Israel Reyes-Ramírez

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

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.

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.

Scaling properties of rainfall records in some Mexican zones

Since the 1990 decade, it has been suggested that atmospheric processes associated with rainfall could be a self-organized critical (SOC) phenomenon similar, for example, to seismicity. In this sense, the rain events taken as the output of the complex atmospheric system (sun’s radiation, water evaporation, clouds, etc.) are analogous to earthquakes, as the output of a relaxation process of the earth crust. A clue on this possible SOC behavior of rain phenomenon has been the ubiquitous presence of power laws in rain statistics. In the present article, we report the scaling properties of rain precipitation data taken from meteorological stations located at six zones of Mexico. Our results are consistent with those that assert that rainfall is a SOC phenomenon. We also analyze the Hurst exponent, which is appropriate to measure long-term memory of time series.