A new approach to analysis and optimization of evaporative cooling system II: Applications

After introducing the concepts of moisture entransy, moisture entransy dissipation and thermal resistance based on moisture entransy dissipation (TRMED) in part I of this study, we further analyze several direct/indirect evaporative cooling processes based on the above concepts in this part. The nature of moisture entransy, moisture entransy dissipation and TRMED during evaporative cooling processes was reexamined. The results demonstrate that it is the moisture entransy, not the enthalpy, that represents the endothermic ability of a moist air, and reducing the entransy dissipation by both enlarging the thermal conductance of heat and mass transfer, and decreasing the temperature potential of the moist air, i.e. the difference between the dry-bulb temperature of moist air over its dew-point temperature, will result in a smaller system TRMED, and consequently a better evaporative cooling performance. Then, a minimum thermal resistance law for optimizing evaporative cooling systems is developed. For given mass flow rates of both moist air and water, with prescribed moist air and water conditions, minimizing the TRMED will actually lead to the most efficient evaporative cooling performance. Finally, the thermal conductance allocation for an indirect evaporative cooling system is optimized to illustrate the application of the proposed minimum thermal resistance law.     

T–q diagram of heat transfer and heat–work conversion

The performance analysis of heat transfer and heat–work conversion is very important in energy utilization. T–q diagram for heat transfer is discussed and extended to heat–work conversion processes. The results show that T–q diagram is convenient for expressing entransy dissipation and analyzing heat transfer performance and can express work entransy and entransy loss intuitively. It could have an application in analyzing the performance of heat–work conversion processes.     

基于火积理论的螺旋折流板换热器的优化结构分析

为了比较平面螺旋折流板换热器和折面螺旋折流板换热器的传热和阻力性能,应用了换热器常用评价标准PEC准则和火积理论对两种换热器实验结果进行了分析,同时采用火积耗散极值原理对两种换热器的传热火积耗散率、阻力火积耗散率以及总火积耗散率进行了对比。结果表明:火积耗散理论分析换热器性能的结果与传统换热器评价标准PEC准则相符,说明了火积耗散理论的可靠性;折面螺旋折流板换热器的综合性能得到了有效的改进,火积耗散率也均优于原始结构,表明折面螺旋折流板换热器的性能得到较大改善;两种换热器传热火积耗散率值要远远大于阻力火积耗散率,约为阻力火积耗散率的一千余倍,说明传热损失为换热器的主要不可逆损失。     

Experimental exergy and entransy analyses on designed and fabricated crossflow heat exchanger

A crossflow heat exchanger (CFHEx) is designed and fabricated in a workshop. For designing this heat exchanger (HEx), the number of passes, frontal areas, HEx volumes, heat transfer areas, free-flow areas, ratios of minimum free-flow area to frontal area, densities, mass flow rates of flowing fluids, maximum/minimum heat capacities, heat capacity ratio, outlet temperatures of hot/cold fluids, average temperatures, mass velocities, Reynolds numbers, and convective heat transfer coefficients are evaluated by considering Colburn/friction factors. After fabrication of the HEx, effectiveness, exergy destruction, entransy dissipation, entransy dissipation-based thermal resistance, entransy dissipation number, and entransy effectiveness for hot/cold fluids sides are found at different flow rates and inlet temperatures of fluids. By experimental results, optimum operating conditions are found, which gives maximum effectiveness and entransy effectiveness but minimum rates of exergy destruction, entransy dissipation, entransy dissipation-based thermal resistance, and entransy dissipation number for the fabricated CFHEx. This study is concluded as follows: minimum exergy destruction and entransy dissipation rates (ie, 3.061 kJ/s·K and 1125.44 kJ·K/s, respectively) are found during experiment 2. Maximum entransy effectiveness of hot/cold fluids (ie, 0.689/0.21) is achieved in experiment 1. Moderate values of entransy dissipation number (ie, 4.689), entransy dissipation-based thermal resistance (ie, 0.04 s·K/J), exergy destruction (ie, 3.845 kJ/s·K), and entransy dissipation (ie, 1374.04 kJ·K/s) rates are found during experiment 1. Maximum effectiveness (ie, 0.4) for the fabricated HEx is also obtained through experiment 1. After comparative analyses, it is found that experiment 1 provides optimum results, which shows the best performance of the fabricated HEx.     

