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.     

Numerical analysis reliability control for a double‐pipe heat exchanger with virtual entropy generation method

There are two primary laws including the first and second laws of thermodynamics that should be used to assess a process. Generally, only the first law of thermodynamics is investigated in numerical solutions, so it is possible to exist some numerical results that do not satisfy the second law of thermodynamics because of numerical errors. To achieve reliable numerical outcomes, it is better to apply two indexes of HEAT BALANCE ERROR and VIRTUAL ENTROPY GENERATION, which come from the second law of thermodynamics. In other words, an approach to develop computational fluid dynamics investigations is to take second law of thermodynamics into consideration. In this study, two different models including counterflow double‐pipe heat exchanger and single‐pipe with constant wall temperature are simulated in various cases with different efficiencies and temperature ratios. It is found that 46 cases of total 523 double‐pipe models and 24 cases of total 402 simulations of single‐pipe models had unacceptable results regarding to two mentioned criteria. The results revealed that it is less likely to gain unreliable results in smaller efficiency and lower inlet temperature for double‐pipe heat exchanger and single‐pipe respectively.     

热力学(火用)及其普遍化表达式的动力学特征

分析了功、热、能和的物理意义以及与热力学定律的关系,做功和传热是能和传递与转换的两种途径,从热力学第一定律定义的能量只有相对意义。是系统相对于环境所具有的做最大有用功的能力,相对于选定的环境,是系统的状态参量。常规的计算式是从热力学第一和第二定律导出的结果,从动力学的角度讨论了及其普遍化表达式的物理含义。起源于系统与环境的不平衡,如果系统与环境之间存在着某种(或几种)强度量差,在强度量差的推动下系统可能自动地变化到与环境相平衡的状态(寂态),在这样的过程中系统可以对外做功,这种做最大有用功的能力就是系统的。在能量公设的基础上,的微分被普遍地表示为强度量差与其共轭的广延量微分的乘积。的普遍化表达式完整地反映了的物理含义及其动力学特征,利用能量和的普遍化表达式导出了损失的普遍化表达式。     

Power-optimization of non-ideal energy converters under generalized convective heat transfer law via Hamilton-Jacobi-Bellman theory

A multistage irreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convective heat transfer law [q∝m(ΔT)] and the irreversibility of heat resistance and internal dissipation is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations, which determine optimal fluid temperature configurations for maximum power output under the conditions of fixed duration and fixed initial temperature of the driving fluid. Based on general optimization results, the analytical solution for the case with Newtonian heat transfer law (m=1) is further obtained. Since there are no analytical solutions for the other heat transfer laws (m≠1), the continuous HJB equations are discretized and dynamic programming (DP) algorithm is adopted to obtain complete numerical solutions of the optimization problem, and the relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail.     

The first and second law analysis of a lithium bromide/water coil absorber

The aim of this paper is to study the irreversibilities in a coil absorber using lithium bromide solution and to determine the variation of the second law efficiency with some variables such as cooling water flow rate, solution flow rate, cooling water temperature and solution concentration. The influence of absorber performance parameters is examined on the basis of the first and second laws of thermodynamics for parallel and counter-current types. In this regard, the heat and mass transfer, the second law efficiency, the magnitude and place of exergy losses in two types of absorbers are estimated and discussed comprehensively. The results showed that increasing the cooling water flow rate and decreasing the cooling water inlet temperature increase the heat and mass transfer, and decrease the second law efficiency. The effect of the solution concentration on the efficiency in general is small. Whereas the irreversibility for the counter-current mode is greater than that of the parallel-current mode, the heat-mass transfer 3–19% and the second law efficiency 1–12% are higher.     

基于热力学第二定律的一次能源折算方法研究

不同的一次能源具有不同的品质和做功能力,在第一定律框架下的基于燃料低位热值的折算标准煤的统计方法存在着理论的缺陷和现实性矛盾。在分析第一定律折算方法的基础上,提出了基于"等价"原则的热力学第二定律的一次能源折算方案,并对理想燃料和典型燃料的折算进行了计算和比较分析。该折算方案有利于揭示能源利用的本质过程,从而实现一次能源统计和核算上"质"和"量"的高度统一,并使得产品能源利用效率的考核和统计具备了现实可能性。     

The Second Law of Thermodynamics for a Two-Temperature Model of Heat Transport in Metal Films

