Constructal design of a rectangular porous fin considering minimization of maximum temperature difference and pumping power consumption

A heat dissipation model of a rectangular porous fin is established based on constructal theory. First, the constructal design of rectangular porous fin is conducted by selecting a complex function minimization, which composed of linear weighting sum of maximum temperature difference and pumping power consumption, as optimization objective. Effects of gap height, air inlet velocity, total porous fin volume and porosity on the optimal constructs are investigated, respectively. The findings show that the complex function can attain its double minimum at a value of 0.802 when the fin length and number are optimized, and the corresponding optimal fin length and number are 8.01 mm and 10, respectively. In comparison to original design, the complex function and maximum temperature difference after twice optimization are decreased by 19.80% and 66.31%, respectively.Second, the comprehensive performance of porous fin is improved by simultaneously optimizing the fin length and number. The artificial neural network is applied to predict the fin performances, which is used to conduct multi-objective optimization based on NSGA-II algorithm. Optimal structure of porous fin for multiple requirements is gained by LINMAP and TOPSIS decisionmaking strategies. The findings in this study can serve as theoretical guides for fin thermal designs of electronic devices.

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.

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 and efficiency optimizations of Maisotsenko-Atkinson,Dual and Miller cycles and performance comparisons with corresponding traditional cycles

Maisotsenko cycle(M-cycle)has been combined with some cooling and power cycles,and behaves important thermodynamic advantage.Finite-time thermodynamics(FTT)is applied to establish three endoreversible models of M-Atkinson,M-Dual and M-Miller cycles.They are performed based on models of endoreversible Atkinson,Dual and Miller cycles by combing FTT model with M-cycle concept.Power output(POW)and thermal efficiency(TEF)of those M-cycles are studied and optimized by numerical calculations.The maximum power output(MPO)and the corresponding pressure ratio and TEF,the maximum TEF and the corresponding pressure ratio and POW,as well as optimal ranges of pressure ratio are obtained.Effects of mass flow rate of circulating water injection,initial cycle temperature and maximum cycle temperature on cycle POW,TEF and optimal pressure ratio range are analyzed.The optimal performances of the three M-cycles are compared with those of traditional Atkinson,Dual and Miller cycles under the same conditions.The results show that for the three M-cycles,end temperature of adiabatic expansion process of M-cycle is less than that of the corresponding traditional cycle,POW and TEF at arbitrary pressure ratio of M-cycle are much higher than those of the corresponding traditional cycle,and performance characteristics of M-cycles are superior to those of the corresponding traditional cycles.

Photothermal hygroscopic hydrogel for simultaneous generation of clean water and electricity

Harvesting water from the air using adsorbents and obtaining fresh water by solar-driven desorption is considered as one of the most effective ways to solve the freshwater crisis in arid and desert regions.Based on a simple and low-cost photothermal hygroscopic hydrogel,a new strategy is proposed to boost solar energy efficiency by coupling solar-driven atmospheric water harvesting technology with thermoelectric power generation technology in this paper.Photothermal hygroscopic hydrogel ink PAM-CaCl_(2)is prepared by in situ polymerization using Acrylamide as monomer,Ammonium persulfate as thermal initiator and CaCl_(2)as hygroscopic component.During the day,the photothermal hygroscopic hydrogel absorbs solar energy and evaporates its own internal water to obtain fresh water.Simultaneously,the residual waste heat is utilized to power the thermoelectric panel,which produces electricity based on Seebeck effect.At night,the hydrogel harvests water molecules in the air to achieve regeneration.This hybrid system can achieve a water production rate of 0.33 kg m^(-2)h^(-1)and an additional electrical energy gain of 124 mW m^(-2)at 1 kW m^(-2)solar intensity.Theoretical model of the hybrid system is developed to understand the heat flow and thermoelectric generation process.The results provide new insights into energy and freshwater replenishment options in arid or desert areas with abundant solar energy.

