Finite time thermodynamic analysis and optimization of water cooled multi-spilit heat pipe system(MSHPS)

This study focuses on the heat transfer characteristics of the evaporation terminal,the cool distribute unit(CDU)and refrigerant flow distribution of a water cooled multi-spilit heat pipe system(MSHPS)used in data center.The finite time thermodynamic analysis,the exergy method and the software SIMULINK was employed to build the simulation model of the combined system.The results show that the IT servers should concentrate on arranging at the location below 1.3 m.The CDU has a heat transfer of about 74 J in a period of 6 s.And the optimum flow rate of the CDU is 0.82 kg/s.The flow distribution characteristic of a CDU which connect 2 heat pipe evaporator terminals of 6 kW was calculated,and the working fluid is R22.Then the free cooling time,part time free cooling and energy saving potential in major cities of China were analysised.The energy saving potential is from 61%to 25%.The results are of great significance for the operational control and practical application of a MSHPS and other pipe-net systems.

Finite time thermodynamics analysis and research of pulsating heat pipe cold storage device

Phase change energy storage technology can effectively solve the energy mismatch in space and time.There are many disadvantages of phase change materials(PCMs),such as high supercooling,phase separation and poor heat transfer performance.As a new type of heat exchange structure,pulsating heat pipe has the advantages of simple structure,high heat transfer coefficient and good economic behavior.The system efficiency can be greatly improved by using pulsating heat pipe combined with cold storage technology.A set of pulsating heat pipe type cold storage device is developed,the finite time thermodynamic analysis is carried out,and the correlation between heat pipe efficiency and power is established.The three-dimensional physical model of pulsating heat pipe is simulated and verified by experiments.The experimental results show that in the cold storage stage,with the increase of the filling rate,the greater the pressure is,the better the heat transfer effect is;in the cold release stage,with the decrease of the filling rate,the smaller the pressure is,the better the heat transfer effect is.

Thermodynamic optimization for a quantum thermoacoustic refrigeration micro-cycle

A model of quantum thermoacoustic refrigeration micro-cycle(QTARMC)is established in which heat leakage is considered.A single particle contained in a one-dimensional harmonic potential well is studied,and the system consists of countless replicas.Each particle is confined in its own potential well,whose occupation probabilities can be expressed by the thermal equilibrium Gibbs distributions.Based on the Schrodinger equation,the expressions of coefficient of performance(COP)and cooling rate for the refrigerator are obtained.Effects of heat leakage on the optimal performance are discussed.The optimal performance region of the refrigeration cycle is obtained by the using ofΩobjective function.The results obtained can enrich the thermoacoustic theory and expand the application of quantum thermodynamics.

Analyses of an air conditioning system with entropy generation minimization and entransy theory

In this paper,based on the generalized heat transfer law,an air conditioning system is analyzed with the entropy generation minimization and the entransy theory.Taking the coefficient of performance（denoted as COP） and heat flow rate Qout which is released into the room as the optimization objectives,we discuss the applicabilities of the entropy generation minimization and entransy theory to the optimizations.Five numerical cases are presented.Combining the numerical results and theoretical analyses,we can conclude that the optimization applicabilities of the two theories are conditional.If Qout is the optimization objective,larger entransy increase rate always leads to larger Qout,while smaller entropy generation rate does not.If we take COP as the optimization objective,neither the entropy generation minimization nor the concept of entransy increase is always applicable.Furthermore,we find that the concept of entransy dissipation is not applicable for the discussed cases.

Optimization of combined endoreversible Carnot heat engines with different objectives

Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.

Optimization criteria of a Bose Brayton heat engine

An irreversible cycle model of the quantum Bose Brayton engine is established, in which finite-time processes and irreversibilities in two adiabatic processes are taken into account. Based on the model, expressions for the power output and the efficiency are derived. By using a numerical computation, the optimal relationship between the power output and the efficiency of an irreversible Bose Brayton engine is obtained. The optimal regions of the power output and the efficiency are determined. It is found that the influences of the irreversibility and the quantum degeneracy on the main performance parameters of the Bose Brayton engine are remarkable. The results obtained in the present paper can provide some new theoretical information for the optimal design and the performance improvement of a real Brayton engine.

