Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process

Based on theories of thermodynamics, the energy equation in terms of entransy in heat transfer process is introduced, which not only describes the change of entransy, but also defines the entransy consumption rate. According to the regularity of entransy change in heat transfer process and the effect of entransy consumption rate on the irreversibility of heat transfer process, it can be found that entransy is a state variable, from which a new expression for the second law of thermodynamics is presented. Then by setting entransy consumption rate and power consumption rate as optimization objective and constraint condition for each other, the Lagrange conditional extremum principle is used to deduce momentum equation, constraint equation and boundary condition for optimizing flow field of convective heat transfer, which are applied to simulate convective heat transfer coupling with energy equation in an enclosed cavity. Through the numerical simulation, the optimized flow field under different constraint conditions is obtained, which shows that the principle of minimum entransy consumption is more suitable than the principle of minimum entropy generation for optimizing convective heat transfer process.     

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 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.     

Application of entransy dissipation theory in heat convection

In the present work, formulas for calculating the rates of the local thermodynamic entransy dissipation in convective heat transfer in general, and the internal and external flows in particular, are established. Practically, these results may facilitate the application of entransy dissipation theory in thermal engineering. Theoretically they shed light on solving the contradiction of the minimum entropy production principle with balance equations in continuum mechanics.     

Application of entransy dissipation theory in heat convection

In the present work, formulas for calculating the rates of the local thermodynamic entransy dissipation in convective heat transfer in general, and the internal and external flows in particular, are established. Practically, these results may facilitate the application of entransy dissipation theory in thermal engineering. Theoretically they shed light on solving the contradiction of the minimum entropy production principle with balance equations in continuum mechanics.     

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.     

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.     

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.     

The thermodynamic basis of entransy and entransy dissipation

In the present work, the entransy and entransy dissipation are defined from the thermodynamic point of view. It is shown that the entransy is a state variable and can be employed to describe the second law of thermodynamics. For heat conduction, a principle of minimum entransy dissipation is established based on the second law of thermodynamics in terms of entransy dissipation, which leads to the governing equation of the steady Fourier heat conduction without heat source. Furthermore, we derive the expressions of the entransy dissipation in duct flows and heat exchangers from the second law of thermodynamics, which paves the way for applications of the entransy dissipation theory in heat exchanger design.     

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.     

Viscous dissipation effect on entropy generation in curved square microchannels

The viscous dissipation effect on the thermodynamic performance of the curved square microchannels in laminar flow is numerically investigated. The classical Navier-Stokes equations are adopted; aniline and ethylene glycol are selected as the working fluids. The results show that the heat transfer entropy generation number and frictional entropy generation number augment relatively under viscous dissipation effect for the case of fluid heated, and the opposite results can be found for the case of fluid cooled. The heat transfer entropy generation number increases with Reynolds number at large Reynolds number region under viscous dissipation effect when ethylene glycol is heated. The total entropy generation number extremum exists for aniline, and the extremum happens earlier when aniline is heated than when aniline is cooled. The smaller the curvature radius is, the earlier the extremum appears. The extremum does not occur for ethylene glycol due to the predomination of frictional entropy generation in the total entropy generation.     

On the minimum entropy production in steady state heat conduction processes

On the basis of minimum entropy generation principle, a new formulation of the boundary value problems is proposed. Applying Euler–Lagrange variational formalism, a new mathematical form of heat conduction equation with additional heat source terms has been derived. To obtain a unique solution a special mathematical form of boundary conditions for 2D and 3D problems is required. As a result, entropy generation rate of the process can significantly be reduced, which leads to the decrease of the irreversibility ratio according to the Gouy–Stodola theorem. Minimization of entropy generation in heat conduction process is always possible by introducing additional heat sources.     

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.     

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.     

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.     

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。     

Heat-transfer distribution for an impinging laminar flame jet to a flat plate

Impinging flame jets are widely used in applications where high heat-transfer rates are needed, for instance in the glass industry. During the heating process of glass products, internal thermal stresses develop in the material due to temperature gradients. In order to avoid excessive thermal gradients as well as overheating of the hot spots, it is important to know and control the temperature distribution inside a heated glass product. Therefore, it is advantageous to know the relation describing the convective heat–flux distribution at the heated side of a glass product. In a previous work, we presented a heat–flux relation applicable for the hot spot of the target [M.J. Remie, G. Särner, M.F.G. Cremers, A. Omrane, K.R.A.M. Schreel, M. Aldén, L.P.H. de Goey, Extended heat-transfer relation for an impinging laminar flame jet to a flat plate, Int. J. Heat Mass Transfer, in press]. In this paper, we present an extension of this relation, which is applicable for larger radial distances from the hot spot.     

Heat Transfer and Thermal Resistance Characteristics of Fin with Built-In Interrupted Delta Winglet Type

The heat transfer and fluid flow characteristics of a new type of fin with built-in interrupted delta winglets is studied in this paper by three-dimensional numerical simulation. In order to ensure reliability of numerical model, plate fin with common-flow-up delta winglets is firstly simulated. The comparison of numerical and experimental results shows a maximum deviation of 11.4% within the entire range of Reynolds number. The computational results show that heat transfer capacity and overall performance increase by 35–60% and 19–64%, respectively. The flow field visualization shows that the interrupted delta winglets can produce longitudinal vortices at the rear of delta winglets and reduce the wake zone behind the tube, so the proposed fin can enhance heat transfer accompanied by low pressure loss. The field synergy theory and entransy dissipation extremum principle are employed on analyzing the mechanism of heat transfer enhancement. The results indicate that enhancement heat transfer mechanism of interrupted delta winglets can be explained as the result of the decrease of synergy angle and reduction of the entransy dissipation.