Thermodynamic performance of Dual-Miller cycle(DMC) with polytropic processes based on power output, thermal efficiency and ecological function

This study reports a new model of an air standard Dual-Miller cycle(DMC) with two polytropic processes and heat transfer loss.The two reversible adiabatic processes which could not be realized in practice are replaced with two polytropic processes in order to more accurately reflect the practical working performance. The heat transfer loss is taken into account. The expressions of power output, thermal efficiency, entropy generation rate(EGR) and ecological function are addressed using finite-time thermodynamic theory. Through numerical calculations, the influences of compression ratio, cut-off ratio and polytropic exponent on the performance are thermodynamically analyzed. The model can be simplified to other cycle models under specific conditions, which means the results have an certain universality and may be helpful in the design of practical heat engines. It is shown that the entropy generation minimization does not always lead to the best system performance.

Thermal performance analysis of non-uniform height rectangular fin based on constructal theory and entransy theory

A model of non-uniform height rectangular fin, in which the variation of base's thickness and width are taken into account, is established in this paper. The dimensionless maximum thermal resistance(DMTR) and the dimensionless equivalent thermal resistance(DETR) defined based on the entransy dissipation rate(EDR) are taken as performance evaluation indexes. According to constructal theory, the variations of the two indexes with the geometric parameters of the fin are analyzed by using a finite-volume computational fluid dynamics code, the effects of the fin-material fraction on the two indexes are analyzed. It is found that the two indexes decrease monotonically as the ratio between the front height and the back height of the fin increases subjected to the non-uniform height rectangular fin. When the model is reduced to the uniform height fin, the two indexes increase first and then decrease with increase in the ratio between the height of the fin and the fin space. The fin-material fraction has no effect on the change rule of the two indexes with the ratio between the height of the fin and the fin space. The sensitivity of the DETR to the geometric parameters of the fin is higher than that of the DMTR to the geometric parameters. The results obtained herein can provide some theoretical support for the thermal design of rectangular fins.

Power and efficiency optimizations for an open cycle two-shaft gas turbine power plant

In finite-time thermodynamic analyses for various gas turbine cycles,there are two common models:one is closed-cycle model with thermal conductance optimization of heat exchangers,and another is open-cycle model with optimization of pressure drop(PD)distributions.Both of optimization also with searching optimal compressor pressure ratio(PR).This paper focuses on an open-cycle model.A two-shaft open-cycle gas turbine power plant(OCGTPP)is modeled in this paper.Expressions of power output(PP)and thermal conversion efficiency(TCE)are deduced,and these performances are optimized by varying the relative PD and compressor PR.The results show that there exist the optimal values(0.32 and 14.0)of PD and PR which lead to double maximum dimensionless PP(1.75).There also exists an optimal value(0.38)of area allocation ratio which leads to maximum TCE(0.37).Moreover,the performances of three types of gas turbine cycles,such as one-shaft and two-shaft ones,are compared.When the relative pressure drop at the compressor inlet is small,the TCE of third cycle is the biggest one;when this pressure drop is large,the PP of second cycle is the biggest one.The results herein can be applied to guide the preliminary designs of OCGTPPs.

Optimization of the power, efficiency and ecological function for an air-standard irreversible Dual-Miller cycle

This paper establishes an irreversible DualMiller cycle (DMC) model with the heat transfer (HT) loss, friction loss (FL) and other internal irreversible losses. To analyze the effects of the cut-off ratio (ρ) and Miller cycle ratio (rM) on the power output (P), thermal efficiency (η) and ecological function (E), obtain the optimal popt and optimal rMopt, and compare the performance characteristics of DMC with its simplified cycles and with different optimization objective functions, the P,η and E of irreversible DMC are analyzed and optimized by applying the finite time thermodynamic (FTT) theory. Expressions of P,η and E are derived. The relationships among P,η, E and compression ratio (ε) are obtained by numerical examples. The effects of ρ and rM on P,η, E, maximum power output (MP), maximum efficiency (MEF) and maximum ecological function (ME) are analyzed. Performance differences among the DMC, the Otto cycle (OC), the Dual cycle (DDC), and the Otto-Miller cycle (OMC) are compared for fixed design parameters. Performance characteristics of irreversible DMC with the choice of P,η and E as optimization objective functions are analyzed and compared. The results show that the irreversible DMC engine can reach a twice-maximum power, a twicemaximum efficiency, and a twice-maximum ecological fiinction, respectively. Moreover, when choosing E as the optimization objective, there is a 5.2% of improvement in η while there is a drop of only 2.7% in P compared to choosing P as the optimization objective. However, there is a 5.6% of improvement in P while there is a drop of only 1.3% in rj compared to choosing as the optimization objective.

