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• An Ericsson refrigeration cycle with MnFe-based composite materials is proposed. • Molar mass ratios of each constituent to composite are optimally determined. • Effects of non-perfect regeneration and applied magnetic field are discussed. • The cooling quantity and coefficient of performance of the cycle are calculated. • Cyclic performances with composite and each constituent materials are compared. From the experimental data of the isofield heat capacity of the MnFe-based magnetocaloric materials, magnetic entropy change versus temperature characteristic curves are obtained by using numerical value calculation procedure. Three kinds of MnFe-based magnetocaloric materials, in which there are all a large magnetocaloric effect, are selected as the constituent materials to establish a novel composite magnetocaloric material, for which keeping large magnetic entropy change over a wide temperature range is desired. By means of thermodynamic analysis and optimal control theory, the molar mass ratios of each constituent material to the composite material are optimally determined for differently applied magnetic fields. The optimum results show that when the applied magnetic field μ 0 H″ =2 T, the optimum molar mass ratios x 1opt , x 2opt , and x 3opt of Mn 1.24 Fe 0.76 P 0.75 Ge 0.25 , Mn 1.2 Fe 0.8 P 0.75 Ge 0.25 , and Mn 1.1 Fe 0.9 P 0.78 Ge 0.22 to the composite are equal to 0.44, 0.11, and 0.45, respectively. Furthermore, the regenerative Ericsson refrigeration cycle employing the composite or constituent materials as the working substance is set up. The effects of the non-perfect regeneration on the net cooling quantity, COP , etc. of the refrigeration cycle are analyzed and evaluated. The cycle performances of the composite material are compared with those of the constituent materials. It shows that the net cooling quantity and COP of the composite are much larger than those of any constituent material. The numerical calculation results obtained can provide some reference for the selection of working substances and the optimal parameter design of room temperature magnetic refrigerators. [ABSTRACT FROM AUTHOR]

Abstract: Based on the experimental isothermal entropy change of the magnetic materials Gd x Dy1−x , the thermodynamic performance of a regeneration Ericsson refrigeration cycle is evaluated and analyzed. The effects of non-perfect regeneration on the cyclic performance are highlighted. For a room temperature hot reservoir, the cooling quantity, non-perfect regeneration heat quantity, and net cooling quantity of the established regeneration Ericsson refrigeration cycle are calculated as a function of the cold reservoir temperature. Furthermore, for several typical compositions x of the Gd x Dy1−x alloys, the values of the cooling quantity, non-perfect regeneration heat quantity, work input, net cooling quantity, and coefficient of performance (COP) are listed for given temperatures of the cold reservoir. The cyclic performance of the Gd x Dy1−x alloys with different composition x is compared and some significant analyses are provided. [Copyright &y& Elsevier]

Abstract: The thermodynamic cycle performance of Gadolinium (Gd) and Gd0.87Dy0.13 used as the working substance in regeneration magnetic Brayton and Ericsson refrigeration cycles are investigated under different external magnetic field conditions. Based on the experimental iso-field heat capacities of Gd with different magnetic fields, the effects of magnetic field change on thermodynamic performances including the magnetic entropy change, cooling quantity, non-perfect regeneration, net cooling quantity, and coefficient of performance (COP) are analyzed and discussed. The present work shows the possibility of reducing the regenerative losses and thereby improving the net cooling quantity for a given field change by selecting optimal initial and final magnetic field values. The similar analysis and calculation of the related thermodynamic performances are further applied to the magnetic material Gd0.87Dy0.13 which exhibits better net cooling quantities when compared to Gd at low temperature. [Copyright &y& Elsevier]