Analyses of thermodynamic performance for the endoreversible Otto cycle with the concepts of entropy generation and entransy

In this paper, the endoreversible Otto cycle is analyzed with the entropy generation minimization and the entransy theory. The output power and the heat-work conversion efficiency are taken as the optimization objectives, and the relationships of the output power, the heat-work conversion efficiency, the entropy generation rate, the entropy generation numbers, the entransy loss rate, the entransy loss coefficient, the entransy dissipation rate and the entransy variation rate associated with work are discussed. The applicability of the entropy generation minimization and the entransy theory to the analyses is also analyzed. It is found that smaller entropy generation rate does not always lead to larger output power, while smaller entropy generation numbers do not always lead to larger heat-work conversion efficiency, either. In our calculations, both larger entransy loss rate and larger entransy variation rate associated with work correspond to larger output power, while larger entransy loss coefficient results in larger heat-work conversion efficiency. It is also found that the concept of entransy dissipation is not always suitable for the analyses because it was developed for heat transfer.

Performance analysis and multi-objective optimization based on a modified irreversible Stirling cycle

The efficiency of the actual Stirling engine is much lower than the ideal Carnot cycle efficiency.To obtain more precise efficiency for Stirling engines,this paper proposes a modified Stirling cycle with a more accurate heat transfer process in Stirling engines based on a thermodynamic function called available potential.The finite-time thermodynamic method is used to analyze the model performance under constant heat source temperature,finite temperature difference heat transfer,and incomplete regenerative processes.A new polytropic process is introduced to model the heat transfer between the working fluid and external heat sources in which only heat above ambient temperature is converted into technical work.The regenerator is divided into numerous smaller heat reservoirs with individual temperature to analyze the incomplete regenerative processes.The expressions of the output power and thermal efficiency are obtained based on the modified irreversible Stirling cycle,and the effects of irreversible losses are analyzed to evaluate the performance of the proposed model.Results indicate that the efficiency of the modified cycle is much lower than that of the ideal Stirling cycle with an isothermal process.With the increase of the average heat transfer temperature difference,there exists an optimum value for the power of the irreversible cycle.The optimum power of the model was obtained for varying thermodynamic parameters by optimizing the average heat transfer temperature difference between the hot and cold sides.To optimize the irreversible model,the multi-objective optimization analysis is carried out based on NSGA-Ⅱ,which results in an optimized output power of 40.87 kW and an optimized thermal efficiency of 44%.

Progress in optimization of mass transfer processes based on mass entransy dissipation extremum principle

The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipalion extremum principle are reviewed. Secondly, the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for opti- mizing the mass transfer processes of one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, and iso- thermal throttling and isothermal crystallization are summarized. Thirdly, the combination of the mass entransy dissipation ex- tremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized. The scientific features of the mass entransy dissipation extremam principle are emphasized.

Performance optimization of a class of combined thermoelectric heating devices

A detailed model of thermally-driven combined thermoelectric(TE) heating device is established. The device consists of twostage TE heat pump(TTEH) and two-stage TE generator(TTEG) with four external heat exchangers(HEXs). Both internal losses and external heat transfer irreversibilities are considered in the model. The heating capacity and the coefficient of performance(COP) of the device are improved through numerical optimization,which is of great significance to the application of the device. The distribution of the total TE element number among four TE devices and the distribution of the total external heat conductance among the four external HEXs are optimized. The results show that both the reservoir temperatures of TTEG and TTEH have significant influences on the performance and the corresponding optimum parameters of the device. The COP can reach 0.14 after optimization when the temperature difference of heat source is 150 K and the temperature difference of heating is 10 K.