Entransy flux of thermal radiation and its application to enclosures with opaque surfaces

Entransy is a new concept developed in recent years to measure the transport ability of heat at a temperature in conduction and convection. This paper develops the concept of entransy flux for thermal radiation in enclosures with opaque surfaces. The entransy balance equation and entransy dissipation function are derived. The minimum principle of radiative entransy loss is developed. The potentials and the heat fluxes distribution which meet the Stefan–Boltzmann’s law and the energy balance equation would make the radiative entransy loss minimum if the net heat flux of each surface or the thermal potentials of the surfaces are given. The extremum entransy dissipation principles (EEDP) for thermal radiation are developed. The minimum radiative entransy dissipation leads to the minimum average radiative thermal potential difference for prescribed total heat exchange and the maximum radiative entransy dissipation leads to the maximum heat exchange for prescribed average radiative thermal potential difference. The minimum and maximum principle can be concluded into the minimum thermal resistance principle (MTRP) for thermal radiation by defining the thermal resistance with the entransy dissipation. The EEDP or MTRP is proved to be reliable when they are used to optimize some radiative heat transfer problems, and a comparison is made between the minimum principle of entropy generation and the EEDP.     

基于火积耗散热阻的新型板式省煤器传热分析

建立了新型板式省煤器的传热模型,计算了新型板式省煤器的火积耗散热阻以及空气侧压降,分析了新型板式省煤器结构参数及空气流速变化时,火积耗散热阻及空气侧压降的变化情况。研究结果表明:增大长轴可以减小火积耗散热阻,有利于提高板式省煤器的传热性能,并且空气侧压降变化幅度不大;增大短轴可以减小火积耗散热阻,有利于提高板式省煤器的传热性能,但空气侧压降增大;减小板束间距可以减小火积耗散热阻,有利于提高板式省煤器的传热性能,但空气侧压降增大,尤其是在板束间距小于20 mm时,继续减小板束间距会造成空气侧压降急剧增大;增大空气进口流速可以减小火积耗散热阻,有利于提高板式省煤器的传热性能,但空气侧压降增大,对换热器的磨损也会增加。     

Experimental performance comparison and trade-off among air-based precooling methods for postharvest apples by comprehensive multiscale thermodynamic analyses

Air-based precooling methods including room cooling and forced-air cooling were traditionally used for postharvest horticultural products. In this study, disturbed-air cooling with different layouts was proposed for the trade-off between room cooling with long cooling time and forced-air cooling with high energy consumption. Lab-scale experiments with 30 bins of postharvest apples were conducted using the aforementioned methods to measure the temperature history. Multiscale thermodynamic analyses from energy, entropy, exergy, and entransy perspectives were then performed. The time evolution of transient quantities and overall comparison of the trade-off performances were further discussed. The ventilation power and transformed heat became more significant respectively for the total energy consumption and heat load during the precooling processes. The rates of entropy generation, exergy destruction, and entransy dissipation reduced in consistent with the tendency of heat rejection from all bins. The major part of these losses was resulted by the ventilation for convective heat transfer between cold air and apples and became more significant during later stage of precooling processes. The middle-parallel disturbed-air cooling achieved the best trade-off between the lowest energy consumption for room cooling and the lowest maximum seven-eighths cooling time for forced-air cooling by respectively reaching 81.68% and 28.82% of the optimization potential. The best trade-off between the lowest thermodynamic loss for room cooling and the lowest heat transfer ability loss for forced-air cooling was also achieved by this method with around 55% to 62% optimization of the coefficients of performance, around 83% optimization of the entropy generation ratio, around 58% to 62% optimization of the exergy destruction ratio, and around 36% optimization of the entransy dissipation ratio.     

