Entransy Dissipation Research Articles

Constructal entransy dissipation rate minimization for X-shaped vascular networks

Combining with entransy theory, constructal designs of the X-shaped vascular networks (XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates (EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives (EDR minimization and entropy generation rate (EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate (DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network (HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number (EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.

Thermo ecological optimization of shell and tube heat exchangers using NSGA II

Shell and tube heat exchangers are the most important equipment in chemical processes plants. The heat exchanger design from the thermodynamic point of view is based on two fundamental aspects, the global heat transfer coefficient and the pressure drop. In 2007 a new thermodynamic property denominated “Entransy” was defined, which expresses the capacity of a body to transfer heat. This property can totally characterize the capacity to transfer heat of a shell and tube heat exchanger. The loss of this capacity is denominated “Entransy Dissipation”. For evaluating the ecological impact of thermal machines, Angulo-Brown created in 1991 the “ecological function”. In this paper the “entransy dissipation” and the ecological function were combined and a new expression for evaluating the ecological impact of shell and tube heat exchangers is proposed. A multi-objective optimization of shell and tube heat exchangers considering irreversibility is also carried out. The ecological function and the cost were used as objective functions. For solving the of multi-objective optimization problem, the method of the Genetic Algorithms is used.

Constructal studies on hexagonal microchannel heat sinks based on multi-physics field coupling calculations

The design prototypes of four kinds of channel structures for three fluid recirculation ways, i.e. without reverting microchannels, with rim reverting microchannels and with central reverting microchannels, respectively, for the hexagonal heat sink are put forward. The influences of the fluid recirculation way, the microchannel branch number and the microchannel distribution on the maximum thermal resistance and the equivalent thermal resistance based on entransy dissipation of the hexagonal heat sink are studied based on thermo-fluid-stress-deformation multi-physics field coupling calculations and the thermal stress and strain analyses are carried out. The results of numerical calculations show that the fluid recirculation way with central reverting microchannels is the best among the three fluid recirculation ways with the objectives of minimizing the maximum thermal resistance and the equivalent thermal resistance. The construct of the hexagonal heat sink with six branch microchannels and central reverting microchannels, in which the upper microchannels distribute along the radius of the hexagonal inscribed circle and the lower microchannels distribute along the hexagonal circumscribed circle, is optimal, and its heat transfer performance is the best. Its maximal thermal strain is 0.28 GPa, and is an order of magnitude smaller than the yield strength of silicon. Its maximal deformation is 1.4 μm. The results can provide some theoretical supports for multidisciplinary design of practical microchannel heat sinks.

Entransy dissipation analysis of interfacial convection enhancing gas–liquid mass transfer process based on field synergy principle

Abstract An exploration of the gas CO2 absorbed into liquid ethanol accompanied with Rayleigh convection is performed by analyzing the mass entransy dissipation; this new statistical quantity is introduced to describe the irreversibility of mass transfer potential capacity. Based on the general advection–diffusion differential equation for an unsteady mass transfer process, the variation of the included angle between the velocity vector and concentration gradient fields is investigated to reveal the underlying mechanism of interfacial convection enhancing mass transfer. Results show some identical characteristics with the qualitative analyses of the synergy effects generated by the concentration and velocity fields after interfacial convection occurring for a boundary condition of fixed surface concentration. And the equivalent mass resistance for convective mass transfer process presents the similar variation with the reciprocal of instantaneous mass transfer coefficient. Accordingly, it is reasonable to be seen that mass transfer dissipation rate could be provided to assess the convection strength and explain fundamentally how Rayleigh convection improves mass transfer performance through establishing a close relationship between the mass transfer capacity and field synergy principle from the view of mass transfer theory.

Application of exergy and entransy concepts to analyses performance of coal fired thermal power plant: a case study

ABSTRACT In this research work, exergy and entransy analyses are done to find best-operating conditions for heat exchangers. Power outputs and heat rates for coal-fired thermal power plant are also calculated at different loads of plant. Mass flow rates, ambient temperature, extraction lines pressure drops and percentage increments of flow rates are chosen as variable parameters. Analyses can be done on developed PACFTPPEEC software. This work is concluded as – exergy rates for boiler and reheater increase with mass flow rates and ambient temperature; entransy dissipation number will be maximum when increment of mass flow rates of fluids are 5%; exergy/entransy dissipation rates, entransy dissipation based thermal resistances and entransy dissipation numbers decrease with extraction line pressure drop and best-operating conditions for heaters were obtained at 0% pressure drop. After analyses, smooth inner surfaces for extraction lines are recommended to minimise exergy and entransy dissipation rates for heaters.