Abstract: The cycle model of an irreversible regenerative magnetic Brayton refrigerator using Gd0.74Tb0.26 as the working substance is established. Based on the experimental characteristics of iso-field heat capacities of the material Gd0.74Tb0.26 at 0T and 2T, the corresponding iso-field entropies are calculated and the thermodynamic performance of an irreversible regenerative magnetic Brayton refrigeration cycle is investigated. The effects of the irreversibilities in the two adiabatic processes and non-perfect regenerative process of the magnetic Brayton refrigeration cycle on the cooling quantity, the heat quantity released to the hot reservoir, the net cooling quantity and the coefficient of performance are discussed in detail. Some significant results are obtained. [Copyright &y& Elsevier]

Abstract: Based on the current model of a phosphoric acid fuel cell (PAFC) system, the electrolyte concentration is optimised. New analytical expressions for the power output and efficiency of the PAFC system are derived by considering the effects of multi-irreversibilities resulting from the activation overpotential, concentration overpotential, ohmic overpotential, and leakage resistance on the performance of the PAFC system. These parameters are used to evaluate the general performance characteristics of the PAFC system. Accordingly, the upper and lower limits of the optimised values for some main parameters, such as the current density, power output, and efficiency, are determined. Moreover, a multi-objective function, including both the power output and efficiency, is introduced and used to further subdivide the parametric optimum regions according to different requirements. In addition, a general formula for the load of the system is derived. The relations between the power output and efficiency of the system and the load are discussed in detail, and the optimum matching conditions of the load are obtained. [Copyright &y& Elsevier]

Abstract: Based on the model of a typical alkaline fuel cell (AFC) with circulating potassium hydroxide (KOH) solution as electrolyte and oxygen as oxidant and the experimental data available in the current literature, thermodynamic–electrochemical analyses on the performance of the AFC are carried out, in which multi-irreversibilities such as charger-transfer, concentration and ohmic overpotentials are taken into account. Expressions for the power output and efficiency of the AFC are derived, from which the general performance characteristics of the AFC are discussed in detail. It is found that the power output and efficiency of the AFC first increase and then decrease as the electrolyte concentration is increased, and consequently, there exist the optimal electrolyte concentrations for different temperatures. It is also found that the power output is not a monotonic function of the electric current density while the efficiency is a monotonically decreasing function of the electric current density. According to the performance characteristic curves of the AFC, the optimal operation regions of some main parameters are determined. Moreover, a new multi-objective function is used to further optimize the characteristics of the AFC. Some significant results for the optimal design and operation of practical AFCs are obtained. [Copyright &y& Elsevier]

Abstract: The model of a new molten carbonate fuel cell (MCFC) system is established, in which multi-irreversibilities resulting from the anode, cathode, and ohm overpotentials are taken into account. Based on thermodynamic-electrochemical analysis and the semi-empirical equations available in literature, expressions of some main parameters such as the cell voltage, power output, efficiency and entropy production rate are derived. The influence of the gas inlet compositions on the electrode overpotentials is discussed in detail. It is found that there exist the optimal anode CO2 concentrations for different anode H2 concentrations. The performance characteristic curves of the MCFC system are represented through numerical calculation and the optimal operation regions of the main parameters are determined. Moreover, a new multi-objective function is used to further optimize the characteristics of the MCFC system, and consequently, the important problem of how to give consideration to both the efficiency and power output in the optimal operation region of the system is expounded. [Copyright &y& Elsevier]

Abstract: Taking into account the finite-rate heat transfer in the heat-transfer processes, heat leak between the two external heat reservoirs, regenerative loss, regeneration time, and internal irreversibility due to dissipation of the cycle working substance, an irreversible magnetic Ericsson heat-pump cycle is presented. On the basis of the thermodynamic properties of magnetic materials, the performance characteristics of the irreversible magnetic Ericsson heat-pump are investigated and the relationship between the optimal heating load and the coefficient of performance (COP) is derived. Moreover, the maximum heating load and the corresponding COP as well as the maximum COP and the corresponding heating load are obtained. Furthermore, the other optimal performance characteristics are discussed in detail. The results obtained here may provide some new information for the optimal parameter design and the development of real magnetic Ericsson heat-pumps. [ABSTRACT FROM AUTHOR]