ABSTRACT

The second law of thermodynamics asserts that heat will always flow “downhill”, i.e., from an object having a higher temperature to one having a lower temperature. For a parabolic rigid heat conductor with a single temperature T and a single heat-flux q this amounts to the statement that the inner product of q and ?T must be non-positive for every point x of the conductor and for every non-negative time t. For a homogeneous and isotropic body in which classical Fourier law with a heat conductivity coefficient k is postulated, the second law is satisfied if k is a positive parameter. For ultra-fast pulse-laser heating on metal films, a parabolic two-temperature model coupling an electron temperature T_e with a metal lattice temperature T_l has been proposed by several authors. For such a model, at a given point of space x and a given time t there are two different temperatures T_e and T_l as well as two different heat-fluxes q _e and q _l related to the gradients of T_e and T_l, respectively, through classical Fourier law. As a result, for a homogeneous and isotropic model the positive definiteness of the heat conductivity coefficients k_e and k_l corresponding to T_e and T_l, respectively, implies that the second law of thermodynamics is satisfied for each of the pairs (T_e, q _e) and (T_l, q _l), separately. Also, the positive definiteness of k_e and k_l, and of the corresponding heat capacities c_e and c_l as well as of a coupling factor G imply that a temperature initial-boundary value problem for the two-temperature model has unique solution. In the present paper, an alternative form of the second law of thermodynamics for the two-temperature model with k_l = 0 and q _l =  0 is obtained from which it follows that in a one-dimensional case the electron heat-flux q_e(x, t) has direction that is opposite not only to that of ?T_e(x, t)/?x but also to that of ?T_l(x, t + τ_T)/?x, where τ_T is an intrinsic small time of the model. Also, for a general two-temperature rigid heat conductor in which k_e, k_l, c_e, c_l, and G are positive, an inequality of the second law of thermodynamics type involving a pair (T_e ? T_l, q _e ?  q _l) is postulated to prove that a two-heat-flux initial-boundary value problem of the two-temperature model has a unique solution. For a one-dimensional case, the semi-infinite sectors of the plane ( q _l, q _e) over which uniqueness does not hold true are also revealed.     

A new method of characterization for stratified thermal energy stores

A new method for characterization of stratified thermal energy stores (TES) that integrates both the first law and the second law concerns is presented here. The first law concern is incorporated into a quantity called energy response factor and the second law concern into an entropy generation ratio. A product of these two quantities is at the heart of the TES efficiency definitions. This approach removes the overemphasis of the existing methods either on the first or the second law of thermodynamics which often biases the characterization results. The information about the evolution of the temperature field of the system in time is the prerequisite of the new method. It may be obtained from experiments or from suitable numerical simulations. The current method can be easily integrated into computational fluid dynamic (CFD) simulations and thus facilitate CFD-based design analysis. As an example of such CFD-integrated analysis, a large-scale hot water seasonal heat store is numerically studied to identify the effects of aspect ratio, containment shape, internal structures, and containment size on their efficiency. The results suggest the effectiveness of the new method in deriving useful design insights.     

热虹吸管传热过程中的熵增分析

以热力学理论为基础，对稳定操作条件下的热虹吸管的重要操作参数、工作特点及其内部工质循环过程进行详细分析，导出了由于存在温度差、工质流动摩擦损失、蒸气温度／压力降等因素而引起的熵增的表达式，并由此得到相应的最小熵增优化准则。所得到的热虹吸管重要操作条件，即蒸发段和冷凝段温度匹配关系以及其它重要影响参数的关系，可以为热管实际设计和应用提供重要的理论参考。     

Entropy analyses for hyperbolic heat conduction based on the thermomass model

This paper is divided into three major sections with the first one introducing the concept of generalized entropy in extended irreversible thermodynamics briefly, that is, the entropy of a non-equilibrium system depend not only on the classical variables but also on the dissipative fluxes, which makes the hyperbolic equation of heat conduction based on the Cattaneo–Vernotte model compatible with the second law of thermodynamics. The second section deals with the hyperbolic heat conduction based on the thermomass model. According to the Einstein’s mass-energy relation, the phonon gas in dielectrics can be viewed as a kind of weighty compressible fluid, and the momentum equation of the phonon (thermomass) gas in the dielectrics, which consists of the driving force, inertia and resistance of phonon (thermomass) gas, is just the damped thermal wave equation. In the third section our analyses show that the contribution of the kinetic energy of the phonon gas in the expression of extended entropy based on the thermomass model is identical with that of the heat flux in the expression of generalized entropy in extended irreversible thermodynamics. It implies that the hyperbolic heat conduction based on the thermomass model is compatible with the second law of thermodynamics.     

