Finite-time Heat Research Articles

Optimal paths for minimizing entropy generation during heat transfer processes with a generalized heat transfer law

An investigation of finite-time heat transfer processes between high- and low-temperature sides with a generalized heat transfer law (q∝[Δ(Tn)]m) is presented in this paper. Optimal heating and cooling strategies for minimizing entropy generation are derived for the fixed initial and final temperatures of the low-temperature side working fluid. Optimal paths are compared with the common strategies of constant heat flux and constant source temperature operation by numerical examples. The condition corresponding to the minimum entropy generation strategy is not only valid for Newton’s [q∝(ΔT)] and linear phenomenological [q∝Δ(T−1)] heat transfer laws but also valid for heat transfer law (q∝[Δ(T−1)]m). The obtained results are general and can provide some theoretical guidelines for the designs and operations of practical heat exchangers.

Numerical Experiments of a Finite-Time Thermodynamic Cycle

Heat engines are ubiquitous in our industrial society and are also crucially important to the basis of thermodynamics. They allow us to extract useful work from the heat flowing from a hot heat reservoir into a cold heat reservoir by expanding and compressing the working substance. We have already known that the upper bound of the efficiencies of all the existing heat engines is limited by the Carnot efficiency ηC ≡ 1− Tc/Th where Th and Tc are the temperatures of the hot and the cold reservoirs, respectively. ηC can be realized only when heat engines are working infinitely slowly (quasistatic limit). This implies that the heat engine working in the quasistatic limit produces zero power because it takes infinite time to produce a finite amount of work. Though the Carnot efficiency is a fundamental result which manifests the natural law of the heat energy conversion and supplies certain guidance for designing efficient heat engines, it is not useful for describing the realistic heat engines which should produce finite power. Therefore, it is important to question: Are there any physical laws which can be applied to finite-time heat engines? Motivated by the above considerations, Curzon and Ahlborn studied the efficiency of a finite-time Carnot cycle and derived the result that the efficiency at the maximal power output ηmax becomes

On the Role of External and Internal Irreversibilities towards Classical Entropy Generation Predictions in Equilibrium Thermodynamics and their Relationship with Heat Transfer

In classical equilibrium thermodynamics description, ambiguities exist in terms of pinpointing external and in- ternal irreversibilities in overall entropy generation prediction, as a system undergoes a thermodynamic process. The pre- sent work attempts to bridge this gap between classical thermodynamics-based irreversibility predictions and finite time heat transfer analysis. By choosing a model problem, expressions for external irreversibilities are quantitatively derived and it is observed that ambiguities may exist in the pertinent quantification depending on the very definition of system, immediate surroundings and surroundings. It is observed that if variations within immediate surroundings are taken into account, more realistic estimates of external irreversibilities can be obtained in equilibrium thermodynamics framework, as a function of heat transfer characteristics of the same. It is also shown that for some special cases, different expressions for external irreversibilities asymptotically converge to the same entropy generation predictions, in effect.

Performance Optimization of a Class of Finite Time Heat Engines

The effect of heat resistance and heat leakage on the optimal performance of finite time heat engines is investigated in this paperbased on a generalized heat transfer law q ∞ Δ(Tn). The analytical relation between optimal power output and efficiency for steady-state flow irreversible heat engines is derived. The analysis includes the optimal performance characteristics of several types of heat engines with different loss item and different heat transfer laws. A numerical example is provided for illustrating the power output versus efficiency characteristics. Results shown that the heat transfer law does affect the performance of these heat engines.

Optimization criteria for the important parameters of an irreversible Otto heat-engine

An irreversible cycle model of an Otto heat-engine is established, in which the main irreversibilities result from the non-isentropic compression and expansion processes; finite-time processes and heat loss through the cylinder wall are taken into account. The power output and efficiency of the cycle are derived. The curves of the power output and efficiency varying with the compression ratio of two isochoric processes are presented. It is found from the curves that there are optimal values of the compression ratio at which the power output and efficiency attain their maxima. Moreover, the maximum power-output and efficiency and the corresponding relevant parameters are calculated, and consequently, the optimization criteria of some important parameters such as the power output, efficiency, compression ratio, and temperatures of the working substance are obtained.

