A Y-shaped porous-rib (PR) model under forced convection is proposed, and its structure is evolved in the investigation framework of constructal design. Firstly, a composite-function (FTW), defined as the linear-weighting-sum of two competing objectives - dimensionless maximum-temperature-difference (ΔT˜) and dimensionless pump-power-consumption (W˜P), is minimized. Secondly, the artificial-neural-network and NSGA-II are further employed to implement bi-objective-optimization (BOO) with three decision-making-methods. For FTW minimization, it indicates that FTW reaches double minimum (FTW,mm=0.777) when the rib length (L) and number (N) are 7.20 mm and 4. The result leads to 22.3% reduction in FTW and corresponding 51.1% decrease in ΔT˜ relative to the initial values. Optimizing both L and N simultaneously helps to improve the overall performance. For BOO, the LINMAP and TOPSIS decision-making-methods yield the deviation index of 0.105, which is the smallest. In this case, ΔT˜ and W˜P are 0.483 and 1.056, and ΔT˜ decreases by 51.7% via constructal design. The optimal construct with Lopt=7.22mm and Nopt=4 emerges as the optimal choice for the design plan of Y-shaped PRs. The innovation of present study lies in extending constructal design to a Y-shaped PR model under forced convection and performing its optimization. This study provides theoretical supports for the thermal-dissipation designs of electronic-devices with PRs.

A model of composite heatsink with microchannel and inner cylindrical porous-fin is built herein. Constructal design for the composite heatsink is conducted, firstly, by selecting a composite-function (FTW) as design objective, which is composed of linear-weighting-sum of the maximum-temperature-difference and pump-powerconsumption. The height-width ratio of microchannel and height-width ratio of element are optimized with the volume constraints of element, microchannel and inner cylindrical porous-fins. The influences of fin radius, number of fins, porosity of porous material, heat flux, inlet water temperature and inlet water mass-flow-rate on optimum construct are analyzed, respectively. The findings show that FTW reaches its double minimum at 0.857. The corresponding optimal height-width ratios are alpha opt=5.0 and beta opt=14.8, respectively. The composite function achieves a 14.26 % reduction after twice optimization compared to the initial design. Therefore, optimizing the height-width ratios is helpful to improve the comprehensive performance. Interpolation method is adopted to predict composite heatsink performance, and multi-objective optimization is then carried out using NSGA-II method. alpha opt intensively distributes across the interval of 3-9, and beta opt intensively distributes across the interval of 9-20. Optimization results are compared using different decision-making approaches, and the optimal construct of composite heatsink is provided by TOPSIS approach with alpha opt= 4.53 and beta opt = 11.05. The innovation contributions herein are setting up a model of composite heatsink with microchannel and inner cylindrical porous-fin, and conducting multi-objective constructal design for it.

A stacked-chip with dual-layer radial-pattern high-thermal-conductivity channel (DLRPHTCC) is proposed, and its constructal design is performed. Dimensionless entropy-generation-rate (EGR) (Sg) and dimensionless maximum-temperature-difference (MTD) (Delta T) are minimized, respectively. Optimum ratios (gamma 0s) of length of channel to radius of stacked-chip are obtained with fixed total-volumes of DLRPHTCC and whole model, as well as with uniform and non-uniform heat generations. Effects of coefficient (G) of non-uniform heat-generation, number of channels, volume ratio of DLRPHTCC and thermal-conductivity of DLRPHTCC on results are analyzed. Results show that with non-uniform heat generation, Sg and Delta When G increases, both the minimum Delta T and Sg slightly grow. Increasing heat-generation non-uniformity leads to decreasing the overall performance of heat dissipation and increasing irreversibility of whole system. The optimum width of construct of the DLRPHTCC obtained when taking Sg as objective is larger than that when taking Delta T as objective. And optimal construct of the DLRPHTCC of the latter extends to the edge a little more than that of the former. Sg and Delta T of the model with DLRPHTCC are decreased by 83.37 % and 80.93 % compared to those of the model without DLRPHTCC with uniform heat-generation, respectively. T decrease first and then increase when gamma 0 grows.

