Local Stability of Curzon-Ahlborn Cycle with Non-Linear Heat Transfer for Maximum Power Output Regime

Delfino Ladino-Luna,Ricardo T Páez-Hernández,Pedro Portillo-Díaz

doi:10.4236/jmp.2013.47a2004

Abstract

The study of local stability of thermal engines modeled as an endoreversible Curzon and Ahlborn cycle is shown. It is assumed a non-linear heat transfer for heat fluxes in the system (engine + environments). A semisum of two expressions of the efficiency found in the literature of finite time thermodynamics for the maximum power output regime is considered in order to make the analysis. Expression of variables for local stability and power output is found even graphic results for important parameters in the analysis of stability, and a phase plane portrait is shown.

Highlights

As it is known the limits in the performance of thermal engines in the Classical Equilibrium Thermodynamics context correspond to reversible processes [1,2,3,4]
A semisum of two expressions of the efficiency found in the literature of finite time thermodynamics for the maximum power output regime is considered in order to make the analysis
In order to analyze the performance of thermal engines, many papers in this context have considered that the heat flux between the system and its environs is made by Newton heat transfer law [5,6,7,8,9,10,11,12,13,14], for the named Curzon and Ahlborn engine [7]

Summary

Introduction

As it is known the limits in the performance of thermal engines in the Classical Equilibrium Thermodynamics context correspond to reversible processes [1,2,3,4] This situation represents a very hard obstacle in the analysis of thermal engines and leads to non adequate values for variables of processes whose values far from to the experimental values were reported in the literature. In order to analyze the performance of thermal engines, many papers in this context have considered that the heat flux between the system and its environs is made by Newton heat transfer law [5,6,7,8,9,10,11,12,13,14], for the named Curzon and Ahlborn engine [7]. To make this paper self-contained, a review of some wellknown results on the Carnot, and Curzon and Ahlborn engines concerning to steady state variables is included

Steady States Variables

Effect of a Non-Linear Heat Transfer Law

The Local Stability of the Curzon and Ahlborn Engine

Linearization and Stability Analysis

Concluding Remarks