Abstract: With the help of the typical model of a water electrolysis hydrogen production system, which mainly includes the electrolysis cell, separator, and heat exchangers, three expressions of the system efficiency in literature are compared and evaluated, from which one reasonable expression of the efficiency is chosen and directly used to analyze the performance of a water electrolysis hydrogen production system under different operation conditions. Several new configurations of a water electrolysis system are put forward and the problem how to calculate the efficiencies of these configurations is solved. Moreover, a solid oxide steam electrolyzer system (SOSES) for hydrogen production is taken as an example to expound that the different configurations of a water electrolysis system should be adopted for different operation conditions. The results obtained here may provide some guidance for the optimum design and operation of water electrolysis systems for hydrogen production. [ABSTRACT FROM AUTHOR]

Abstract: An irreversible solar-driven Braysson heat engine system is presented, in which the temperature-dependent heat capacity of the working fluid, the radiation–convection heat losses of the solar collector and the irreversibilities resulting from heat transfer and non-isentropic compression and expansion processes are taken into account. Based on the thermodynamic analysis method and the optimal control theory, the mathematical expression of the overall efficiency of the system is derived and the maximum overall efficiency is calculated, and the operating temperatures of the solar collector and the cyclic working fluid and the ratio of heat-transfer areas of the heat engine are optimized. By using numerical optimization technology, the influences of the variable heat capacity of the working fluid, the radiation–convection heat losses of the solar collector and the multi-irreversibilities on the performance characteristics of the solar-driven heat engine system are investigated and evaluated in detail. Moreover, it is expounded that the optimal performance and important parametric bounds of the irreversible solar-driven Braysson heat engine with the constant heat capacity of the working fluid and the irreversible solar-driven Carnot heat engine can be deduced from the conclusions in the present paper. [Copyright &y& Elsevier]

Abstract: A new irreversible cyclic model of a class of two-source chemical pumps, which are affected by not only finite-rate mass transfer and mass leak but also the internal dissipation resulting from friction, eddy currents and other irreversible effects inside the cyclic working fluid, is established. By using the optimal control theory, the optimal relation between the coefficient of performance and the rate of energy pumping for the two-source irreversible chemical pump cycles is derived. The maximum coefficient of performance and some other important performance bounds of the cycle are determined. The optimal mass-transfer time, minimum entropy production rate and minimum power input are calculated. Consequently, the influences of the main irreversibilities usually existing in real engineering systems on the performance characteristics of the chemical pump operating between two mass sources are revealed. Moreover, it is expounded that some relevant important conclusions in the literature can be directly deduced from the results in the present paper. [Copyright &y& Elsevier]

Abstract: The coefficient of performance and specific heating load of an irreversible three-heat-source heat pump are given by using a general cycle model affected by the finite-rate heat transfer, heat leak and internal irreversibility of the cyclic working fluid. The heat pumping load divided by the total cost per unit time is taken as a new objective function and used to investigate the performance of the heat pump. The thermoeconomic and thermodynamic performance characteristics of the heat pump are discussed in detail. Some important performance parameters such as the thermoeconomic objective function and coefficient of performance are optimized. The optimally operating regions of the heat pump and the bounds of several performance parameters are determined. Finally, it is pointed out that the Carnot heat pump may be taken as a special case of a three-heat-source heat pump and consequently its optimal performance can be directly derived from the results obtained here. [Copyright &y& Elsevier]

Abstract: A three-source irreversible chemical pump model is established, in which three key irreversibilities usually existing in a real chemical pump system are taken into account. By using the new cyclic model, the influences of finite-rate mass transfer, mass leak, and internal dissipation of a cyclic working substance on the optimal performance of the chemical pump are revealed. The expression for optimal relation between the coefficient of performance and the rate of energy pumping is derived. Based on the optimal relationship, some new important performance bounds of the chemical pump, e.g., the maximum coefficient of performance and the corresponding rate of energy pumping, the maximum rate of energy pumping and the corresponding coefficient of performance, and so on, are obtained and the optimal operating region of the chemical pump is determined. Moreover, the optimal chemical potentials of the cyclic working substance and the optimal mass-exchange times in the three mass-exchange processes are further discussed. The results obtained in the present paper can provide some new theoretical guidance for the optimal design and development of a class of chemical pumps. [Copyright &y& Elsevier]