Entransy dissipation minimization for generalized heat exchange processes

This paper investigates the MED （Minimum Entransy Dissipation） optimization of heat transfer processes with the generalized heat transfer law q ∝ （A（T^n））m. For the fixed amount of heat transfer, the optimal temperature paths for the MED are obtained The results show that the strategy of the MED with generalized convective law q ∝ （△T）^m is that the temperature difference keeps constant, which is in accordance with the famous temperature-difference-field uniformity principle, while the strategy of the MED with linear phenomenological law q ∝ A（T^-1） is that the temperature ratio keeps constant. For special cases with Dulong-Petit law q ∝ （△T）^1.25 and an imaginary complex law q ∝ （△（T^4））^1.25, numerical examples are provided and further compared with the strategies of the MEG （Minimum Entropy Generation）, CHF （Constant Heat Flux） and CRT （Constant Reservoir Temperature） operations. Besides, influences of the change of the heat transfer amount on the optimization results with various heat resistance models are discussed in detail.

Power output analyses and optimizations of the Stirling cycle

Based on the finite time thermodynamics theory,the entransy theory and the entropy theory,the Stirling cycles under different conditions are analyzed and optimized with the maximum output power as the target in this paper.The applicability of entransy loss(EL),entransy dissipation(ED),entropy generation(EG),entropy generation number(EGN) and modified entropy generation number(MEGN) to the system optimization is investigated.The results show that the maximum EL rate corresponds to the maximum power output of the cycle working under the infinite heat reservoirs whose temperatures are prescribed,while the minimum EG rate and the extremum ED rate do not.For the Stirling cycle working under the finite heat reservoirs provided by the hot and cold streams whose inlet temperatures and the heat capacity flow rates are prescribed,the maximum EL rate,the minimum EG rate,the minimum EGN and the minimum MEGN all correspond to the maximum power output,but the extremum ED rate does not.When the heat capacity flow rate of the hot stream increases,the power output,the EL rate,the EG rate and the ED rate increase monotonously,while the EGN and the MEGN decrease first and then increase.The EL has best consistency in the power output optimizations of the Stirling cycles discussed in this paper.

Entransy dissipation minimization for a class of one-way isothermal mass transfer processes

A class of one-way isothermal mass transfer processes with Fick’s diffusive mass transfer law[g ∝Δ(c)]is investigated in this paper.Based on the definition of the mass entransy,the entransy dissipation function which reflects the irreversibility of mass transfer ability loss is derived.The optimal concentration allocations of the key components corresponding to the highand low-concentration sides for the minimum entransy dissipation of the mass transfer process are obtained by applying opti- mal control theory and compared with the strategies of the minimum entropy generation,constant mass transfer flux(constant concentration difference),and constant concentration ratio(constant chemical potential difference).The results are as follows. For the optimal mass transfer strategy of the minimum entransy dissipation,the product of the square of the key component concentration difference between the high-and the low-concentration sides and the inert component concentration at the low-concentration side is a constant,while for that of the minimum entropy generation,the ratio of the square of the key com-ponent concentration difference between the high-and the low-concentration sides to the key component concentration at the low-concentration side is a constant;when the mass transfer process is not involved in energy conversion process,the optimi-zation principle should be the minimum entransy dissipation;the mass transfer strategy of constant concentration difference is superior to that of constant concentration ratio.The results obtained in this paper can provide some theoretical guidelines for optimal designs and operations of practical mass transfer processes.

Performance optimization of thermionic refrigerators based on van der Waals heterostructures

In this paper, an irreversible thermionic refrigerator model based on van der Waals heterostructure with various irreversibilities is established by utilizing combination of non-equilibrium thermodynamics and finite time thermodynamics. The basic performance characteristics of the refrigerator are obtained. The effects of key factors, such as bias voltages, Schottky barrier heights and heat leakages, on the performance are studied. Results show that cooling rates and coefficients of performances(COPs) can attain the double maximum with proper modulation of barrier heights and bias voltages. Increasing cross-plane thermal resistance as well as decreasing electrode-reservoir thermal resistance and reservoir-reservoir thermal resistance can enhance the performance of the device. The optimal performance region is the interval between the maximum cooling rate point and the maximum COP point. By modulating the bias voltage, the working state of the device can fall into the optimal performance region. The optimal performance of the refrigerator when using single layer graphene and a few layers graphene as electrode material is also compared.