Entransy dissipation analysis of heat exchangers under heat leakages and varying heat capacity ratios

Entransy dissipation analysis of heat exchangers under heat leakages and varying heat capacity ratios

Thermal performance analysis and optimization of multiple stage latent heat storage unit based on entransy theory

In this paper, a one dimensional transient model for HTF and PCM capsules is developed to predict the cold storage performance of a cascaded cold storage unit. The heat conduction in PCM capsules is considered by applying equivalent specific heat method. Then, the application of entransy theory on phase change process is discussed. The thermal resistance based upon entransy dissipation is also derived as a criterion to optimize the system. Finally, the optimization on stage numbers, solidification temperature offset between first and last layer and dimensionless capsule diameter are carried out. The results show that the entransy theory applies to analyze the thermal performance during phase change process. In addition, the utilization of multiple stage could make the phase change process faster and more uniform. The optimized parameters including stage number of 3–6, solidification temperature offset of 2.5 °C and the dimensionless capsule diameter of 0.05–0.1 are recommended. With the optimized structure, the integral average equivalent thermal resistance can be reduced by 75.7%.

Performance analysis of heat exchanger for fluids with variable properties

The Span and Wagner’s state equation and the segmental design were employed to accommodate the sharp changes of thermophysical properties of supercritical CO2 (S-CO2). The distributions of some important parameters along heat exchanger were discussed. The total entransy dissipation decreases as the coordination between heat transfer rate and temperature difference improves when the total heat transfer rate is fixed and divided evenly, which agrees with the equipartition principle of entransy dissipation. A new dimensionless temperature difference, which comprehensively considers the effectiveness and exchanger area, was proposed without the assumption of fixed thermophysical properties. The new evaluation criterion could represent the ‘efficiency’ of heat exchanger. The present work may be helpful for the design and optimization of heat exchanger using fluids with sharply variable properties.

Numerical Study on Heat Transfer Performance in Packed Bed

Packed beds are widely used in industries and it is of great significance to enhance the heat transfer between gas and solid states inside the bed. In this paper, numerical simulation method is adopted to investigate the heat transfer principle in the bed at particle scale, and to develop the direct enhanced heat transfer methods in packed beds. The gas is treated as continuous phase and solved by Computational Fluid Dynamics (CFD), while the particles are treated as discrete phase and solved by the Discrete Element Method (DEM); taking entransy dissipation to evaluate the heat transfer process. Considering the overall performance and entransy dissipation, the results show that, compared with the uniform particle size distribution, radial distribution of multiparticle size can effectively improve the heat transfer performance because it optimizes the velocity and temperature field, reduces the equivalent thermal resistance of convection heat transfer process, and the temperature of outlet gas increases significantly, which indicates the heat quality of the gas has been greatly improved. The increase in distribution thickness obviously enhances heat transfer performance without reducing the equivalent thermal resistance in the bed. The result is of great importance for guiding practical engineering applications.

Analyses of entropy generation and entransy for a Stirling cycle system based on generalized heat transfer law

In this paper, a Stirling cycle heated by a finite reservoir is analyzed and optimized with the entropy generation minimization and the entransy theory based on generalized heat transfer law. Taking the output power and the heat-work conversion efficiency as the optimization objectives, we discuss the optimization applicability of the concepts of entransy loss rate, entransy variation rate associated with work, entransy dissipation rate, entransy loss coefficient, entropy generation rate, entropy generation number and revised entropy generation number in detail. Three numerical cases are presented. The results show that both the entransy loss rate and the entransy variation rate associated with work always increase with the increase of output power, and the entransy loss coefficient always increases with the increase of heat-work conversion efficiency. However, larger entransy dissipation rate and smaller entropy generation rate do not always lead to larger output power, while smaller entropy generation number and smaller revised entropy generation number do not always lead to larger heat-work conversion efficiency, either. Therefore, with the three numerical cases discussed in this paper, we can conclude that the concepts of entransy loss rate, entransy variation rate associated with work and entransy loss coefficient are applicable for the optimization analysis, while the other parameters are not always applicable. Based on the results above, the controversy about the entransy theory is also discussed. The main problems in some negative comments of the entransy theory are summerized and analyzed, such as tampering the original text, logical inconsistency, simple repetition of academic views, renaming key concepts and even personal attacks, etc. It should be noticed that these negative comments are not real academic discussions. To some extent, the results in this paper can also be a responce to some negative comments.