球突翅片的传热流动特性及等效热阻数值分析

为了提高翅片管换热器的传热系数和减小压降,提出了一种球突型翅片,通过数值模拟研究其传热与流动性能,同时应用(火积)耗散理论对其传热的不可逆性进行分析。计算结果表明:与平片相比,其传热能提高26.21%～39.53%,而阻力系数仅提高16.62%～27.04%,同时综合性能增加16.54%～32.56%;这说明该翅片具有高传热系数低压降的特点,是一种性能优良的翅片。通过(火积)耗散分析可以看出:球突翅片的等效热阻减小,其传热的不可逆性减弱。     

Two energy conservation principles in convective heat transfer optimization

Improving heat transfer performance is very beneficial to energy conservation because heat transfer processes widely existed in energy utilization systems. In this contribution, in order to effectively optimize convective heat transfer, such two principles as the field synergy principle and the entransy dissipation extremum principle are investigated to reveal the physical nature of the entransy dissipation and its intrinsic relationship with the field synergy degree. We first established the variational relations of the entransy dissipation and the field synergy degree with the heat transfer performance, and then derived the optimization equation of the field synergy principle and made comparison with that of the entransy dissipation extremum principle. Finally the theoretical analysis is then validated by the optimization results in both a fin-and-flat tube heat exchanger and a foursquare cavity. The results show that, for prescribed temperature boundary conditions, the above two optimization principles both aim at maximizing the total heat flow rate and their optimization equations can effectively obtain the best flow pattern. However, for given heat flux boundary conditions, only the optimization equation based on the entransy dissipation extremum principle intends to minimize the heat transfer temperature difference and could get the optimal velocity and temperature fields.     

Entransy and exergy analyses for optimizations of heat-work conversion with carnot cycle

The concept of entransy has been newly proposed in terms of the analogy between heat and electrical conduction and could be useful in analyzing and optimizing the heat-work conversion systems.This work presents comparative analyses of entransy and exergy for optimizations of heat-work conversion.The work production and heat transfer processes in Carnot cycle system are investigated with the formulations of exergy destruction,entransy loss,work entransy,entransy dissipation,and efficiencies for both cases of dumping and non-dumping of used source fluid.The effects of source and condensation temperatures on the system performance are systematically investigated for optimal condition of producing maximum work or work entransy.     

Experimental Performance Comparison of Shell-Side Heat Transfer for Shell-and-Tube Heat Exchangers with Different Helical Baffles

In this study, experiments were carried out to study the effects of baffle overlap proportion on the shell-side flow resistance and heat transfer performance of the shell-and-tube heat exchangers with helical baffles (STHXsHB). Three STHXsHB with an overlap proportion of 10% and helix angles of 20°, 30°, and 40° were tested. Comparisons were made of the experimental data of the STHXsHB with the same helix angles but 50% overlap proportion. The theory of entransy dissipation was employed to evaluate the irreversible loss in STHXsHB with different helix angles and overlap proportions. The results indicated that both the baffle overlap proportion and the helix angle have a great effect on the shell-side flow resistance and heat transfer. For a given helix angle, the comprehensive performance of STHXsHB with small overlap proportion is always better than that with large overlap proportion at the same mass flow rate or Reynolds number on the shell side. However, for the same heat transfer area, working conditions, and helix angle, the STHXsHB with large baffle overlap proportion has less irreversibility in the heat exchange process, according to the theory of entransy dissipation. In addition, experimental results demonstrated that the configuration of the relatively large helix angle and baffle overlap proportion is the preferred alternative in STHXsHB.     