Modeling and performance analysis of energy selective electron (ESE) engine with heat leakage and transmission probability

A model of an energy selective electron (ESE) engine with linear heat leakage and Lorentzian transmission probability is established in this paper.The expressions for the main performance parameters of the ESE engine operating as a heat engine or a refrigerator are derived by using the theory of finite time thermodynamics.The optimum performances of the ESE engine are explored and the influences of the heat leakage,the central energy level of the resonance,and the width of the resonance on the performance of the ESE engine are analyzed by using detailed numerical examples.The optimal operation regions of power output and efficiency (or cooling load and coefficient of performance (COP)) are also discussed.Moreover,the performances of the ESE engine with Lorentzian transmission probability are compared with those with rectangular transmission probability.It is shown that the power output versus efficiency (or cooling load versus COP) characteristic curves with and without heat leakage are all closed loop-shaped ones.The efficiency (or COP) of the ESE engine decreases as the heat leakage increases.It is found that as the resonance width increases,the power output and efficiency (or cooling load and COP) increase to a maximum and then decrease due to the finite range of energies which contribute positively to the power generation or refrigeration in the electron system.Especially,when heat leakage is taken into account,the characteristic curves of maximum efficiency (or maximum COP) versus half resonance width are parabolic-like ones,which are quite different from the monotonic decreasing characteristic curves obtained in previous analyses without considering heat leakage.The results obtained in this paper can provide some theoretical guidelines for the design and operation of practical electron energy conversion devices such as solid-state thermionic refrigerators.

Influences of external heat transfer and Thomson effect on the performance of TEG-TEC combined thermoelectric device

A thermodynamic model of a thermoelectric generator(TEG)-driven thermoelectric cooler(TEC) device considering Thomson effect and external heat transfer(HT) is established based on the combination of non-equilibrium and finite time thermodynamic theories. The expressions of cooling capacity and coefficient of performance(COP) are obtained. Performances are compared with and without considering Thomson effect using numerical optimization method. The influences of Thomson effect on the optimal performances, optimum allocations of thermoelectric(TE) element number and HT surface area are discussed. The results indicate that Thomson effect decreases the maximum cooling capacity and COP. More TE elements should be allocated to TEG, and more HT area should be allocated to the heat exchanger(HEX) of TEG, the hot-side HEX of TEG and the cold-side HEX of TEC in the design of the device considering Thomson effect. The results obtained can be used to help design TEG-TEC devices.

Entransy dissipation/loss-based optimization of two-stage organic Rankine cycle(TSORC)with R245fa for geothermal power generation

Based on organic Rankine cycle(ORC), the two-stage evaporation strategy is adopted to replace the single-stage evaporation to improve the system performance. In order to evaluate the temperature matching of the two-stage evaporation, a theoretical optimization model was established to optimize the two stage organic Rankine cycle(TSORC) based on the entransy theory and thermodynamics, with the ratio of the entransy dissipation rate of the TSORC to that of the ORC as the objective function. This paper aims to illuminate the improving degree of the system performance of the TSORC. The results show that the TSORC enhances the average evaporating temperature, thereby reducing the entransy dissipation rate in the evaporator and the total entransy dissipation rate. The maximal net power output is proportional to the entransy loss rate and inversely proportional to the entransy dissipation rate. However, compared with the ORC, the TSORC can output more power but requires a higher total thermal conductance. Moreover, there exists an optimal intermediate geothermal water temperature(IGWT) to maximize the net power output of the TSORC. The TSORC can be considered in engineering applications.

Multi-objective optimization for membrane reactor for steam methane reforming heated by molten salt

A membrane reactor for steam methane reforming heated by molten salt(MS-SMRMR)is studied based on finite time thermodynamics for decreasing carbon emissions and improving hydrogen production rate(HPR).Effects of flow directions of sweep gas and molten salt on MS-SMRMR are researched.Profiles of temperatures,HPR,and local entropy generation rates(EGRs)of MS-SMRMR are analyzed.Hybrid particle swarm optimization algorithm is utilized to obtain the minimum of specific EGR(SEGR),ratio of EGR to HPR.Multi-objective optimization about HPR maximization and EGR minimization is performed by utilizing NSGA-II.The EGR caused by the mass transfer process is the largest among all irreversible processes in the MS-SMRMR.The membrane length should be slightly shorter than the reactor length when the flow direction of sweep gas is different from that of reaction mixture.When flow directions of molten salt and sweep gas are opposite to that of reaction mixture,SEGR is the smallest.Compared with SEGR calculated by utilizing initial parameters,SEGRs after primary,twice and triple optimizations reduce by 1.2%,5.5%and 5.7%,respectively.SEGR can be further decreased by adjusting other operating parameters.Pareto front provides many optimization results,and it contains SEGR minimization.In Pareto front,an optimum decision point is obtained based on decision-making of TOPSIS,and its EGR and HPR,respectively,increase by 7.12%and13.24%,compared with those obtained by using initial parameters.The results have certain theoretical guiding significance for optimization designs of MS-SMRMR.