Energy and exergy analyses and optimizations for two-stage TEC driven by two-stage TEG with Thomson effect

Based on the non-equilibrium thermodynamics and energy and exergy analyses,a thermodynamic model of two-stage thermoelectric(TE)cooler(TTEC)driven by two-stage TE generator(TTEG)(TTEG-TTEC)combined TE device is established with involving Thomson effect by fitting method of variable physical parameters of TE materials.Taking total number of TE elements as constraint,influences of number distributions of TE elements on three device performance indictors,that is,cooling load,maximum COP and maximum exergetic efficiency,are analyzed.Three number distributions of TE elements are optimized with three maximum performance indictors as the objectives,respectively.Influences of hot-junction temperature of TTEG and coldjunction temperature of TTEC on optimization results are analyzed,and difference between optimization results corresponding to three performance indicators are studied.Optimal performance intervals and optimal variable intervals are provided.Influences of Thomson effect on three general performance indicators,three optimal performance indicators and optimal variables are comparatively discussed.Thomson effect reduces three general performance indicators and three optimal performance indicators of device.When hot-and cold-junction temperatures of TTEG and TTEC are 450,305,325 and 295 K,respectively,Thomson effect reduced maximum cooling load,maximum COP and maximum exergetic efficiency from 9.528 W,9.043×10^(-2)and2.552%to 6.651 W,6.286×10^(-2)and 1.752%,respectively.

Constructal design of printed circuit recuperator for S-CO_(2)cycle via multi-objective optimization algorithm

Based on a constructal theory,the structure design of a printed circuit recuperator with a semicircular heat transfer channel for supercritical CO_(2)cycle is carried out.First,a complex function composed of weighted sum of the reciprocal of total heat transfer rate and total pumping power consumption is regarded as an optimization objective,and total volumes of the recuperator and heat transfer channel are regarded as constraints.The optimal heat transfer channel radius and minimum complex function of the recuperator are obtained.It turns out that heat transfer rate,pumping power consumption,and complex function under the optimal construct of recuperator are reduced by 15.10%,82.44%,and 32.33%,respectively.There exists the optimal single plate channel number which results in the double minimum complex function.Second,for the purpose of minimizing the reciprocal of heat transfer rate and pumping power consumption,NSGA-II algorithm is used to achieve multi-objective optimization,and the minimum deviation index derived by the decision-making methods is 0.076,which can be taken as multi-objective optimal design scheme for printed circuit recuperator with semicircular heat transfer channels.The findings presented here can serve as theoretical recommendations for the structure design of printed circuit recuperator.

Constructal design of a rectangular parallel phase change microchannel in a three-dimensional electronic device

Based on constructal theory,a rectangular parallel phase change microchannel model in a three-dimensional electronic device(TDED)is established with R134a as the cooling fluid.Based on the minimization of a complex function(CF)composed of linear weighting sum of maximum temperature difference and pumping power consumption,constructal design of the TDED is conducted first;and then,maximum temperature difference and pumping power consumption are minimized by non-dominated sorting genetic algorithm-II methods.The results reveal that there exist an optimal mass flow rate(0.0012 kg/s)and a quadratic optimal aspect ratio(AR)(0.39)of the microchannel which lead to quadratic minimum CF(0.817).Compared with the original value,the CF after optimization is reduced by 18.34%.Reducing the inlet temperature of cooling fluid and microchannel number appropriately can help to enhance the overall performance of TDED.By using the artificial neural network and genetic algorithms in the toolboxes of Matlab software,the optimal AR gained in the Pareto solution set is located between 0.2–0.45.The smallest deviation index among three discussed strategies is 0.346,and the corresponding optimal AR is 0.413,which is selected as the optimal design strategy of the microchannel in the TDED under multiple requirements.The findings in this study can serve as theoretical guides for thermal designs of electronic devices.