A new cyclic model of a class of chemical engines is set up, in which not only finite-rate mass transfer and mass leakage but also the internal irreversibility resulting from friction, eddy currents and other irreversible effects inside the cyclic working fluid are taken into account. The influences of these irreversibilities on the performance of the cycle are revealed. The optimal relation between the power output and the efficiency of the cycle is derived. On the basis of the optimal relation, some optimal performances and important performance bounds of the cycle are determined and evaluated. For example, the maximum power-output and the corresponding efficiency, the maximum efficiency and the corresponding power output, the optimal mass-transfer time, the minimum rate of energy loss and so on are calculated and analyzed. The results obtained here cannot only enrich the application of thermodynamic theory but also provide some theoretical guidance for the effective application of energy resources and for the optimal design and development of a class of chemical engines. Moreover, some important conclusions relative to the isothermal endoreversible chemical engines, which have been investigated previously, can be directly deduced from the results in this paper. [Copyright &y& Elsevier]

A new cyclic model of a class of chemical engine-driven chemical pumps, which operate among three reservoirs at different chemical potentials, is set up. The influence of the irreversibility of finite-rate mass transfer between the cyclic working fluid and the three reservoirs on the performance of the chemical pumps is taken into account. The optimal chemical potentials of the cyclic working fluid and the optimal relation between the coefficient of performance and the rate of energy pumping for the chemical pumps are derived. On the basis of the optimal relation, some other optimal performances of the chemical pumps are discussed. For example, the maximum rate of energy pumping and the corresponding coefficient of performance, the optimal mass-transfer time, the minimum rate of entropy production, and so on, are calculated and their general expressions are given. The results obtained here cannot only enrich the theory of thermodynamics but also provide some theoretical guidance for the optimal design and development of a class of chemical engine-driven chemical pumps. Moreover, some important conclusions relative to the chemical pumps operating between two reservoirs at different chemical potentials, which have been investigated in the literature, can be deduced directly from the results in this paper. [Copyright &y& Elsevier]

A chemical potential transformer operating among three reservoirs at different chemical potentials is analogous to a heat transformer operating among three heat reservoirs. When the influence of finite-rate mass transfer between the working fluid and the reservoirs is taken into account, a chemical potential transformer may be conceived as a combined system having a chemical pump driven by a chemical engine. The fundamental optimal relations of the chemical engine and pump operating between two reservoirs are used to derive the fundamental optimal relation of the chemical potential transformer. Consequently, it is proved that such a combined cycle system is equivalent to the chemical potential transformer operating among three reservoirs at different chemical potentials. Moreover, the main optimal performances of the chemical potential transformer are discussed. The results obtained here may reveal some inherent connections between the chemical potential transformer and the chemical engine and provide a theoretical base for the development of chemical potential transformers. [Copyright &y& Elsevier]

On the basis of the Langevin theory of classical statistical mechanics, the magnetization, entropy, and iso-field heat capacity of ferromagnetic materials are analyzed and their mathematical expressions are derived. An irreversible regenerative Ericsson refrigeration cycle by using a ferromagnetic material as the working substance is established, in which finite heat capacity rates of low and high temperature reservoirs, non-perfect regenerative heat of the refrigeration cycle, additional regenerative heat loss, etc. are taken into account. Based on the regenerative refrigeration cycle model, a thermoeconomic function is introduced as one objective function and optimized with respect to the temperatures of the working substance in the two iso-thermal processes. By means of numerical calculation, the effects of the effective factor of the heat exchangers in high/low temperature reservoir sides, efficiency of the regenerator, heat capacity rate of the low temperature reservoir, and applied magnetic field on the optimal thermoeconomic function as well as the corresponding cooling rate and coefficient of performance are revealed. The results obtained in this paper can provide some theoretical guidance for the optimal design of actual regenerative magnetic refrigerator cycle. [ABSTRACT FROM AUTHOR]

