In the present article, an endoreversible Curzon–Ahlborn engine is studied by considering a non-linear heat transfer law, particularly the Dulong–Petit heat transfer law, using the `componendo and dividendo' rule as well as a simple differentiation to obtain the Curzon–Ahlborn efficiency as proposed by Agrawal in 2009. This rule is actually a change of variable that simplifies a two-variable problem to a one-variable problem. From elemental calculus, we obtain an analytical expression of efficiency and the power output. The efficiency is given only in terms of the temperatures of the reservoirs, such as both Carnot and Curzon–Ahlborn cycles. We make a comparison between efficiencies measured in real power plants and theoretical values from analytical expressions obtained in this article and others found in literature from several other authors. This comparison shows that the theoretical values of efficiency are close to real efficiency, and in some cases, they are exactly the same. Therefore, we can say that the Agrawal method is good in calculating thermal engine efficiencies approximately.

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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.

An analysis of the Stirling and Ericsson cycles from the point of view of the finite time thermodynamics is made by assuming the existence of internal irreversibilities in an engine modeled by these cycles, and the ideal gas as working substance is considered. Expressions of efficiency in both regimes maximum power output and maximum ecological function are also shown. Appropriate variables are introduced so that the objective functions, namely power output, ecological function and efficiency can be functions of the reservoirs temperatures ratio and certain "measurable" parameters as a thermal conductance, the general constant of gases and the compression ratio of the cycle. Several results from the finite time thermodynamics literature are used, so that the developed methodology leads directly to appropriate expressions of the objective functions in order to simplify the optimization process.

Abstract:In this work, a dynamical model of the heartbeat is studied using nonlinear dynamics and considering the time delays inherent in the system. Two fixed points are associated to sustained oscillations which might be interpreted as the diastole and systole. These parameters are associated with blood flow in human body called arterial pressure and are very important in the cardio-vascular diagnostic.