Endoreversible Heat Engine Research Articles

Optimal configuration of a class of endoreversible heat engines for maximum efficiency with radiative heat transfer law

Optimal configuration of a class of endoreversible heat engines with fixed duration, input energy and radiative heat transfer law (q ∝ Δ(T 4)) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using optimal-control theory, and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches, four maximum-efficiency branches, and two adiabatic branches. The interval of each branch is obtained, as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton’s heat transfer law for the maximum efficiency objective, those with linear phenomenological heat transfer law for the maximum efficiency objective, and those with radiative heat transfer law for the maximum power output objective.

Power versus efficiency characteristic of an endoreversible Carnot heat engine with heat transfer law q α (Δ Tn)m

SYNOPSIS The relationship between optimal power output and efficiency of an endoreversible Carnot heat engine is derived based on a new generalised heat transfer law, including a generalised convective heat transfer law and a generalised radiative heat transfer law, q ∞ (ΔTn)m The results include those obtained in many references and can provide some theoretical guidance for the design of practical heat engines.

Irreversible Otto heat engine with friction and heat leak losses and its parametric optimum criteria

A more realistic simplified model for an irreversible Otto cycle is established by considering the heat leak losses through the cylinder and internally dissipative friction, in which it is assumed that the piston velocity in the adiabatic processes obeys a pure sinusoidal law. The optimally operating region of the irreversible Otto heat engine is determined. The model avoids the usual hypotheses of endoreversible heat engines and the simple description of irreversible heat engines so that the results obtained here may include the performance characteristics of some simplified Otto cycle models.

Optimal configuration of an endoreversible heat engine for maximum power output with fixed duration and linear phenomenological heat transfer law

Optimal configuration of an endoreversible heat engine with fixed duration and linear phenomenological heat transfer law is determined. The optimal cycle that maximizes the power output of the engine is obtained by using optimal control theory. It is shown that the optimal cycle has six branches including two isothermal branches, four maximum power branches, and no adiabatic branches. The interval of each branch and the temperature of heat reservoirs and working fluid are obtained. The maximum power and the corresponding efficiency of the engine are obtained. The calculation results show that the process time of the maximum power branch, the maximum power output, the input energy and the efficiency of the cycle decrease with the decrease of the heat source temperature. The process time of the maximum power branch and the input energy increase and the maximum power output and the efficiency of the cycle decrease with the decrease of the change rate of cylinder volume. The process time of the maximum power branch, the maximum power output and the input energy decrease and the efficiency of the cycle increase with the decrease of the heat conductivity. The obtained results are compared with those obtained with the Newton’s heat transfer law. The compared re- sults show that the optimal cycles with two heat transfer laws both contain two isothermal branches and four maximum power branches, and no adiabatic branches. For two different heat transfer laws, the temperature of their isothermal branches is different, and the process paths of four maximum power branches are different as well. The process times are different for different branches under two different optimal configurations, the maximum work outputs, the required input energies and the thermal efficiencies of the cycles are different.

Local Stability of an Endoreversible Heat Engine Working in an Ecological Regime

We present a local stability analysis of an endoreversible engine working in an ecological regime, for three common heat transfer laws. From our local stability analysis we conclude that the system is stable for every value of the heat conductivity g, the heat capacity C and the ratio of temperatures τ = T2/T1with T1> T2. After a small perturbation the system decays exponentially to the steady state determined by two different relaxation times. We observe that the stability of the system improves as r increases whereas the steady-state energetic properties of the engine decline. Moreover, we compare the stability properties of the engine working in the ecological regime and under maximum power output. Finally, qualitative phase-space portraits for the evolution of the system are presented for representative cases.

Local stability analysis of an irreversible heat engine working in the maximum power output and the maximum efficiency

In this paper the local stability of an irreversible heat engine working in the maximum power output and the maximum efficiency is analyzed. At two optimal steady-states of the maximum power output and the maximum efficiency the expressions of the relaxation time of an irreversible heat engine are derived. It is found that the relaxation time is a function of the heat-transfer coefficient α and β, internal irreversibility factor ϕ, heat leak rate q, heat capacity C, the total heat-transfer surface area F, and temperatures of the heat reservoirs T H and T L. The influence of heat resistance, internal irreversibility and heat leak rate on the relaxation time is discussed and some new results are gained. The local stability of the optimal steady-state of the maximum power output is better than that of the maximum efficiency. The results obtained here are more general and useful for an irreversible heat engine than an endoreversible heat engine.