Optimal paths for minimizing lost available work during usual finite-time heat transfer processes

A system of uniform temperature in contact with a thermal bath must be heated in a fixed time interval between given initial and final temperatures. Several ways of defining the lost work associated with the heating process are presented. The minimum entropy generation is generally not equivalent to the minimum lost available work. Two optimal control problems are defined and solved for various heat transfer mechanisms, among them Newtonian heat convection and radiative heat transfer. The optimal paths are obtained for both objective functions (i.e., entropy generation and lost available work). The results of the optimal strategies are different from those associated with the usual industrial heating strategy that keeps a constant heat reservoir temperature. Much better results are obtained by using another simple heating procedure, namely the constant heat flux strategy. The difference between various heating strategies is higher in the case of Newtonian convection than in the case of radiative heat transfer and increases by increasing the final temperature of the heating process. The analytical expressions of the optimal paths are presented in dimensionless form, allowing easy implementation.

Environmental impact and design of an OTEC plant

This paper presents a critical examination of the environmental impact and design optimization of a potential OTEC (Ocean Thermal Energy Conversion) power plant on the island of Diego Garcia in the Indian Ocean. Specific power of a finite-time thermodynamic heat engine is chosen to be the objective function in the design of the OTEC. ICAI (Intelligent Computer Aided Instruction) computer software, CyclePad, is used in the analysis process. Through manipulation of the boiler pressure and condenser pressure, the specific power of the OTEC plant is optimized. (author)

Finite time thermodynamic evaluation of irreversible Ericsson and Stirling heat engines

This paper presents an investigation on finite time thermodynamic evaluation of Ericsson and Stirling heat engines. Finite time thermodynamics has been applied to optimise the power output and thermal efficiency of both engines, including finite heat capacitance rates of the heat source and sink reservoirs external fluids, finite time heat transfer, regenerative heat losses and direct heat leak losses from source to sink reservoirs. The presence of these effects causes irreversibilities and affects the performance of the Ericsson and Stirling heat engines using ideal or real gas as the working fluid/substance. It is found that both cycles with an ideal regenerator ( ϵ R=1.00) are as efficient as an endoreversible Carnot heat engine operating at the same conditions, but this is not practical because an ideal regenerator requires either infinite regenerator area or infinite regeneration time. It is also found that the regenerative heat losses, regenerator effectiveness and the direct heat leak losses do not affect the maximum power output of either heat engine. Some special cases are also described.

Cooling load versus COP characteristics for an irreversible air refrigeration cycle

The effect of heat resistance on the performance of an air refrigeration cycle is analyzed with a finite time heat transfer analysis. The present work extends the recent studies on refrigerator performance by incorporating nonisentropic compression and expansion. Relations between cooling load and pressure ratio and between COP (coefficient of performance) and pressure ratio for the air refrigeration cycle in which the irreversibilities of heat resistance losses in the hot and cold-side heat exchangers and nonisentropic losses in the compression and expansion processes are derived. The results show that there exists a maximum value of COP and that the cooling load has a parabolic dependence on COP, unlike the monotonically decreasing behaviour in the case of an endoreversible air refrigeration cycle.

Theoretical analysis of the performance of a regenerative closed Brayton cycle with internal irreversibilities

Using the technique of finite-time thermodynamic analysis, the performance of a closed Brayton cycle with regeneration is assessed. Specifically, analytical expressions for the power output and the thermal efficiency, as functions of the pressure ratio and the reservoir temperatures, are derived. The analysis also takes into account all the irreversibilities associated with finite-time heat transfer processes. The paper also shows that the power output can be maximized with judicious selection of parameters such as the heat exchanger surface areas and the heat conductances. Maximum power is obtained when the effectiveness of the hot- and cold-side heat exchangers are related in a specific manner, and this power output is a strong function of the regenerator effectiveness.