Buoyancy effects on coupled heat transfer of supercritical pressure CO2 in horizontal semicircular channels

The buoyancy has great influence on the convective heat transfer of supercritical pressure fluids whose thermal properties change drastically near the pseudocritical point. Thus, numerical investigations on the coupled heat transfer characteristics of supercritical pressure CO2 (S-CO2) in horizontal semicircular channels are conducted in the present study. The effect of the secondary flow induced by buoyancy on the local thermal performance is analyzed in detail, and the dimensionless number Se, which represents the absolute vorticity flux in the main flow, is employed to describe the secondary flow and estimate the buoyancy effect. The numerical results show that the buoyancy effect gets smaller with the increase of the mass flow rate, and the heat transfer performance in the asymmetric flow is superior to that in symmetric flows at low mass flow rate. The buoyancy could significantly improve the thermal performance on the top wall but deteriorate that on the bottom wall in the hot side, which is exactly opposite in the cold side. The local wall heat transfer enhancement could be attributed to thinner thermal boundary layer due to the secondary flow, and the entransy dissipation theory could well explain the local heat transfer behavior. The criterion Se/Re gives better prediction for the buoyancy effect on both overall and local heat transfer than the existing ones.

Irreversibility characterization and analysis of coupled heat and mass transfer processes in an absorption system

Irreversibility analyses identify system inefficiencies and the potential for improving each component. Absorption systems do not involve heat-work conversion, so the irreversibilities can be characterized by the entransy dissipation. However, previous entransy analyses were not developed for coupled heat and mass transfer processes involving concentration changes of the liquid absorbent. Thus, a “concentration entransy” is defined in this paper based on the saturation temperature of the absorbent. The concentration entransy associates the vapor transfer with the latent heat transfer so that entransy dissipation can be used to characterize the mass transfer irreversibility. An entransy balance equation is then derived by taking into account the concentration entransy change and the entransy dissipation in the vapor transfer process. In addition, an equivalent T-Q diagram for the vapor absorption process is introduced to intuitively analyze the main factors causing the irreversibilities. An entransy analysis for an absorption chiller is then compared with conventional entropy and exergy analyses, which shows that these methods are generally consistent in identifying the key source of the irreversibility with the entransy analysis supplying more information and more detailed guidance. This analysis provides insights into the internal processes in the absorber and explicitly indicates how the flow rates should be adjusted and whether the heat transfer or mass transfer should be enhanced.

An inverse optimisation for heat exchangers with entransy dissipation minimisation

ABSTRACT A class of finite-time heat transfer processes (HTPs) for entransy dissipation minimisation is studied in this paper. Based on optimal control theory, the optimality condition is derived firstly, and then the general characteristics of heat transfer laws (HTLs) for three special temperature distributions including uniform temperature difference field, constant heat transfer rate per unit area, and constant entransy dissipation rate operations are obtained based on the optimality condition. The results show that the condition that the difference of temperature for the minimum entransy dissipation of heat transfer process (EDOHTP) is a constant is not only valid for Newtonian HTL, but also valid for generalised convective HTL and complex HTL .

A quantity-quality-based optimization method for indoor thermal environment design