In this paper, exergy-based ecological-function (ECF) optimal performances for endoreversible three-reservoir chemical potential (CHP) transformer with linear and diffusive mass transfer (MT) laws are studied. Exergy output is the output chemical energy of heating space. The optimal relationship between dimensionless ECF and coefficient-of-performance is derived firstly. Influences of CHP ratio of mass reservoirs and MT coefficient ratios on the cycle dimensionless ECF optimal performance are analyzed. Moreover, in order to maximize coefficient-of-performance, rate-of-energy-pumping, minimize entropy-generation-rate and maximize ECF, multi-objective optimizations for endoreversible three-reservoir CHP transformer with linear and diffusive MT laws are performed using NSGA-Ⅱ. MT law only changes the values of ECF and coefficient-of-performance, but the shape of the characteristic relationship curve remains unchanged. The linear MT law is a special case of diffusion MT law. Compared with single-objective optimization result for maximizing ECF, multi-objective optimization greatly decreases entropy-generation-rate and increases coefficient-of-performance at the expense of small sacrifices of rate-of-energy-pumping and ECF. Taking quadru-objective optimization as an example, the rate-of-energy-pumping of 17.5% and ECF of 7.14% are sacrificed, which greatly decreases the entropy-generation-rate by 42.86% and increases coefficient-of-performance by 9.69%. Multi-objective optimization can better coordinate the contradiction among objectives and improve comprehensive performance of three-reservoir CHP transformers.

This study develops a finite-time-thermodynamic model of dye-sensitized solar cell-thermoelectric generator (DSSC-TEG) hybrid device. Considering external heat transfers, optical loss, Fourier heat leakage, Joule heat, Thomson effect, convection and radiation losses, expressions for energy conservation equations and performance parameters are derived by combining thermodynamics and heat transfer. Under a fixed overall heat exchanger thermal conductance, the maximum power, maximum efficiency and optimal DSSC operating temperatures are provided by simultaneously optimizing thermal conductance distribution, current density, thin-film thickness, thermoelectric leg length and thermoelectric element number. The design parameters and irreversibilities effects on optimal performance are investigated, the DSSC-TEG hybrid device and standalone DSSC device performances are compared, and a modified performance comparison method is proposed. Results indicate that TEG can effectively recover DSSC waste heat, and hybrid device delivers higher power than standalone DSSC. DSSC operating temperature and TEG operating temperature-difference first decrease and then increase with current density, and DSSC power is larger than TEG power in hybrid device. External thermal resistances, Thomson effect, convection and radiation losses degrade the optimal performance. At optimal performance, the total thermal conductance is distributed almost equally between two heat exchangers. The temperature-dependent coefficients affect hybrid device performance, which decrease as they increase.

Based on finite-time-thermodynamics and thermal-Brownian-engine cycle with external heat transfers, expressions for ecological function and efficient ecological function are derived firstly herein. Two temperatures for hot and cold viscous mediums are solved by combining heat flow balance equations, and ecological performances are analyzed. Next, with thermal-conductance-ratio, barrier-height and external-load as optimization variables, 15 combinations including power, efficiency, ecological-function and efficient-ecological-function as optimization objectives, single- and multi-objective optimizations are conducted utilizing non-dominated sorting genetic algorithm-II (NSGA-II), and Pareto frontiers for different combinations are obtained. Finally, the optimal schemes for different multi-objective optimizations are determined using three decision-making methods. Results indicate that this engine can operate under maximal ecological function or efficient ecological function objectives. Ecological-function, efficient-ecological-function and multi-objective optimizations can achieve trade-offs between power and efficiency, and multi-objective optimizations provide more suitable solutions. For four-objective optimization, optimal scheme with Shannon-Entropy method is closer to ideal solution, and barrier height and external load corresponding to Pareto frontier are distributed uniformly within their ranges, while thermal conductance ratio is concentrated around 0.5. Adjusting barrier height and external load is an effective way to achieve coordinated optimization of these four objectives.