Abstract: The active thermal potentiostatting system proposed by Martinovskii and Tsirlin is directly generalized to a more practical case, in which one intermediate chamber, besides a thermal potentiostatting chamber, and two irreversible refrigeration cycles are included and the influence of the thermal resistance between the working fluid and the reservoirs, the heat leakages from the environment to the intermediate chamber and from the intermediate chamber to the potentiostatting chamber are taken into account. Expressions for the main parameters of the system are derived. By using the optimal control theory, the minimum total power input of the system with non-zero cooling rates is calculated and the temperatures of the working fluid in the isothermal processes of the refrigeration cycles are optimized. The optimal allocation of the heat-transfer areas of the heat-exchangers in the refrigeration cycles is discussed in detail. The results obtained here are more general and useful than the relevant results in literature and can provide some valuable guidance for the optimal design and operation of real active thermal potentiostatting systems. [Copyright &y& Elsevier]

A novel model of the solar-driven thermodynamic cycle system which consists of a solar collector and a Braysson heat engine is established. The performance characteristics of the system are optimized on the basis of the linear heat-loss model of a solar collector and the irreversible cycle model of a Braysson heat engine. The maximum efficiency of the system and the optimally operating temperature of the solar collector are determined and other relevant performance characteristics of the system are discussed. The results obtained here may provide some theoretical guidance for the optimal design and operation of solar-driven Braysson and Carnot heat engines. [Copyright &y& Elsevier]

Highlights • A spectrum splitting photovoltaic-thermoelectric generator system is updated. • Maximum efficiencies of the system are calculated for differently given parameters. • The area ratio of the collector to the photovoltaic cell is optimized. • Optimal values of some key parameters are determined. • Advantages of the system are revealed, compared to the single photovoltaic cell. Abstract An updated model of the solar spectrum splitting photovoltaic cell-thermoelectric generator system is used to derive the analytical expression of the systemic efficiency. The cutoff energy of the system, cell voltage, and dimensionless current of the thermoelectric generator are optimized. Particularly, the influences of the area ratio of the collector to photovoltaic cell on the performance of the spectrum splitting system are discussed in detail. The maximum efficiencies of the spectrum splitting system are calculated for given solar concentration factors. The results obtained are compared with those of the single photovoltaic cell with the same solar concentration factor. It is found that the maximum efficiency of the system can be further improved when the area ratio is optimized. The expressions of the upper and lower bounds of the optimized area ratio are derived. The spectrum splitting system can more efficiently harvest the full solar spectrum than the single photovoltaic cell, especially at low solar concentration factors. For example, when solar concentration factors are, respectively, equal to 30 and 100, the maximum efficiencies of the spectrum splitting system attain 39.5% and 40.2% and increase approximately 2.67% and 2.19%, compared to those of the single photovoltaic cell. [ABSTRACT FROM AUTHOR]

An unreported model of the cylindrical thermophotovoltaic cell (TPVC) composed of an emitter and a photovoltaic (PV) cell is proposed and used to recycle the waste heat released by the automobile exhaust pipe to generate electricity. To theoretically analyze the performance of this system, expressions of the power output and the conversion efficiency of the thermophotovoltaic cell driven by the automobile exhaust are derived analytically. The optimal functions of the temperature distributions of the automobile exhaust pipe and TPVC are obtained by the variational method and the modified Lagrangian formulation. The maximum power output is calculated. The performance characteristics of the whole system at the maximum power output are represented. The optimal regions of the voltage output of the PV cell, the energy gap of the material in the PV cell, and the inlet heat flow of the gas pipe are determined. The effects of the size of the gas pipe on the performance of the TPVC are discussed. The theoretical efficiencies of the TPVC and thermoelectric generator driven by the automobile exhaust are compared. The advantages of the TPVC are revealed. The results obtained show that the optimally designed TPVC can significantly harvest the waste heat of the automobile exhaust. [ABSTRACT FROM AUTHOR]