This paper proposes a quantity-quality-based optimization method of indoor thermal environment design that emphasizes entransy and exergy analysis. We scrutinized the different focuses of entransy and exergy in examining an energy-related phenomenon or process, and pointed out the need for integrating entransy and exergy for the optimization of indoor thermal environment design. The proposed method contributes to identifying the most energy-efficient solution for attaining the same level of indoor thermal comfort for end users by quantifying the entransy and exergy efficiency of active technologies. With this method, a benchmark technical solution was properly determined and benchmarks for entransy dissipation and exergy loss during the process of thermal environment design were quantified. Entransy dissipation and exergy loss under common technologies were compared with the benchmark values. The concepts of relative entransy savings and relative exergy savings were defined as the evaluation indexes of technical energy efficiency. Referencing winter indoor thermal environment design for residential buildings in hot-summer and cold-winter (HSCW) regions in China, the proposed method was applied to assess the energy efficiency of different heating methods, including an inverter air conditioner, an “air source heat pump + floor radiation,” a “wall-hanging gas heater + floor radiation,” a “wall-hanging gas heater + radiator,” and an oil-filled radiator. This paper recommended that the “air source heat pump + floor radiation” be used for residential buildings in winter in HSCW regions to improve energy efficiency. In addition, the optimization results of the proposed method were compared with that of traditional energy and exergy analysis methods. The results showed that the new method more accurately analyzed the energy flow in indoor thermal environment design, and therefore can serve as an improved way of thinking about follow-up studies on the optimization of heat pump units and the operation strategies of floor radiant heating systems.

Effects of channel configuration on hydrothermal performance of the cylindrical mini-channel heat sinks

This work presents the numerical and experimental studies of the thermal and hydraulic performances of cylindrical mini-channel heat sinks (CMCHSs) based on the constructal theory and the entransy principle. Helical and wavy channels were proposed to enhance the heat transfer of CMCHSs in comparison with a conventional channel configuration (straight channel). A numerical simulation was performed using a three-dimensional finite volume method. On the basis of constructal theory, five degrees of freedom (DOFs) were presented, analyzed and discussed to show the geometrical impacts on the performance of CMCHSs when the laminar flow of water was less than 500. The DOFs of the design were channel configuration (straight, helical and wavy), channel aspect ratio (0.467–4), solid void fraction (80%, 85% and 90%), pitch ratio (1.5, 1.8, 2.1, 2.4 and 2.7) and wave amplitude ratio (0.032, 0.048, 0.062, 0.080 and 0.095). The experimental work examined the impacts of parameters on the thermal performance of fabricated CMCHSs with the optimum channel dimensions obtained from predicted numerical simulation and validated the computational simulation. In addition to the energy analysis of the performance of CMCHSs, a performance analysis was also conducted according to the entransy principle to determine the lowest entransy dissipation rate (EDR) and entransy dissipation thermal resistance. The numerical predicted results corroborated that DOFs have significant impacts on the performance of CMCHSs. The best solid void fraction and channel aspect ratio are 90% and 0.46, respectively. For the proposed CMCHSs with helical and wavy channels, Nusselt number and friction factor ratios increase with the increase of pitch and amplitude ratios. The preferred pitch and amplitude ratios are 2.1 and 0.08 because of their high-performance factor. The comparison between the channel configurations affirmed that the slight difference is in the values of the total EDR amongst the three channels. Moreover, the comparison of the best thermo-hydraulic performance of CMCHSs between helical and wavy channels indicated that the best performance was achieved in the helical channel with the lowest total EDR.

Entransy analysis on the performance of the counter-flow heat exchangers for a double evaporating temperature chiller

The double evaporating temperature (DET) chiller has been considered as a credible method to realize temperature and humidity independent control (THIC). Energy performance optimization is of great significance for the extensive application of the DET chiller. In this paper, entransy method is employed to analyze heat transfer performance of heat exchangers based on the extremum principle of entransy dissipation (EPED) and the minimum entransy dissipation-based thermal resistance (EDTR). The entransy dissipation rate and EDTR are discussed in detail to indicate the impacts of tl,c, th,c (i.e., temperature of low temperature chilled water, high temperature chilled water), MC(R32): MC(R236fa) (i.e., mass concentration ratio of R32 to R236fa), and structural parameters on heat transfer performance of heat exchangers. The results indicate that the lowest entransy dissipation rate of heat exchangers are achieved when MC(R32): MC(R236fa) is 40%: 60%. The design tl,c/th,c are suggested to be set at 7/16 °C to reduce the entransy dissipation rate and EDTR of heat exchangers, which is beneficial to strengthen energy utilization of the chiller for energy saving. Considering the significant effect of heat capacity ratio of two steams on the EDTR, mr (i.e., mass flow rate of refrigerant) and ml,c/mh,c/mc (i.e., mass flow rates of low/high temperature chilled water/cooling water) should be increased and decreased, respectively.