By combining finite-piston-speed thermodynamics, direct method and finite-time thermodynamics and assuming that piston motion speeds in each stroke are not equal, more practical irreversible air standard reciprocating Brayton, Dual and Miller cycle models with finite-time heat-transfer, finite-speed piston friction and other irreversibilities are established herein. Performance relationships between important objective functions (including ecological coefficient of performance (ECOP), ecological function, power and efficiency) and design variables (including compression ratio, piston speed of adiabatic process and ratio of piston speed of isobaric process to that of adiabatic compression process) are derived. Numerical calculation method is used to analyze the effects of piston speed and its ratio on cycle objective functions. For three irreversible cycles, the research results indicate that, after considering finite piston speed, the performance relationship curves among ECOP, ecological function, efficiency, power and compression ratio are parabolic-like ones, while the performance relationship curves among power, ecological function and efficiency are loop-shaped ones, and these characteristics of performance curves present the substantive characteristics of actual cycles; finite piston speed has significant impacts on cycle performances, and introducing finite piston speed in performance research of air standard reciprocating cycles is expected to provide theoretical guidelines for design of actual reciprocating engines.

An endoreversible three-reservoir non-isothermal chemical-pump (NICP) cycle is modeled by equivalent combined-cycle method, taking it as combined-cycle of endoreversible two-reservoir NICP driven by endoreversible two-reservoir non-isothermal chemical-engine. Applying finitetime thermodynamics and considering heat-and-mass-transfer coupling effect following Lewis criterion, 3-D graphical illustration of NICP cycle is obtained, and expressions of rate of energy pumping (REP) and vector coefficients-of-performance (COPs) are derived. Effects of some fixed parameters on general relationship surface of REP and COPs are analyzed. At a fixed total masstransfer coefficient, optimal distribution of mass-transfer coefficient is studied, and optimal relationship surface of three-reservoir NICP is obtained. Influence of working fluid physical properties on performance of three-reservoir NICP is analyzed and compared. 3-D graphical illustrations for three-reservoir NICP are conducive to understanding cycle processes. Results indicate that as both heat-transfer flow rate and mass-transfer flow rate increase, REP increases tonically decreasing. Compared with three-reservoir heat-pump, REP of three-reservoir NICP

Abstract Based on finite-time thermodynamics and single-stage thermoelectric cooler model from prior literature, this study introduces the cost of energy, it is defined as COE = Q L / I , which quantifies heat flux per unit current passing through thermoelectric cooler from cold end, and fills a gap in finite-time thermodynamics as a new thermodynamic index. The cost of energy expression is derived, and the current and area allocation of heat-exchangers are optimized to maximize the cost of energy under fixed total heat-exchanger area. Using NSGA-II, 1- to 4-objective optimizations are performed for cooling load, coefficient of performance, efficient cooling load and cost of energy. TOPSIS, LINMAP and Shannon Entropy methods are used to identify optimal solutions. The maximum cost of energy increases with the thermoelectric unit number and total heat transfer area, but decreases with heat reservoir temperature difference. When external heat-transfer loss is considered, the maximum cost of energy decreases by 22.1 %. For four-objective optimization, the optimal current is distributed between 5 A and 40 A, and optimal heat-exchanger area allocation ratio ranges from 0.5 to 0.63 and clusters mainly between 0.55 and 0.6. Key contributions are cost of energy analysis and four-objective optimization for single-stage thermoelectric cooler by using finite-time-thermodynamics and multi-objective methods.

The heat source models of cylinder with constant and variable cross-sections under the condition of natural convection are established herein. According to constructal theory, constructal designs for the models are performed with the minimum dimensionless maximum thermal resistance as goal. Influences of heat source height, thermal conductivity ratio, and cylindrical shape on optimal constructs of cylinder heat sources are analyzed. The results show that under natural convection condition, with increase of the height of constant cross-section cylinder heat source, the optimal heat source position and radius ratio ( b_opt ) of cylinder heat source all decrease first, then increase, and eventually stabilize. Increasing the thermal conductivity can effectively enhance heat-transfer capability of heat source, but the increase is no longer obvious after it is increased to a certain extent. When the variable cross-section cylinder heat source model is used, the optimal radius ratio is f_opt = 0.476 for the cylinder heat source with any height, so that dimensionless maximum thermal resistance of variable cross-section cylinder heat source can be minimized. When the dimensionless heat source height is H̃ = 0.7 , minimum dimensionless maximum thermal resistance of variable cross-section cylinder heat source is 23.8