Optimization for a heat exchanger couple based on the minimum thermal resistance principle

Following the brief introduction to the concept of a physical quantity, entransy, the equivalent thermal resistance of a heat exchanger couple is defined based on the entransy dissipation. The minimum thermal resistance principle is applied to obtain the optimal heat capacity rate of the medium fluid and the optimal allocation of heat exchangers thermal conductance, which correspond to the maximum heat transfer rate in the heat exchanger couple. In addition, analytical expression for the optimal heat capacity rate of the medium fluid is derived, whose reciprocal equals the sum of the reciprocal of the individual heat capacity rate of the hot and cold fluids, just like the case of two electrical capacitors in series. Numerical results in the variation of the thermal resistance and the heat transfer rate with the medium fluid heat capacity rate or the thermal conductance allocation agree with the theoretical analyses. Finally, for comparison, the entropy generation rate is also calculated to obtain its relation with the thermal performance of the heat exchanger couple. The results show that there is no one-to-one correspondence of the minimum entropy generation rate and the maximum heat transfer rate. This indicates that the minimum entropy generation principle cannot be used for optimizing the heat exchanger couple.     

An entransy dissipation-based optimization principle for building central chilled water systems

The recently developed entransy theory is introduced in this paper to tackle the heat transfer processes in building central chilled water systems so as to improve their energy efficiency. We first divide the irreversible heat transfer processes into four categories: (1) air mixing processes; (2) heat transfer processes between chilled water and air; (3) chilled water mixing processes; and (4) heat transfer processes between chilled water and refrigerant. The formulas of entransy dissipation rates for each irreversible process are derived, and then the total entransy dissipation rate in the whole chilled water systems is obtained, which connects the geometrical structures of each heat exchanger and the operating parameters of each fluid directly to the demands of users and the supply of refrigerating unit. Based on the formula of entransy dissipation rate together with the conditional extremum method in mathematics, two optimization equation groups are deduced theoretically. Simultaneously solving such equation groups will easily find the optimal central chilled water system with the highest energy efficiency. Finally, a simple building central chilled water system with two users is taken as an example to illustrate the applications of the newly proposed optimization principle.     

A thermal resistance analysis on forced convection with viscous dissipation in a porous medium using entransy dissipation concept

The analytical solution of a two-equation model presented in an earlier study is examined. Heat transfer characterization is classified into two regimes which are dominated by fluid conduction or solid conduction and interstitial heat exchange, respectively by using the entransy dissipation concept. The computed pattern of variation of thermal resistance with shape factor S at a fixed Brinkman number for a low ratio of the fluid to solid effective thermal conductivities implies the occurrence of temperature gradient bifurcation as S decreases. Therefore, the thermal diffusion term in the fluid phase in the two-equation model is not negligible for both regimes.     

Numerical study of the thermal–hydraulic performance of evaporative natural draft cooling towers

In this paper, the mathematical and physical models governing the flow, mass and heat energy of moist have been set up for an evaporative natural draft cooling tower. The models consider the effect of non-spherical shape of water drops on the flow, heat and mass transfer. Experimental data has been adopted to validate the numerical scheme. Average difference between the measured and the predicted outlet water temperature is 0.26°C. Distributions of the velocity components of the moist air, density, pressure, enthalpy and moisture content, the water temperature and its mass flux have been predicted. The simulation shows that some recirculation exits under the lower edge of the shell, where the air enthalpy, temperature, humidity and moisture content are higher, but the density is lower. The simulation also proves that the main transfer processes take place in the fill region where the percentage of latent heat transfer is predicted as 83%. However, about 90% of the heat energy is transferred via evaporation in the rain region although the total heat transfer rate there is very small compared to the fill region. Hourly performance of a natural draft cooling tower under the meteorological condition of Singapore has also been predicted.     