Power-optimization of multistage non-isothermal chemical engine system via Onsager equations,Hamilton-Jacobi-Bellman theory and dynamic programming

The research on the output rate performance limit of the multi-stage energy conversion system based on modern optimal control theory is one of the hot spots of finite time thermodynamics.The existing research mainly focuses on the multi-stage heat engine system with pure heat transfer and the multi-stage isothermal chemical engine(ICE)system with pure mass transfer,while the multi-stage non ICE system with heat and mass transfer coupling is less involved.A multistage endoreversible non-isothermal chemical engine(ENICE)system with a finite high-chemical-potential(HCP)source(driving fluid)and an infinite low-chemical-potential sink(environment)is researched.The multistage continuous system is treated as infinitesimal ENICEs located continuously.Each infinitesimal ENICE is assumed to be a single-stage ENICE with stationary reservoirs.Extending single-stage results,the maximum power output(MPO)of the multistage system is obtained.Heat and mass transfer processes between the reservoir and working fluid are assumed to obey Onsager equations.For the fixed initial time,fixed initial fluid temperature,and fixed initial concentration of key component(CKC)in the HCP source,continuous and discrete models of the multistage system are optimized.With given initial reservoir temperature,initial CKC,and total process time,the MPO of the multistage ENICE system is optimized with fixed and free final temperature and final concentration.If the final concentration and final temperature are free,there are optimal final temperature and optimal final concentration for the multistage ENICE system to achieve MPO;meanwhile,there are low limit values for final fluid temperature and final concentration.Special cases for multistage endoreversible Carnot heat engines and ICE systems are further obtained.For the model in this paper,the minimum entropy generation objective is not equivalent to MPO objective.

Power output and efficiency optimization of endoreversible non-isothermal chemical engine via Lewis analogy

Compared with endoreversible heat engine with pure heat transfer and endoreversible isothermal chemical engine with pure mass transfer,endoreversible non-isothermal chemical engine(ENICE)is a more reasonable model of practical mass exchanger,solid device and chemo-electric systems.There exists heat and mass transfer(HMT)simultaneously between working fluid and chemical potential reservoir in ENICE.There is coupled HMT effect that in ENICE should be considered.There are two ways to consider this coupled effect.One is based on Onsager equations,and another is based on Lewis analogy.For the mathematical and physical description of the above HMT process,the model using Onsager equations are more appropriate in the linear HMT region not far from the equilibrium state,while that based on Lewis analogy is more appropriate in nonlinear HMT region far from the equilibrium state.Different from the previous research on the power optimization of ENICEs with Onsager equations,this paper optimizes power and efficiency of ENICE based on Lewis analogy.HMT processes are assumed to obey Newtonian heat transfer law(q∝ΔT,and T is temperature)and Fick's diffusive mass transfer law(g∝Δc,and c is concentration),respectively.Analytical results of power output and corresponding vector efficiency(η_(T)andη_(μ))of ENICE are obtained,which provide important parallel results with those based on Onsager equations.They include special cases for endoreversible Carnot heat engine with q∝ΔT and endoreversible isothermal chemical engine with g∝Δc.Adopting Lewis analogy in the modelling of ENICEs with simultaneous HMT is an important work.It provides important analytical and numerical results different from those with Onsager equations obtained previously and enriches the research contents of FTT.The research results in this paper have a certain guiding significance for the optimal designs of single irreversible NICEs,multistage NICE systems,practical mass exchangers,solid devices,chemo-electric systems,and so on.