A new composite heat-dissipation structure model is established, consisting of a Phi-shaped high-thermal-conductivity channel inside a square heat-generating-body with external connection of T-shaped fin. Finite element analysis of the composite heat dissipation structure is performed via COMSOL Multiphysics. Based on the steadystate heat conduction equation, constructal design from single to multiple degree-of-freedom is conducted under the constraint of fixed area ratio of high-thermal-conductivity-material with maximum-temperature-difference (MTD) and entropy-generation-rate (EGR) as performance indexes respectively. Meanwhile, effects of high-tolow thermal conductivity ratio and high-thermal-conductivity-material area ratio on optimal values of ring inner-outer diameter ratio R, center offset L0, ring area distribution ratio omega r and fin main-strut width ratio D2/D1 are investigated. When ring part of Phi-shape is tangent to square boundary, MTD is lower; when ring part of Phishape is tangent to left boundary, EGR is lower. When area ratio is 0.1, MTD of composite heat-dissipation structure consisting of X-shaped channel and T-shaped fin is 3.93% lower than that of Phi-shaped design. In contrast, when area ratio is 0.15, MTD of Phi-shaped design is 6.37% lower than that of X-shaped design. Compared with composite heat-dissipation structures consisting of fan-shaped, clover-shaped, and "arrow"-shaped channels, EGR of Phi-shaped design is reduced by 32.0%, 31.1% and 10.6%, respectively.

Combining constructal theory with entropy-generation-minimization theory, a model of a stacked chip with tree-shaped high-thermal-conductivity channels (TSHTCC) is established, and its performance are optimized with minimizing non-dimensional maximum temperature-difference (MTD) and non-dimensional entropy-generation-rate (EGR), respectively. Effects of length ratio of first order channel to elemental channel, length and width of first order channel, heat-generation-rate per volume, temperature of heat sink and thermal-conductivity of TSHTCC on its MTD and EGR are analyzed. The results show that optimal construct of TSHTCC obtained with minimum EGR objective stretches slightly towards the center than that with minimum MTD objective. When thickness is 28μm and width of second order channel is 1500μm, non-dimensional MTD reaches its minimum at value of 0.824, and is reduced by 17.6% compared to initial design. When thickness is 29μm and width of second order channel is 1500μm, non-dimensional EGR reaches its minimum at value of 0.759, and is reduced by 24.1% compared to initial design. Non-dimensional MTD and non-dimensional EGR are reduced by 67.9% and 83.5%, respectively, compared to those of a model without TSHTCC. Therefore, heat dissipation performances of stacked chip are increased.

Constructal theory, as an important theory to carry out constructal designs for various engineering issues, has been widely used in fin design. In order to further improve comprehensive heat-dissipation performance of porous fins, a two-stage 3D T-shaped porous-fin model is established herein. Firstly, under the condition of specified material volume, constructal design is aimed at minimizing a composite-function composed of linearweighting-sum of maximum-temperature-difference and pump-power consumption, and optimal slenderness ratio (L-opt) and fin length ((aopt)) are gained. Secondly, artificial-neural-network and NSGA-II are used to perform constructal design. The results of composite-function minimization show that composite-function has twice minimum of 0.837 when the fin slenderness ratio and fin length are optimized at 17.17 and 8.36 mm, respectively. At this point, the composite-function and maximum-temperature-difference lower by 16.33 % and 53.06 %, correspondingly. Results of multi-objective constructal design show that the optimal fin slenderness ratio relevant to Pareto optimal-solution-set mainly distributes between 10 similar to 20, and optimal fin length mainly distributes between 4 mm similar to 14 mm, respectively. The optimal construct of two-stage porous-fin is obtained by LINMAP or TOPSIS decision-making-approach, which is Lopt = 19.34mm and aopt = 7.54. The findings can be used as a theoretical reference for designing heat dissipation in electrical device using porous fin. The significant contributions herein are the proposal of two-stage 3D T-shaped porous-fin model and realization of multiobjective constructal designs for it via composite-function, NSGA-II and ANN.