Application of Entransy Optimization to One-Stream Series-Wound and Parallel Heat Exchanger Networks

Entransy theory has developed in recent years to describe heat transfer behavior from another point of view. Entransy dissipation is proposed to evaluate the irreversibility of heat transfer and is used to optimize heat transfer processes. We apply this theory to the one-stream series-wound and parallel heat exchanger (HE) networks. The heat transfer optimization for the HE networks includes the distribution of the heat transfer area or heat load. The distribution of the cold fluid flow rate in parallel HE networks can also be optimized. For these problems, physical and mathematical models are set up, analyzed, and discussed with the entransy theory. It is found that the optimization objectives of these problems and the optimization directions of the extremum entransy dissipation principle are consistent. The optimized results for the distribution optimization problem with given heat load are in agreement with the uniformity principle of temperature difference field. Examples of simple one-stream HE networks are given; the distributions of the heat transfer area or heat load are optimized by the extremum entransy dissipation method.     

Improvement of constructal tree-like network for “volume-point” heat conduction with variable cross-section conducting path and without the premise of optimal last-order construct

The constructal “tree-like” network has been proved an effective way for “volume-point” heat conduction. This paper aims to further improve the constructal “tree-like” network with the optimization objectives of minimizations of maximum thermal resistance and entransy dissipation rate respectively. By removing the constraint that the last-order construct must be optimal, and using variable cross-section conducting path, the maximum thermal resistance and entransy dissipation rate can be greatly reduced. It is also found that the optimal construct for minimum peak temperature is similar to the optimal one for minimum entransy dissipation rate. They hold the same shape and configuration, and the main difference of them is the shape of high-conductivity path.     

基于火积理论的多级套管式相变蓄热系统优化

本文基于最小火积耗散热阻原理,在考虑相变材料导热热阻以及非稳态传热过程的基础上,对多级套管式相变蓄热系统的融化温度进行了数值优化,获得了最优融化温度分布。在此基础上,研究了相变材料导热系数和传热管长度对最优融化温度、火积耗散热阻和平均蓄热速率的影响。研究结果表明,与现有理论优化方法相比,本文提出的数值优化方法具有更好的适用性;优化后多级套管式相变蓄热系统可有效提高相变蓄热系统的平均蓄热速率,降低火积耗散热阻;随着相变材料导热系数增大和传热管长度增加,多级套管式相变蓄热系统最优融化温度的温差愈加明显,其强化传热性能呈上升趋势。     

Recent researches in indirect evaporative cooler III: optimization of the cooling potential of a room–coupled indirect evaporative cooler

A mathematical model based on heat transfer principles, for characterizing the cooling performance of a room coupled indirect evaporative cooler (tube type) has been developed. Two dimensionless parameters, i.e. environment factor, ϕ and cooling factor, CF have been defined to characterize the performance of IEC coupled with a room. The optimum values of these parameters have been obtained for different environmental and thermal load conditions. In addition to this, a linear relationship has been obtained for the optimum size of a cooler to remove maximum heat from a room of given size. © 1998 John Wiley & Sons, Ltd.     

A three-dimensional thermal-fluid analysis of flat heat pipes

A detailed, three-dimensional model has been developed to analyze the thermal hydrodynamic behaviors of flat heat pipes without empirical correlations. The model accounts for the heat conduction in the wall, fluid flow in the vapor chambers and porous wicks, and the coupled heat and mass transfer at the liquid/vapor interface. The flat pipes with and without vertical wick columns in the vapor channel are intensively investigated in the model. Parametric effects, including evaporative heat input and size on the thermal and hydrodynamic behavior in the heat pipes, are investigated. The results show that, the vertical wick columns in the vapor core can improve the thermal and hydrodynamic performance of the heat pipes, including thermal resistance, capillary limit, wall temperature, pressure drop, and fluid velocities due to the enhancement of the fluid/heat mechanism form the bottom condenser to the top evaporator. The results predict that higher evaporative heat input improves the thermal and hydrodynamic performance of the heat pipe, and shortening the size of heat pipe degrades the thermal performance of the heat pipe.