamics are analyzed in terms of the contact times between the engine and the external heat reservoirs, which determine the amount of heat exchanged by the system. We study two different scenarios that secure the existence of a single stable steady state. In these scenarios, contact times dynamics are governed by restitutive forces that are linear functions of either the heat amounts exchanged per cycle, or the corresponding heat fluxes. In the first case, according to our results, preferably locating the system irreversibility sources at the hot-reservoir coupling improves the system stability and increases its efficiency. On the other hand, reducing the thermal gradient increases the system efficiency but deteriorates its stability properties, because the restitutive forces are smaller. Additionally, it is possible to compare the relaxation times with the total cycle time and obtain some constraints upon the system dynamics. In the second case, where the restitutive forces are assumed to be linear functions of the heat fluxes, we find that although the partial contact time presents a locally stable stationary value, the total cycle time does not; instead, there exists an infinite collection of steady values located in the neighborhood of the fixed point, along a one-dimensional manifold. Finally, the role of dissipation asymmetries on the efficiency, the stability, and the ratio of the total cycle time to the relaxation time is emphasized.

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  • Received 9 August 2017

DOI:https://doi.org/10.1103/PhysRevE.96.042128

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsGeneral Physics

Authors & Affiliations

I. Reyes-Ramírez*

  • Instituto Politécnico Nacional-UPIITA, Av. IPN 2580, Ciudad de México 07340, México

J. Gonzalez-Ayala

  • Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain

A. Calvo Hernández

  • Departamento de Física Aplicada, Facultad de Ciencias and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, 37008 Salamanca, Spain

M. Santillán

  • Centro de Investigación y Estudios Avanzados del IPN Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66600 Apodaca NL, Mexico

  • *ireyesram@hotmail.com
  • msantillan@cinvestav.mx

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Issue

Vol. 96, Iss. 4 — October 2017

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