Marco A. Barranco-Jiménez

Thermoeconomic Optimum Operation Conditions of a Solar-driven Heat Engine Model

In the present paper, the thermoeconomic optimization of an endoreversible solardriven heat engine has been carried out by using finite-time/finite-size thermodynamic theory. In the considered heat engine model, the heat transfer from the hot reservoir to the working fluid is assumed to be the radiation type and the heat transfer to the cold reservoir is assumed the conduction type. In this work, the optimum performance and two design parameters have been investigated under three objective functions: the power output per unit total cost, the efficient power per unit total cost and the ecological function per unit total cost. The effects of the technical and economical parameters on the thermoeconomic performance have been also discussed under the aforementioned three criteria of performance.

Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model

In the present paper, the thermoeconomic optimization of an irreversible solar-driven heat engine model has been carried out by using finite-time/finite-size thermodynamic theory. In our study we take into account losses due to heat transfer across finite time temperature differences, heat leakage between thermal reservoirs and internal irreversibilities in terms of a parameter which comes from the Clausius inequality. In the considered heat engine model, the heat transfer from the hot reservoir to the working fluid is assumed to be Dulong-Petit type and the heat transfer to the cold reservoir is assumed of the Newtonian type. In this work, the optimum performance and two design parameters have been investigated under two objective functions: the power output per unit total cost and the ecological function per unit total cost. The effects of the technical and economical parameters on the thermoeconomic performance have been also discussed under the aforementioned two criteria of performance.

Stability Analysis of an Endoreversible Heat Engine with Stefan-Boltzmann Heat Transfer Law Working in Maximum-Power-Like Regime

A local stability study of an endoreversible Stefan-Boltzmann (SB) engine, working in a maximum-power-like regime, is presented. This engine consists of a Carnot engine that exchanges heat with heat reservoirs T1 and T2, (T1 > T2) through a couple of thermal links, both having the same conductance g. In addition, the working fluid has the same heat capacity C in the two isothermal branches of the cycle. From the local stability analysis we conclude that the SB engine is stable for every value of g, C and τ = T2/T1. After a small perturbation, the system decays to the steady state with either of two different relaxation times; both being proportional to C/g, and τ. Finally, when we plot some of the thermodynamic properties in the steady state versus τ, we find how an increment of τ can improve the stability of the system, at the same decreasing the efficiency and the power of the system. This suggests a compromise between the stability and the energetic properties of the engine driven by τ.

Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine

In this work we present a local stability analysis of the thermo-economic model of an irreversible heat engine working at maximum power conditions. The thermo-economic model is based on the maximization of a benefit function which is defined by the ratio of the power output and the total cost involved in the plant’s performance. Our study shows that, after a small perturbation, the system decays exponentially to the steady state determined by two different relaxation times. In particular, we show that the relaxation times are function of the temperature ratio τ = T2/T1 (T1 > T2), the cost function ƒ and the parameter R (a parameter related to the degree of internal irreversibilities). We observe that the stability of the system improves as τ increases whereas for changes in ƒ and R, the stability properties are characterized by a rapid decay along the fast eigendirection as ƒ increases and R decreases. Finally, we discuss our results in the context of energetic properties.

Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes

A recent work reported a local stability analysis of a thermo-economical model of an irreversible heat engine working under maximum power conditions. That work showed that after small perturbations to the working temperatures, the system decreases exponentially to the steady state characterized by two different relaxation times. This work extends the local stability analysis considering other performance regimes: the Maximum Efficient Power (MEP) and the Ecological Function (EF) regimes. The relaxation time was shown under different performance regimes as functions of the temperature ratio τ = T2/T1, with T1 g T2, the fractional fuel cost f and a lumped parameter R related to the internal irreversibilities degree. Under Maximum Efficient Power conditions the relaxation times are less than the relaxation times under both Maximum Ecological function and Maximum Power. At Maximum Power Efficient conditions, the model gives better stability conditions than for the other two regimes.

Global Stability Analysis of a Curzon-Ahlborn Heat Engine under Different Regimes of Performance

We present a global stability analysis of a Curzon–Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilities and a linear heat transfer law at the thermal couplings. The conditions of the global stability are explored for three regimes of performance: maximum power (MP), efficient power (EP) and the so-called ecological function (EF). Moreover, the analytical results were corroborated by means of numerical integrations, which fully validate the properties of the global asymptotic stability.

Thermoeconomic Optimization of an Irreversible Novikov Plant Model under Different Regimes of Performance

The so-called Novikov power plant model has been widely used to represent some actual power plants, such as nuclear electric power generators. In the present work, a thermo-economic study of a Novikov power plant model is presented under three different regimes of performance: maximum power (MP), maximum ecological function (ME) and maximum efficient power (EP). In this study, different heat transfer laws are used: The Newton’s law of cooling, the Stefan–Boltzmann radiation law, the Dulong–Petit’s law and another phenomenological heat transfer law. For the thermoeconomic optimization of power plant models, a benefit function defined as the quotient of an objective function and the total economical costs is commonly employed. Usually, the total costs take into account two contributions: a cost related to the investment and another stemming from the fuel consumption. In this work, a new cost associated to the maintenance of the power plant is also considered. With these new total costs, it is shown that under the maximum ecological function regime the plant improves its economic and energetic performance in comparison with the other two regimes. The methodology used in this paper is within the context of finite-time thermodynamics.

A Finite-Time Thermal Cycle Variational Optimization with a Stefan-Boltzmann Law for Three Different Criteria

This work shows the power of the variational approach for studying the efficiency of thermal engines in the context of the Finite Time Thermodynamics (FTT). Using an endoreversible Curzon–Ahlborn (CA) heat engine as a model for actual thermal engines, three different criteria for thermal efficiency were analyzed: maximum power output, ecological function, and maximum power density. By means of this procedure, the performance of the CA heat engine with a nonlinear heat transfer law (the Stefan–Boltzmann law) was studied to describe the heat exchanges between the working substance and its thermal reservoirs. The specific case of the Muser engine for all the criteria was analyzed. The results confirmed some previous findings using other procedures and additionally new results for the Muser engine performance were obtained.

The Faint Young Sun Paradox: A Simplified Thermodynamic Approach

Classical models of the Sun suggest that the energy output in the early stage of its evolution was 30 percent less than today. In this context, radiative balance alone between The Sun and the Earth was not sufficient to explain the early presence of liquid water on Earth’s surface. This difficulty is called the faint young Sun paradox. Many proposals have been published to solve this paradox. In the present work, we propose an oversimplified finite-time thermodynamic approach that describes the air convective cells in the Earth atmosphere. This model introduces two atmospheric modes of thermodynamic performance: a first mode consisting in the maximization of the power output of the convective cells (maximum power regime) and a second mode that consists in maximizing a functional representing a good trade-off between power output and entropy production (the ecological regime). Within the assumptions of this oversimplified model, we present different scenarios of albedo and greenhouse effects that seem realistic to preserve liquid water on the Earth in the early stage of formation.