燃气机热泵的热力学分析

燃气机热泵是以燃气机作为动力来驱动的压缩式热泵。对燃气机热泵的热力学第一定律、Yong分析和能级平衡理论分析结果表明：其一次能源利用率可达1.76，Yong效率为0.291，能级平衡系数为0.394。与电动热泵等其他供热装置相比，燃气机热泵有着较高的热力学完善性，是一项高效节能技术。由于能级平衡理论分析考虑了Wu的作用，而热泵供暖时其性能系数的提高主要是利用了环境热量，所以建议采用能级平衡理论来分析评价热泵的性能。     

关于换热系统优化目标函数的探讨

通过对影响换热系统可用能费用损失的各种因素进行分析,综合考虑换热器的材料消耗费用,提出了基于热力学第二定律的对换热系统进行优化的目标函数,并利用工程热力学、流体力学及热经济学的理论对目标函数进行了推导,得到了目标函数的计算公式。     

The influence of heat resistance and heat leak on the performance of a four-heat-reservoir absorption refrigerator with heat transfer law of Q∝Δ(T)

On the basis of an endoreversible absorption refrigeration cycle model with Newton's heat transfer law, an irreversible four-heat-reservoir cycle model with another linear heat transfer law of Q∝Δ(T⁻¹) is built by taking account the heat leak and heat resistance losses. The fundamental optimal relation between the coefficient of performance (COP) and the cooling load, the maximum COP and the corresponding cooling load, as well as the maximum cooling load and the corresponding COP of the cycle with another linear heat transfer law coupled to constant-temperature heat reservoirs are derived by using finite-time thermodynamics. The optimal distribution relation of the heat-transfer surface areas is also obtained. Moreover, the effects of the cycle parameters on the COP and the cooling load of the cycle are studied by detailed numerical examples. The results obtained herein are of importance to the optimal design and performance improvement of a four-heat-reservoir absorption refrigeration cycle.     

内可逆四热源吸收式热变换器的基本优化关系及其性能分析

应用内可逆四热源吸收式热变化器循环模型，分析热变换器受传热不可逆性影响时的基本性能。导出了牛顿传热定律下循环的比泵热率和泵热系数的基本优化关系以及工质的最佳工作温度和传热面积的最佳分配关系。由此讨论了循环的各种优化性能，并通过数值算例，得出循环参数对循环特性的影响规律。所得结果对实际四热源吸收式热变换器的优化设计具有一定指导意义。     

Dynamical energy limits in traditional and work-driven operations I. Heat-mechanical systems

Using irreversible thermodynamics we define and analyze dynamic limits for various traditional and work-assisted processes of sequential development with finite rates important in engineering. These dynamic limits are functions rather than numbers; they are expressed in terms of classical exergy change and a residual minimum of dissipated exergy, or some extensions including time penalty. We consider processes with heat and mass transfer that occur in a finite time and with equipment of finite dimension. These processes include heat-mechanical and (in Part II) separation operations and are found in heat and mass exchangers, thermal networks, energy convertors, energy recovery units, storage systems, chemical reactors, and chemical plants. Our analysis is based on the condition that in order to make the results of thermodynamic analyses usable in engineering economics it is the dynamical limit, not the maximum of thermodynamic efficiency, which must be overcome for prescribed process requirements. A creative part of this paper outlines a general approach to the construction of “Carnot variables” as suitable controls. In this (first) part of work we restrict to dynamic limits on work that may be produced or consumed by a single resource flowing in an open heat-mechanical system. To evaluate these limits we consider sequential work-assisted unit operations, in particular those of heating or evaporation which run jointly with “endoreversible” thermal machines (e.g., heat pumps). We also compare structures of optimization criteria describing these limits. In particular, we display role of endoreversible limits in conventional operations of heat transfer and in work-assisted operations. Mathematical analogies between entropy production expressions in these two sorts of operations are helpful to formulate optimization criteria in both cases. Finite-rate models include minimal irreducible losses caused by thermal resistances to the classical exergy potential. Functions of extremum work, which incorporate residual minimum entropy production, are formulated in terms of initial and final states, total duration and (in discrete processes) number of stages.     