Local stability analysis of an irreversible Carnot heat engine

The local stability of an irreversible Carnot heat engine has been studied based on the linearization technique for dynamical systems and local stability analysis. At two steady-states of the maximum power output and the maximum efficiency the expressions of the relaxation time of an irreversible Carnot heat engine are derived. It is found that the relaxation time is a function of the heat-transfer coefficient α and β, heat capacity C, temperatures of the heat reservoirs T H and T L , the degree of internal irreversibility ϕ and the internal heat conductance k. The influence of heat resistance, internal irreversibility and heat leak on the relaxation time is discussed. Phase portraits for the trajectories are presented in some representative cases. The results obtained here are more general and useful for the realistic irreversible heat engine than endoreversible heat engine.

Optimal configuration of a class of endoreversible heat-engines for maximum power-output with linear phenomenological heat-transfer law

The optimal configuration of an endoreversible heat-engine with the linear phenomenological heat-transfer law q ∝ Δ ( T - 1 ) , has been determined. The optimal cycle that maximizes the power-output of the heat-engine has been obtained using optimal control theory. It is shown that the optimal cycle has six branches including two isothermal ones, four maximum power branches, and is without an adiabatic branch. The interval of each branch, the temperatures of the heat reservoirs and working fluid, the maximum power and the corresponding efficiency of the heat-engine are obtained. The results are compared with those obtained assuming Newton’s heat-transfer law applies.

Endoreversible heat-engines for maximum power-output with fixed duration and radiative heat-transfer law

Optimal configuration of a class of endoreversible heat-engines, with fixed duration and subject to the radiative heat-transfer law q ∝ Δ( T 4), has been determined. The optimal cycle that maximizes the power output of the engine has been obtained using optimal-control theory, and the differential equations are solved by a Taylor-series expansion. It is shown that the optimal cycle has six branches, including two isothermal branches and four maximum-power branches, without adiabatic branches. The interval of each branch has been obtained, as well as the solutions of the temperatures of the heat reservoirs and working fluid. A numerical example is given. The results are compared with those obtained using the Newton’s heat-transfer law for maximum power output and those using a linear phenomenological heat-transfer law for maximum power output.

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, (T 1 > 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.

Maximum profit performance for a class of universal endoreversible steady flow heat engine cycles

SYNOPSIS The operation of a universal steady flow endoreversible heat engine cycle mode consisting of a constant thermal-capacity heating branch, a constant thermal-capacity cooling branch and two adiabatic branches is viewed as a production process with exergy as its output. The finite time exergoeconomic performance optimisation of the engine is investigated by taking profit optimisation criterion as the objective. The relationships between profit rate and temperature ratio of the working fluid, between thermal efficiency and temperature ratio of the working fluid, as well as the optimal relationship between profit rate and efficiency of the cycle are derived. The focus of this paper is to investigate the compromised optimisation between economics (profit) and the utilisation factor (efficiency) for endoreversible cycles. Moreover, analysis and optimisation of the model are carried out in order to investigate the effect of cycle process on the performance of the cycles, using numerical examples. The results obtained herein include the performance characteristics of Diesel, Otto, Atkinson, and Brayton cycles.

Universal ecological performance for endo-reversible heat engine cycles

SYNOPSIS The optimal ecological performance of a universal endoreversible steady flow heat engine cycle consisting of a constant thermal-capacity heating branch, a constant thermal-capacity cooling branch and two adiabatic branches with heat transfer loss is derived by taking an ecological optimisation criterion as the objective, which consists of maximising a function representing the best compromise between the power output and exergy loss rate of the heat engine. Some special examples are discussed. A numerical example is given to show the effects of heat reservoir temperature ratio on the ecological criterion versus the efficiency characteristic of the cycle. The results include the performance characteristics of endoreversible steady flow Diesel, Otto, Atkinson and Brayton cycles. The results can provide some theoretical guidance for the design of practical engines.

05/02260 Ecological performance analysis of an endoreversible regenerative Brayton heat-engine

05/02260 Ecological performance analysis of an endoreversible regenerative Brayton heat-engine

A comparative performance analysis of an endoreversible heat engine with thermal reservoir of finite heat capacitance under maximum power density and maximum power conditions

SYNOPSIS This paper presents a finite time thermodynamic optimisation based on maximum power density criterion for an endoreversible Carnot heat engine model coupled to variable temperature heat reservoirs. Expressions for the power density and optimal efficiency at maximum power density conditions are derived with heat resistance losses in the hot and cold side heat exchangers. The results obtained are compared with those using the maximum power criterion. The influences of some design parameters on the maximum power density are provided by numerical examples, and the advantages and disadvantages of maximum power density are analysed. Power plant design for maximum power density leads to higher efficiency and smaller size.