Thermodynamic analyses and optimization for thermoelectric devices:The state of the arts

Thermoelectric effect is the most efficient way to convert electric energy directly from the temperature gradient. Thermoelectric effect-based power generation, cooling and heating devices are solid-stated, environmentally friendly, reliable, long-lived, easily maintainable, and easy to achieve miniaturization and integration. So they have unparalleled advantages in the aerospace, vehicle industry, waste heat recovery, electronic cooling, etc. This paper reviews the progress in thermodynamic analyses and optimizations for single- and multiple-element, single- and multiple-stage, and combined thermoelectric generators, thermoelectric refrigerators and thermoelectric heat pumps, especially in the aspects of non-equilibrium thermodynamics and finite time thermodynamics. It also discusses the developing trends of thermoelectric devices, such as the heat sources of thermoelectric generators, multi-stage thermoelectric devices, combined thermoelectric devices, and heat transfer enhancement of thermoelectric devices.

Constructal entransy optimizations for insulation layer of steel rolling reheating furnace wall with convective and radiative boundary conditions

Based on the entransy dissipation extremum principle for thermal insulation process,the constructal optimizations for a plane insulation layer of the steel rolling reheating furnace wall with convective and radiative boundary conditions are carried out by taking the minimization of entransy dissipation rate as optimization objective.The optimal construct of the plane insulation layer is obtained.The results show that for the convective heat transfer boundary condition,the optimal constructs of the insulation layer obtained based on the minimizations of the entransy dissipation rate and heat loss rate are obviously different.Comparing the optimal construct obtained based on the minimization of the entransy dissipation rate with that based on the minimization of the heat loss rate,the entransy dissipation rate is reduced by 5.98%,which makes the global thermal insulation performance of the insulation layer improve.For the combined convective and radiative heat transfer boundary condition,compared the insulation layer having an increasing thickness with that having constant thickness and a decreasing thickness,the entransy dissipation rates are reduced by 16.59%and39.72%,respectively,and the global thermal insulation performance of the insulation layer is greatly improved.There exits an optimal constant coefficient a2;optwhich leads to the minimum dimensionless entransy dissipation rate of the insulation layer.The difference between the optimal constant coefficients a2;optobtained based on the minimizations of the entransy dissipation rate and the maximum temperature gradient of the insulation layer is small.This makes the corresponding thermal stress obtained based on the minimum dimensionless entransy dissipation rate also be small,and the global thermal insulation performance and thermal safety of the insulation layer are improved simultaneously.The results obtained can provide some guidelines for the optimal designs of the insulation layers.

Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory

Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory. Three types of 3-D circular disc heat sink models, i.e. without collection microchannels, with center collection microchannels, and with edge collection microchannels, are established respectively. Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels, that of circular disc heat sink with center collection microchannels is the minimum, so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages. Furthermore, the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes. With the mass flow rate increasing, both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease. With the heat flux increasing, the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged. With the same mass flow rate and heat flux, the larger the microchannel branch number, the smaller the maximum thermal resistance. While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.

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.

A multi-objective study on the constructal design of non-uniform heat generating disc cooled by radial-and dendritic-pattern cooling channels