A new mathematical model for multi-scale thermal management of data centers using entransy theory

Based on entransy theory, this paper proposes a new mathematical model for multi-scale data center thermal management. A comparison of heat transfer optimizing is made first, using exergy/entropy method and entransy dissipation, to verify the fitness of entransy theory. Based on which, a complete model of entransy dissipation for data center heat transfer is built, from CPU level to data center room level, with detailed computational derivation. Specifically, the calculating method of entransy dissipated by undesired air mixing has been derived, which can give quantitative evaluation on air mixing to the entire thermal performance of data center. A case study of a CFD simulation and a CRAC retrofitting engineering have been performed to verify the entransy model. In the case study, the temperature penalty caused by undesired air mixing is calculated using the entransy analysis model and testified by the retrofitting test, which directly reduces the free cooling potential and decrease data center energy performance. This entransy theory based model offers a new method to better optimize the thermal management and gives specific measures to improve the thermal performance of data centers.

Match property analysis of falling film absorption process

A one-dimensional three-fluid heat transfer model is presented here to analyze coupled heat and mass transfer process in falling film absorption process. In this model, mass transfer process is converted to its heat transfer equivalent process through the heat and mass transfer analogy. The analytic solutions can be gained by solving the equations in the model for the match property analysis. Thermal resistance of heat transfer process is defined based on the entransy dissipation theory. Conditions of matched flow and matched inlet parameter are deducted. Then thermal resistance is decompounded into thermal resistance caused by finite heat and mass transfer capability Ra, thermal resistance caused by unmatched flow Rf and thermal resistance caused by unmatched inlet-parameter Rp. The properties of Ra, Rf and Rp are quantitatively analyzed. Match property analysis method presented here provides a quantitatively optimization criteria of the absorber, and a new perspective to understand absorption process.

An inverse optimization of convection heat transfer in rectangle channels with ribbed surface based on the extremum principle of entransy dissipation

The ribbed surface is a widely used convection heat transfer enhancement technology. The geometric parameters of the ribbed surface have great influences on its heat transfer performance. It is crucial to determine the optimum geometric parameters. In the present work, the optimal arrangement of ribs mounted in a rectangular channel is provided by solving the inverse optimization problem with the entransy dissipation as the objective function. The parameter analysis based on the direct solution is firstly carried out to get an approximate range near the optimal pitch ratio which can provide the initial value for the inverse optimization problem; afterwards, the inverse optimization problem is solved by a modified simplified conjugate gradient method, and the accurate optimal pitch ratio is obtained; finally the optimization results are discussed in detail. The results indicate that, (1) the inverse optimization analysis presented in this paper can provide an accurate optimal value of the pitch ratio; (2) taking the entransy dissipation as the objective function could lead to a faster converge process and give a more stable result than taking the temperature data as the objective function; (3) the optimal value under the fixed heat flux boundary condition is slightly larger than that under the fixed temperature boundary condition.

Entropy and Entransy Dissipation Analysis of a Basic Organic Rankine Cycles (ORCs) to Recover Low-Grade Waste Heat Using Mixture Working Fluids.

Mixture working fluids can reduce effectively energy loss at heat sources and heat sinks, and therefore enhance the organic Rankine cycle (ORC) performance. The entropy and entransy dissipation analyses of a basic ORC system to recover low-grade waste heat using three mixture working fluids (R245fa/R227ea, R245fa/R152a and R245fa/pentane) have been investigated in this study. The basic ORC includes four components: an expander, a condenser, a pump and an evaporator. The heat source temperature is 120 °C while the condenser temperature is 20 °C. The effects of four operating parameters (evaporator outlet temperature, condenser temperature, pinch point temperature difference, degree of superheat), as well as the mass fraction, on entransy dissipation and entropy generation were examined. Results demonstrated that the entransy dissipation is insensitive to the mass fraction of R245fa. The entropy generation distributions at the evaporator for R245/pentane, R245fa/R152a and R245fa/R227ea are in ranges of 66–74%, 68–80% and 66–75%, respectively, with the corresponding entropy generation at the condenser ranges of 13–21%, 4–17% and 11–21%, respectively, while those at the expander for R245/pentane, R245fa/R152a and R245fa/R227ea are approaching 13%, 15% and 14%, respectively. The optimal mass fraction of R245fa for the minimum entropy generation is 0.6 using R245fa/R152a.