Development of an analytical model useful for micro heat engine analysis

A general endo-reversible heat engine model is presented for a combustion driven system. It is composed of a Carnot heat engine and a combustor operating at a specified temperature. The model is inspired by past work on ideal engine/combustor systems and the need for an analysis technique incorporating heat losses suffered by all practical micro engines. This latter consideration results from the necessary structural connections existing between the hot and ambient temperature sections of the engine. In the model developed here, a counterflow heat exchanger provides this structural connection while recovering a portion of the sensible heat in the exhaust flow. A thermal shunt resistance to the surroundings is used to account for conductive heat loss. Finally, a high degree of idealization is employed to obtain a closed form analytical solution for the operating conditions of the engine/combustor system which, in this case, is assumed to be at the maximum power point of the device.

The effect of heat transfer laws and thermal conductances on the local stability of an endoreversible heat engine

In a recent paper (Santillán et al 2001 J. Phys. D: Appl. Phys. 34 2068–72) the local stability of a Curzon–Ahlborn–Novikov (CAN) engine with equal conductances in the coupling with thermal baths was analysed. In this work, we present a local stability analysis of an endoreversible engine operating at maximum power output, for common heat transfer laws, and for different heat conductances α and β, in the isothermal couplings of the working substance with the thermal sources T1 and T2 (T1 > T2). We find that the relaxation times, in the cases analysed here, are a function of α, β, the heat capacity C, T1 and T2. Besides, the eigendirections in a phase portrait are also functions of τ = T1/T2 and the ratio β/α. From these findings, phase portraits for the trajectories after a small perturbation over the steady-state values of internal temperatures are presented, for some significant situations. Finally, we discuss the local stability and energetic properties of the endoreversible CAN heat engine.

Optimal Allocation of Heat Transfer Area for a Heat Engine

AbstractFor an endoreversible heat engine operates steadily between two fixed temperatures, Bejan found the engine's best performance can be obtained if the total thermal conductance is evenly divided for hot-end and cold-end heat exchangers. In this study, a heat by-pass model is used to represent the losses due to internal irreversibilities, and the more general formulations are derived for both the optimal area allocation and the maximum thermal efficiency. The results calculated from the present formulations when there is no internal irreversibility(a special case) are consistant with that obtained by Bejan.

New and old regimes for the endoreversible heat engine

We revisit the simple model of the cyclic endoreversible heat engine with linear heat transfer. With W being the delivered work, t, the total contact time with the reservoirs and α the total heat transfer coefficient, we (i) introduce the regime of maximum W/α given the contact times with each reservoir; (ii) reinterpret the regime of maximum W/t for given t and α as a regime of maximum W/(tα); and (iii) introduce the regime of maximum W/γ (where the total contact coefficient γ is the sum of the product of each contact time and the corresponding heat transfer coefficient). We conclude that to compare cyclic and stationary operation with regard to the performance in using time and heat transfer coefficients, the regime of maximum W/γ is the most adequate, because γ accounts only for the resources that are actually employed during the cycle.

Thermo-economics for endoreversible heat-engines

The thermoeconomics of endoreversible heat engines has been studied based on the linear phenomenological heat-transfer law [i.e., the heat flux Q ∝ Δ(1/ T), where T is the absolute temperature]. Analytical formulae for profit, the maximum profit and the corresponding efficiency are derived.

Maximum power processes for multi-source endoreversible heat engines

The maximum power processes of multi-source endoreversible engines with stationary temperature reservoirs are investigated. We prove that the optimal solution is always time independent with a single hot and a cold engine contact temperature. The heat reservoirs fall into three groups: the hot reservoirs which are connected at all times for heat delivery, the cold reservoirs which are connected at all times for heat drain, and possibly a group of reservoirs at intermediate temperatures which are unused. This phenomenon is demonstrated for a three-source system. We find that for a commonly used class of heat transfer functions, including Newtonian, Fourier, and radiative heat transport, the efficiencies at maximum power are the same as for two-reservoir engines with appropriately chosen properties.