Efficiency and Its Bounds for Thermal Engines at Maximum Power using a Newton's Law of Cooling

TL;DR

This paper analyzes a simple thermal engine model obeying Newton's law of cooling to derive efficiency bounds at maximum power, applicable to various engine types and providing insights for engine design.

Contribution

It introduces a unified model applying Newton's law to derive new efficiency bounds for different engine cycles, including long and short contact time limits.

Findings

New tighter efficiency bounds for long contact time limit.

Efficiency bounds match previous results in the short contact time limit.

Efficiency decreases with increasing heat capacity ratio.

Abstract

We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be applied not only to Carnot engines but also to four other types of engines. For the long thermal contact time limit, new bounds, tighter than what were known before, are obtained. In this case,this model can simulate Otto, Joule Brayton, Diesel, and Atkinson engines. While in the short contact time limit, which corresponds to the Carnot cycle, the same efficiency bounds as Esposito et al's are derived. In both cases, the thermal efficiency decreases as the ratio between the heat capacities of the working medium during heating and cooling stages increases. This might provide instructions for designing real engines.