A two-stage combined T-Y-shaped fin model is established in present study. According to the constructal theory, the model structure is optimized with goal of minimizing maximum dimensionless thermal resistance (MDTR). By releasing degree-of-freedoms (DOFs) one by one, the optimal results under optimizations with 1-DOF to 6DOF and the temperature distributions corresponding to optimal constructs are obtained. The optimal results with different DOF optimizations are compared and analyzed. The results show that the minimum MDTR of fins decreases from 33.668 with 1-DOF optimization to 26.795 in 6-DOF optimization, with a decrease rate of 20.41%. Moreover, the influences of different DOFs on performance of fins are different, and the one-stage branched fin length-width ratio has greatest influence. Under the same conditions, the minimum MDTR of the two-stage combined T-Y-shaped fin is 33.69% lower than that of single-stage T-Y-shaped fin. Meanwhile, the minimum MDTR is reduced by 1.49% compared to T-Y-shaped fin with variable branched fin angle. It is worth noting that the minimum MDTR of two-stage combined T-Y-shaped fin is greater than that of twice Y-shaped fin, and influence of cavity structure on the fin performance needs to be further studied and discussed.

A simple Brayton cycle space power plant includes two parts: closed Brayton cycle with a compressor, a turbine and two heat exchangers, and radiator panel to dissipate heat to cosmic space. A model of simple irreversible closed Brayton cycle space power plant is established by utilizing finite-time thermodynamics herein, cycle thermal efficiency and cycle power output are deduced and optimized. When heat transfer areas of two heat exchangers and radiator panel are FH = FL = 15.7m2 and FR = 122.4m2, and low temperature heat sink is TL = 490 K, cycle power of initial design scheme is P = 33.72 kW. When three area distributions (fH, fL and fR) are optimized and TL = 490 K, the maximum cycle power is Pmax= 34.75 kW, with an increase of about 3.05% compared with P. When TL is further optimized, the double maximum cycle power is Pmax,2 = 39.45 kW, with an increase of about 13.53 % compared with Pmax, and an increase of about 17 % compared with P. The curve between Pmax and the corresponding efficiency 7opt is loop-shape one, that is, there is the maximum optimal efficiency (7opt) max and the corresponding power output P(7opt)max . The reasonable working range of irreversible plant should be P(7opt)max <= P <= Pmax,2 and (7opt) Pmax,2 <= 7 <= (7opt) max.

Based on the definition of exergy-based efficient ecological-function (EEF) proposed in the existing literature, which is the product of energy conversion coefficient-of-performance ( ɛ ) and exergy-based ecological-function ( E ), this paper will introduce the exergy-based EEF into performance optimization for Carnot refrigerator cycle. Via endoreversible Carnot refrigerator model established in previous literature, expression of the exergy-based EEF of refrigerator is derived based on finite-time thermodynamic theory, relationships of dimensionless exergy-based EEF versus ɛ and cooling load ( R ) are studied, and performance differences of refrigerator cycles at the maximum exergy-based EEF, at the maximum E , and at the maximum efficient cooling-load conditions are compared. The results demonstrate that relationships of dimensionless exergy-based EEF versus R and ɛ are parabolic-like ones; in actual design, the refrigerator should be designed at the larger R and ɛ points. When exergy-based EEF is taken as optimization-objective, although R decreases slightly, ɛ is increased, and entropy-generation-rate ( σ ) is greatly decreased, so exergy-based EEF does not only reflect the compromise between the R and σ , but also reflect the compromise between the R and ɛ .

According to the definition of exergy-based efficient ecological-function (EBEEF) which is proposed as product of exergy-based ecological-function (EF) and coefficient of performance (COP) in previous literature, this paper applies the EBEEF to analyze and optimize performance of endoreversible Carnot heat-pumps (ECHPs). Via the ECHP cycle model established in previous literature, EBEEF expression for ECHP cycle model is deduced, relationships among the EBEEF and heating load (HTL) and COP are researched, and performance comparison for ECHP cycle working at the maximum EBEEF and the maximum EF conditions are performed. Results show that relationships among the EBEEF and the HTL and COP are parabolic like ones and the design points of the larger COP and HTL should be selected for designing heat pumps. When the maximum EBEEF is taken as primary objective, the optimized ECHP cycle can improve its COP and reduce its entropy-generation-rate by sacrificing a small amount of its HTL. The EBEEF not only considers the trade-off between the HTL and entropy-generation-rate, but also considers the trade-off between HTL and COP.