A finite-time heat engine with fixed-capacity heat transfers

We consider a finite-time heat engine in which the temperature T(t) of the working fluid during heat exchanges with the hot and cold reservoirs is determined passively by the heat capacity of the fluid. The set of feasible operations of this engine, whose irreversibility arises solely from the temperature difference between the reservoir(s) and the working fluid, is described in terms of an inequality which sets limits on the rate P of work output and the rate D of entropy production associated with a cycle that takes place in time . Those operations that lie on the boundary of this set are the ones that achieve a specified work output and entropy production in minimum time; this leads naturally to a notion of time efficiency for any operation within the set. The results obtained here extend our previous framework for Carnot-like processes to examine the time efficiency, as well as the power efficiency, of the corresponding Otto- and Brayton-cycle based engines. The present results and the earlier ones can be seen as two extremes of a continuum in which the external control on the temperature of the working fluid varies between (i) passively allowing the T(t) corresponding to a constant heat capacity response and (ii) actively achieving any desired T(t).

The maximum coefficient of performance of internally irreversible refrigerators and heat pumps

A class of irreversible refrigeration cycles is investigated to determine the maximum coefficient of performance in the heat pump mode and the refrigerator mode. For the purpose of generality and simplicity of the results, finite-time heat transfer in the condenser and evaporator is expressed in terms of arithmetic mean temperature differences. The generic source of internal irreversibility is measured by a single irreversibility factor which transforms the Clausius inequality into an equality to simplify the cycle model. These optimum cycle performances are obtained as closed form analytical expressions in which the irreversibility factor has been shown to be simply related to the ratio of the actual and endoreversible cycle coefficients of performance.

Carnot-like processes in finite time. I. Theoretical limits

The set of feasible operations of a finite-time heat engine subject only to thermal losses is described in terms of a new inequality, which sets a lower bound for the time required by a Carnot-like process in terms of the entropy changes of the reservoirs. This leads to an analogue of the second law of thermodynamics and to a general notion of time efficiency for the class of processes considered.

Optimal paths for minimizing entropy generation in a common class of finite-time heating and cooling processes

For a common class of finite-time heat transfer processes, we derive optimal heating and cooling strategies for minimizing entropy generation. Solutions pertain to a generalized heat transfer law, and are illustrated quantitatively for cases of practical interest, including Newtonian and radiative heat transfer. Optimal paths are compared with the common strategies of constant heat flux and constant source (reservoir) temperature operation, including evaluation of the savings in entropy generation and the relative requirements for installed heating/cooling capacity.

Power Performance of a Nonisentropic Brayton Cycle

Work and power optimization of a Brayton cycle are analyzed with a finite-time heat transfer analysis. This work extends the recent flurry of publications in heat engine efficiency under the maximum power condition by incorporating nonisentropic compression and expansion. As expected, these nonisentropic processes lower the power output as well as the cycle efficiency when compared with an endoreversible Brayton cycle under the same conditions.

Finite-time optimizations of a heat engine

We study the power and efficiency of a finite-time heat engine. We consider an endoreversible Carnot heat engine coupled to heating and cooling fluids and determine the maximum power output and efficiency to obtain a bound on the power-conversion systems. While the maximum power and the operating temperatures of the heat engine are functions of the heat-reservoir temperatures, heat-reservoir capacity rates and heat-transfer rates, the efficiency at maximum power depends primarily on the initial temperatures of the heating and cooling fluids. The efficiency at maximum power provides a measure of the power available in a practical heat engine.

Power optimization of a finite-time Rankine heat engine

The power output of a single, finite-time Rankine heat engine is studied. The model adopted is a reversible Rankine cycle coupled to a heat source and a heat sink by heat transfer. Both the heat source and the heat sink have finite heat capacity rate. A mathematical expression is derived for the power output of the irreversible heat engine. The maximum power output is found. The maximum bound provides the basis for designing a real heat engine and for a performance comparison with existing power plants.

Power optimization of a finite-time Carnot heat engine

The power output of a simple, finite-time Carnot heat engine is studied. The model adopted is a reversible Carnot cycle coupled to a heat source and a heat sink by heat transfer. Both the heat source and the heat sink have finite heat-capacity rates. A mathematical expression is derived for the power output of the irreversible heat engine. The maximum power output is found. The maximum bound provides the basis for designing a real heat engine and for a performance comparison with existing power plants.