A three-dimensional disc model with non-uniform heat generating is built.A series of cooling channels are inserted to cool this disc which is strewn in a hierarchical pattern.To reveal thermal and flow characteristics,a composite objective function comprised of the maximum temperature difference(MTD)and pumping power is constructed.The deployment pattern of cooling channels contains two cases,i.e.,the radial-pattern and dendritic-pattern.By capitalizing on constructal design method together with finite element method,the diameter of radial-pattern cooling channels is optimized in the first place.Next,the diameter,angle coefficient and length coefficient of dendritic-pattern cooling channels are three degrees-of-freedom to be stepwise optimized at different heat generating conditions.Furthermore,NSGA-II algorithm is introduced into the multiobjective problem.Upon obtaining its Pareto optimal solution set,Topsis method is invoked to yield the optimal solutions under given weighted coefficients.The heat generation over the entire body and the volume ratio of cooling channels operate as the primary constraints.Based on these premises,constructal design will be stepwise performed by varying three degrees-offreedom.The obtained results state that more heating components or devices should be installed as close to the cooling water inlet as possible.This can further reduce MTD at the same cost of pumping power,thereby improve thermal and flow performance and prolong the lifespan of devices.As optimized with two degrees-of-freedom,the MTD is reduced by 18.6%compared with the counterpart obtained from single degree-of-freedom optimization,while the pumping power is increased by 59.8%.As optimized with three degrees-of-freedom,the MTD is decreased by 6.2%compared with the counterpart from two degrees-of-freedom optimization,while the pumping power is increased by 3.0%.It is manifest that when two sub-objectives form a composite objective,the performance improvement of one sub-objective will inevitably elicit the vitiation of the alternative.

Thermodynamic Analysis and Optimization of an Irreversible Maisotsenko-Diesel Cycle

So far,Maisotsenko cycle has been applied to many fields such as heating ventilation and air-conditioning,power industry,chemical production,and so on.A lot of researches about classical thermodynamic analyses of Maisotsenko cycle have been made.A new cycle model of combined Diesel and Maisotsenko cycles considering heat transfer loss(HTL),piston friction loss(PFL)and internal irreversible loss(IIL)was proposed in this paper.By using the finite time thermodynamic(FTT)theory,the power and efficiency performances of the Maisotsenko-Diesel cycle(MDC)were studied.Effects of mass flow rate(MFR)of water injection in the Maisotsenko air saturator(MAS)and the other parameters related to the design of Diesel engine on the optimal cycle performances were analyzed.Furthermore,it was testified that irreversible MDC was superior than conventional irreversible Diesel cycle in both power output and thermal efficiency.The results can expand the application of Maisotsenko cycle(M-cycle)and provide some theoretical guidelines for the practical devices.

量子热声制冷微循环的热力学优化

本文建立了一个考虑热漏影响的量子热声制冷微循环模型。研究主要围绕一维谐振势阱中的单个粒子展开,而系统是由无数个这样的粒子组成的。每个粒子都被限制在一定的势阱中,其出现几率可用热平衡吉布斯分布来描述。本文基于薛定谔方程推出了制冷机性能系数和制冷速率的表达式;讨论了热泄漏对循环优化性能的影响;利用Ω目标函数得出了制冷循环的最优性能区域。所得结果不仅丰富了热声理论,而且拓展了量子热力学的应用。

Thermodynamic Analysis and Experimental Research of Water-Cooled Small Space Thermoelectric Air-Conditioner

This paper aims to find a more general analysis method for the refrigeration performance,and to design a high efficiency modular cooling structure of water-cooled plate.A new analysis method,namely current and refrigeration rate density analysis,is proposed.The general refrigeration performance calculation equations are obtained.A finite-time thermodynamic model of the thermoelectric device is established considering Thomson effect.The basic structure of water-cooled thermoelectric air-conditioner is designed and the specific calculation method is given.The influences of input current density,filling factor and heat transfer conditions on refrigeration performance of the thermoelectric air-conditioner are analyzed,which is compared with refrigeration performance of air-cooled thermoelectric air-conditioner.The results show that the maximum refrigeration rate density of the water-cooled thermoelectric air-conditioner is 8.65 k W/m^(2),and the maximum coefficient of performance(COP)is 2.27 in the case of the cooling temperature differenceΔT=5 K.Compared withΔT=5 K,the maximum refrigeration rate density and the maximum COP ofΔT=15 K decreases by 27.98%and 76.65%,respectively.At the filling factorθ=0.43,the refrigeration rate density and COP are 2.57 k W/m~2 and 1.24,respectively.The experimental device of thermoelectric air-conditioner is established to verify the model.The experimental results show that the maximum value of input current and COP is 4 A and 0.95 with the efficient water-cooling method,respectively.The experimental data coincides with the theoretical calculation,which shows the validity of the analysis method and cooling method.