Based on the current models of the direct carbon fuel cell and thermophotovoltaic cell, a new hybrid system is proposed to efficiently exploit the waste heat from a direct carbon fuel cell by terms of a thermophotovoltaic cell. The expressions of the power output and the efficiency of the hybrid system are analytically derived and the maximum power output density is numerically calculated. It is found that under some given conditions, the maximum power output density of the hybrid system can attain 734.7 W m −2 , which is more than 2 times of that of a single direct carbon fuel cell. Moreover, the optimal region of the hybrid system is determined through the introduction of a new objective function (i.e., the product of the efficiency and the power output). The selective criteria of some key parameters such as the power output density, efficiency, current density of the direct carbon fuel cell, and area ratio of the direct carbon fuel cell to the thermophotovoltaic cell are provided. The effects of the carbon particle slabs in the packed bed anode of the fuel cell on some key parameters are discussed. The maximum power output density of the hybrid system under the differently operating temperatures of the direct carbon fuel cell are calculated and compared with those of other direct carbon fuel cell-based hybrid systems. The results of this study indicate that the thermophotovoltaic cell can efficiently harvest the waste heat produced in the direct carbon fuel cell and the direct carbon fuel cell-thermophotovoltaic cell hybrid system have some obvious advantages over other direct carbon fuel cell-based hybrid systems. [ABSTRACT FROM AUTHOR]

A new model of the thermal amplifier consisting of three electronic reservoirs connected by two energy filters and an electronic conductor with negligible resistance is proposed. The thermal amplifier may have two different connective methods and can be regarded as the equivalent system composed of an energy selective electron (ESE) heat engine and an ESE heat pump. With the help of the theory of the ESE devices operating between two electronic reservoirs, the coefficient of performance and rate of heat-pumping of the thermal amplifier are directly derived. The effects of the center energy levels and the half width (or the half width at the half maximum) of two energy filters on the performance of the thermal amplifier are discussed. The maximum coefficient of performance and rate of heat-pumping are calculated. The optimally operating regions of the thermal amplifier are determined. Moreover, the optimum performance characteristics of the thermal amplifier with two configurations of energy filters are compared. [ABSTRACT FROM AUTHOR]

A new model of the hybrid system composed of a molten carbonate fuel cell (MCFC) and a thermophotovoltaic cell (TPVC) is proposed to recovery the waste heat produced by the MCFC. Expressions for the power output and the efficiency of the hybrid system are analytically derived. The performance characteristics of the hybrid system are evaluated. It is found that when the current density of the MCFC, voltage output of the TPVC, electrode area ratio of the MCFC to the TPVC, and energy gap of the material in the photovoltaic cell are optimally chosen, the maximum power output density of the hybrid system is obviously larger than that of the single MCFC. Moreover, the improved percentages of the maximum power output density of the proposed model relative to that of the single MCFC are calculated for differently operating temperatures of the MCFC and are compared with those of some MCFC-based hybrid systems reported in the literature, and consequently, the advantages of the MCFC-TPVC hybrid system are revealed. [ABSTRACT FROM AUTHOR]

The thermodynamic performance and optimization of a three-terminal quantum dot nano-device consisting of two capacitively coupled quantum dots connected to electron reservoirs in the Coulomb-blockade regime are investigated. Based on the master equation, the existing model with configuration A and a previously unreported model with configuration B of the device are studied and compared systematically. The maximum power output and efficiency of the two configurations under different given conditions are analyzed. The results obtained indicate that the working regions of the output voltage and Coulomb interaction of configuration B are significantly larger than those of configuration A. Moreover, the optimum ranges of the output voltage and Coulomb interaction of both configuration A and B are determined. A key measure of performance, i.e. the efficiency at the maximum power output, is further studied. It is found that the efficiency at the maximum power output is approximately equal to 0.035 for configuration A and 0.058 for configuration B. When the temperature difference between the two electron reservoirs is large enough, the maximum power output and efficiency at the maximum power output of configuration B are significantly larger than those of configuration A. [ABSTRACT FROM AUTHOR]