Previous studies proposed exergy-based efficient-ecological-function (E phi) as a new cycle performance index. In this study, E phi is introduced into a generalized irreversible Carnot heat-pump (CHP) cycle with heat-leak rate (q), heat-transfer loss and internal-irreversibility-factor (Phi). Cycle performances working under the maximum coefficient-of-performance (phi), maximum E phi and maximum ecological-function (E) conditions are compared firstly. Then, single-, dual-, triple-, and quadruple-objective optimizations for the irreversible CHPs are performed with E phi, phi, heating load (pi) and E as well as their different combinations as optimization objectives, and working-fluid temperature-ratio (x) as optimization variable, by utilizing NSGA-II algorithm. Pareto-frontiers (PFs) under different objective combinations are obtained. Finally, the PF value is selected by using three decision-making-methods (DMMs): TOPSIS, LINMAP, and Shannon entropy. With the same objective function combination, the deviation indexes (Ds) of three DMMs are compared and the optimal scheme is selected according to the smallest D. The results for endoreverisble CHP case are also provided. The findings show that E phi places greater emphasis on the trade-off among phi, pi, exergy-output-rate, and entropy-generation-rate. Heat-leak-rate transforms curve of E phi - phi from parabolic to loop-shaped. The curve of E phi - pi is parabolic shape, E phi decreases with increases of q and Phi. In practical heat-pump design, it is necessary to choose a designing point with higher phi and pi in order to improve performance. On the PF, each point represents an optimal equilibrium-state achieved by objective function. For four-objective optimization, the optimal x (xopt) for the generalized irreversible CHP cycle ranges between 0.768 and 0.866, while the xopt of endoreversible CHP cycle is between 0.765 and 0.866, which mean the optimal selecting ranges of working-fluid temperature-ratio for the two CHP cycle models. The important contributions herein are introducing E phi into generalized irreversible CHP and performing multi-objective optimizations with 15 objective combinations considering four performance indicators.

Assuming that the heat-and-mass-transfer process obeys the Onsager equations in linear irreversible thermodynamics, a model for an endoreversible non-isothermal-chemical-pump cycle is built, and its performance is optimized. The analytical results of rate of energy-pumping and vector coefficient of performances (See Eq. (20) in this paper for its definition) are obtained. Effects of cycle design parameters on the cycle optimal performances are analyzed. The findings show that: With the increase of energy flux, the rate of energy-pumping increases, and vector coefficient of performances decrease. With the increase of mass-transfer flux, the rate of energy-pumping is unchanged. The surfaces of rate of energy-pumping versus vector coefficient of performances are monotonically decreasing ones, and with increase of cross-phenomenological coefficient of heat-and-mass-transfer, the vector coefficient of performances increase. Research results involve two special cases: the optimal performance for an endoreversible Carnot heat-pump cycle with linear phenomenological heat-transfer law and the optimal performance for an endoreversible isothermal chemical pump with linear mass-transfer law.

An endoreversible air-standard Rallis-cycle model with heat-transfer loss is established using finite-time thermodynamics herein. Firstly, power (P), efficiency (n), efficient power (Ep) and power density (Pd) expressions are derived. Secondly, impacts of compression ratio, heat transfer loss, pressure ratio and cut-off ratio on performances are analyzed. Thirdly, applying NSGA-II, multi-objective optimizations (MOOs) based on dimensionless P (P), n, dimensionless Ep (Ep), dimensionless Pd (Pd) and their different combinations, totally fifteen combinations including 1 four-objective, 4 three-objectives, 6 two-objectives, and 4 single-objectives, are carried out with expansion ratio (6) of isothermal process as optimization variable. For the same combination, deviation-indexes (Ds) obtained by LINMAP, TOPSIS and Shannon Entropy decision-making methods are compared, and scheme with the smallest value is the best. Results show that, cycle n can be improved with sacrifice of less P when Ep is chosen as objective; compared with the maximum P objective, although part of n is sacrificed, the size is reduced when the maximum Pd is taken as objective; when optimizing objective combination of P-Pd-Ep-n, the optimal 6 is mainly distributed between 7 and 13, and D obtained by TOPSIS method is the smallest. The most significant contributions are establishment of endoreversible Rallis-cycle model, comparative analyses under different performance indicators, and MOOs with four objectives.