广义不可逆布雷森循环生态学性能系数分析

以反映热机循环输出和损失之比的生态学性能系数(ECOP)为目标,用有限时间热力学理论,对广义不可逆布雷森循环进行性能分析。导出了在牛顿传热律下广义不可逆布雷森循环无因次功率、效率、无因次熵产率、无因次生态学函数和生态学性能系数的解析式;并通过数值算例得到它们之间的关系。结果表明,内不可逆性对该热机各种性能参数产生一定的影响,以ECOP为目标优化具有效率较高,熵产率较低的优势。     

A GDQ approach to thermally nonlinear generalized thermoelasticity of disks

Generalized thermoelasticity response of an annular disk subjected to thermal shock on its inner surface is analyzed in this research. The Lord–Shulman theory, which accounts for one relaxation time in the conventional Fourier law, is used to avoid the infinite speed of thermal wave propagation. Unlike the other available works in which the first law of thermodynamics is linearized, the nonlinearity arising from the temperature change is taken into consideration. The first law of thermodynamics in this case becomes nonlinear and the analysis under such formulation is called thermally nonlinear. Two coupled equations, i.e., the radial displacement wave equation and temperature wave propagation equation are obtained. These equations and the associated boundary conditions are discreted through the generalized differential quadrature method. Solution of the time-dependent system of equations is obtained using the Newmark time marching scheme and the successive Picard method. Numerical results are provided for both thermally linear and thermally nonlinear temperature and radial displacement wave propagations. Parametric studies reveal that at higher temperature levels, thermally nonlinear first law of thermodynamics should be considered instead of thermally linear one. Furthermore, the higher the coupling parameter and/or relaxation time, the higher the divergence of thermally nonlinear-/linear-based results.     

传热强化管管内熵产分析与热力性能评价

根据热力学第二定律,对传热强化管管内热力过程进行熵产分析,建立了基于流动与传热过程熵增原理的管内传热熵产方程,导出恒热流和恒壁温2种常见工况下的无因次熵产数表达式.在不同雷诺数和进口温差条件下,对2种螺旋槽管和光管进行恒壁温工况的熵产分析和热力性能评价,分析了传热和流动摩阻引起的熵产变化规律及2种不可逆损失占总熵产的份额.结果表明,熵产分析可用于评价传热强化管的综合热力性能,确定合理的运行工况、结构参数及强化换热形式,为强化管的应用评估及优化设计提供参考.     

不可逆半导体固态热离子制冷器性能分析和优化

建立了考虑外部有限速率传热过程和热源间热漏的不可逆半导体固态热离子制冷器模型,基于非平衡热力学和有限时间热力学理论导出了热离子制冷器的制冷率和制冷系数的表达式;对比分析了不可逆热离子制冷器与可逆热离子制冷器的发射电流密度特性、电极温度特性以及制冷系数特性;研究了不可逆系统的制冷率与制冷系数最优性能,得到了制冷率和制冷系数的最优运行区间;通过数值计算,详细讨论了外部传热以及内部导热、热源间热漏损失、热源温度、外加电压、半导体材料势垒等设计参数对热离子装置性能的影响。在总传热面积一定的条件下,进一步优化了高、低温侧换热器的面积分配以获得最佳的制冷率和制冷系数特性。结果表明,由于存在内部和外部的不可逆性,热离子装置的发射电流密度及制冷系数都会明显降低;不可逆半导体固态热离子制冷器的制冷率与制冷系数特性呈扭叶型;合理地选外加电压、势垒等参数,可以使制冷器设计于最大制冷率或最大制冷系数的状态。     

Optimal performance of a spin quantum Carnot heat engine with multi-irreversibilities

By using quantum master equation, semi-group approach and finite time thermodynamics (FTT), this paper derives the expressions of cycle period, power and efficiency of an irreversible quantum Carnot heat engine with irreversibilities of heat resistance, internal friction and bypass heat leakage, and provides detailed numerical examples. The irreversible quantum Carnot heat engine uses working medium consisting of many non-interacting spin-1/2 systems and its cycle is composed of two isothermal processes and two irreversible adiabatic processes. The optimal performance of the quantum heat engine at high temperature limit is deduced and analyzed by numerical examples. Effects of internal friction and bypass heat leakage on the optimal performance are discussed. The endoreversible case, frictionless case and the case without bypass heat leakage are also briefly discussed.