A model of the three-terminal nano-scaled energy conversion system as a heat engine based on two capacitively coupled quantum dots in the Coulomb-blockade regime is established within four quantum states that include the essential physical features. The dynamical properties of the model are calculated by master equation approach account for the quantitative behavior of such a system. Expressions for the power output and efficiency of the three-terminal quantum dot heat engine are derived. The characteristic curves between the power output and the efficiency are plotted. Moreover, the optimal values of main performance parameters are determined by the numerical calculation. The influence of dissipative tunnel processes on the optimal performance is discussed in detail. The results obtained here can provide some theoretical guidelines for the design and operation of practical three-terminal quantum dot heat engines. [ABSTRACT FROM AUTHOR]

Abstract: A new solar-driven high temperature steam electrolysis system for hydrogen production is presented, in which the main energy consumption processes such as steam electrolysis processes, heat transfer processes, and product compression processes are included. The detailed thermodynamic-electrochemical modeling of the solid oxide steam electrolysis (SOSE) is carried out, and consequently, the electrical and thermal energy required by every energy consumption process are determined. The efficiency of the system is derived, from which the effects of some of the important parameters such as the operating temperature, component thickness of the SOSE, leakage resistance, effectiveness of heat exchangers, and inlet rate of water on the performance of the system are discussed. It is found that the efficiency attains its maximum when a proper current density is chosen. The ratio of the required electric energy to the total energy input of the system is calculated, and consequently, the problem how to rationally operate the solar concentrating beam splitting device is investigated. The results obtained will be helpful for further understanding the optimal design and performance improvement of a practical solar-driven high temperature steam electrolysis system for hydrogen production. [Copyright &y& Elsevier]

Abstract: The performance of a new acid water electrolyzer system for hydrogen production is investigated, based on semi-empirical equations of a phosphoric acid water electrolyzer. The circulating electrolyte concentrations under differently operating temperatures are optimized so that the minimum input voltages of the electrolyzer are determined for other given conditions. The optimum electrochemical characteristics of the electrolyzer are revealed. Moreover, it is expounded that the Joule heat resulting from the irreversibilities inside the electrolyzer is larger than the thermal energy needed in the water splitting process. The general performance characteristics of the phosphoric acid water electrolyzer system are discussed, from which the lower bound of the operating current density is determined. The upper bound of the operating current density is further determined by introducing a multi-objective function including the system efficiency and hydrogen production rate. Consequently, some optimum design strategies of a phosphoric acid water electrolyzer system are obtained and may be chosen according to different practical requirements. [Copyright &y& Elsevier]

Abstract: An irreversible magnetic Brayton refrigeration-cycle model is established, in which the thermal resistance and irreversibility in the two adiabatic processes are taken into account. Based on the model, the performance characteristics of the magnetic Brayton refrigeration-cycle are investigated and the effects of the irreversibilities and the ratio of the magnetic fields in the two iso-field processes on the performance of the refrigeration cycle are revealed. On the basis of the thermodynamic properties of a paramagnetic material, by using the optimal control-theory, the mathematical expressions for the cooling load and the coefficient of performance are derived and some important performance parameters, e.g., the temperatures of the working substance at several important state-points, are optimized. By means of numerical predictions, the optimal performance characteristic curves of the magnetic Brayton refrigeration-cycle are obtained and analyzed. Furthermore, some optimal operating-regions including those for the cooling load, coefficient of performance and the temperatures of the cyclic working substance at the two important state-points are determined and evaluated. Finally, several special cases are discussed in detail. [Copyright &y& Elsevier]