This paper reviews how ideas have evolved in this field from the pioneering work of CARNOT right up to the present. The coupling of thermostatics with thermokinetics (heat and mass transfers) and entropy or exergy analysis is illustrated through study of thermomechanical engines such as the Carnot heat engine, and internal combustion engines. The benefits and importance of stagnation temperature and irreversibility parameters are underlined. The main situations of constrained (or unconstrained) optimization are defined, discussed and illustrated. The result of this study is a new branch of thermodynamics: Finite Dimensions Optimal Thermodynamics (FDOT).

The paper presents a comparison of various CHP system configurations, such as Vapour Turbine, Gas Turbine, Internal Combustion Engine, External Combustion Engine (Stirling, Ericsson), when different thermodynamic criteria are considered, namely the first law efficiency and exergy efficiency. Thermodynamic optimization of these systems is performed intending to maximize the exergy, when various practical related constraints (imposed mechanical useful energy, imposed heat demand, imposed heat to power ratio) or main physical limitations (limited heat availability, maximum system temperature allowed, thermo-mechanical constraints) are taken into account. A sensitivity analysis to model parameters is given. The results have shown that the various added constraints were useful for the design allowing to precise the influence of the model main parameters on the system design. Future perspective of the work and recommendations are stated.

In recent decades, the approach known as Finite-Time Thermodynamics has provided a fruitful theoretical framework for the optimization of heat engines operating between a heat source (at temperature ) and a heat sink (at temperature ). The aim of this paper is to propose a more complete approach based on the association of Finite-Time Thermodynamics and the Bond-Graph approach for modeling endoreversible heat engines. This approach makes it possible for example to find in a simple way the characteristics of the optimal operating point at which the maximum mechanical power of the endoreversible heat engine is obtained with entropy flow rate as control variable. Furthermore it provides the analytical expressions of the optimal operating point of an irreversible heat engine where the energy conversion is accompanied by irreversibilities related to internal heat transfer and heat dissipation phenomena. This original approach, applied to an analysis of the performance of a thermoelectric generator, will be the object of a future publication.

In recent decades, the approach known as Finite-Dimension Thermodynamics has provided a fruitful theoretical framework for the optimization of heat engines operating between a heat source (at temperature T_hs) and a heat sink (at temperature T_cs). We will show in this paper that the approach detailed in a previous paper [1] can be used to analytically model irreversible heat engines (with an additional assumption on the linearity of the heat transfer laws). By defining two dimensionless parameters, the intensity of internal dissipation and heat leakage within a heat engine were quantified. We then established the analogy between an endoreversible heat engine and an irreversible heat engine by using the apparent temperatures (T_cs → Tλ,φ cs, T_hs → Tλ,φ hs) and apparent conductances (K_h → Kλ h, K_c → Kλ c). We thus found the analytical expression of the maximum power of an irreversible heat engine. However, these apparent temperatures should not be used to calculate the conversion efficiency at the optimal operating point by analogy with the case of an endoreversible heat engine.

The purpose of this work is to precise and complete one recently proposed in the literature and relative to a general criterion to maximize the first law efficiency of irreversible heat engines. It is shown that the previous proposal seems to be a particular case. A new proposal has been developed for a Carnot irreversible thermomechanical heat engine at steady state associated to two infinite heat reservoirs (hot source, and cold sink): this constitutes the studied system. The presence of heat leak is accounted for, with the most simple form, as is done generally in the literature. Irreversibility is modeled through , created internal entropy rate in the converter (engine), and , total created entropy rate in the system. Heat transfer laws are represented as general functions of temperatures. These concepts are particularized to the most common heat transfer law (linear one). Consequences of the proposal are examined; some new analytical results are proposed for efficiencies.