Entropy Generation and Thermo‐Economic Analysis of Constructal Heat Exchanger

Comparison of a constructal heat exchanger (CHE) and normal heat exchanger (NHE) is analyzed by using second law analysis. Analysis is carried out by considering the three irreversibilities due to heat transfer, pressure drop, and production of the materials and the construction of the heat exchanger. The entropy generation minimization method is used to formulate the entropy generation number expressions of all three irreversibilities for both CHE and NHE to study the differences. Also to realize the advantages of the CHE over the NHE, ratios of each of the entropy generation numbers are considered. Additionally, the thermo‐economic aspect of the heat exchanger is considered to further analyze the economic differences between the CHE and NHE. Graphical results are presented to investigate the influence of different parameters such as the number of pairing levels and initial length‐to‐diameter ratio on the behavior of the three entropy generation numbers along with effectiveness and NTU. From the overall results, we can find that there is an increase in the performance and a cost reduction in the CHE when compared to the NHE. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 39–60, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21062     

Thermodynamic optimization of a coiled tube heat exchanger under constant wall heat flux condition

In this paper the second law analysis of thermodynamic irreversibilities in a coiled tube heat exchanger has been carried out for both laminar and turbulent flow conditions. The expression for the scaled non-dimensional entropy generation rate for such a system is derived in terms of four dimensionless parameters: Prandtl number, heat exchanger duty parameter, Dean number and coil to tube diameter ratio. It has been observed that for a particular value of Prandtl number, Dean number and duty parameter, there exists an optimum diameter ratio where the entropy generation rate is minimum. It is also found that with increase in Dean number or Reynolds number, the optimum value of the diameter ratio decreases for a particular value of Prandtl number and heat exchanger duty parameter.     

Second law analysis of counter flow cryogenic heat exchangers in presence of ambient heat-in-leak and longitudinal conduction through wall

Performance of highly effective heat exchangers is governed by the various internal and external irreversibilities. In low temperature applications, the performance of these heat exchangers strongly depends on the irreversibilities such as ambient heat-in-leaks, longitudinal heat conduction through separating wall of heat exchanger and conduction through high temperature connecting tubes when they are integrated to the system. The special focus of present analysis is the study of effect of these irreversibilities on the performance of heat exchangers through second law analysis. It is observed that the effect of ambient heat-in-leak is different for the balanced and imbalanced counter flow high NTU heat exchangers. Study also makes it possible to compare the different irreversibilities for varying range of NTU and analyze the influence of external irreversibilities on the performance of heat exchangers when either hot fluid or cold fluid is minimum capacity fluid.     

Entropy Generation in a Heat Exchanger

The entropy generation (irreversibility) concept founded on the second law of thermodynamics may be applied in heat exchanger analysis. In this paper the quantity termed enthalpy exchange irreversibility norm (EEIN) is the measure of the internal heat exchanger irreversibilities. The behavior of EEIN as a function of the heat exchanger thermal size is discussed for an arbitrary flow arrangement and more precisely for two characteristic limiting cases: cocurrent and countercurrent heat exchangers.     

Performance analysis and optimization of heat exchangers: a new thermoeconomic approach

A thermoeconomic performance optimization has been carried out for a single pass counter-flow heat exchanger model. In the considered model, the irreversibilities due to heat transfer between the hot and cold stream are taken into account and other irreversibilities such as pressure drops and flow imbalance are ignored. The objective function is defined as the actual heat transfer rate per unit total cost considering lost exergy and investment costs. The optimal performance and design parameters which maximize the objective function have been investigated. The effects of the technical and economical parameters on the general and optimal thermoeconomical performances have been also discussed.     

Planning the optimum cleaning schedule based on simulation of heat exchangers under fouling

An investigation of variations in outlet temperatures of heat exchangers under fouling was carried out. The simulation of heat exchangers was performed by employing a linear fouling deposit function. The formation of deposits reduces heat exchangers effectiveness. There is inherently a linear nature between outlet and inlet temperatures of heat exchangers. The outlet temperatures can also be affected by up‐stream exchangers serving the same streams, and the up‐stream influence can be transferred in the heat system. The mathematical model of the cleaning cycle was outlined, based on the objective function of minimizing cost in unit operation time. According to the results, some heat exchangers can be given cleaning priority when the system is shut down, in order to maximize economic benefit. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20384     

换热器系统的热力学性能评价

引入可用能损率这一指标对串联组合的换热器系统的热力学性能进行了 分析和评价,得到了换热器系统可用能损率的一般计算式,讨论了换热器系统的总流动趋势、冷热流体热容量流率比、传热单元数及单台换热器的流型、传热有效度和数目等对换热器系统可用能损率的影响。     

An analysis of the heat transfer rate and efficiency of TE (thermoelectric) cooling systems

The heat transfer rate and efficiency of TE (thermoelectric) cooling systems were investigated. The emphasis of the present study is focused on the use of large-scale TE refrigerators for air conditioning applications. A one-dimensional heat transfer analysis was performed to determine the cooling power and electricity consumption of the TE elements. The constant-property results are in good agreement with the variable-property solutions for TE materials and temperatures typical for air conditioning applications. A heat transfer analysis was also carried out for TE refrigerators equipped with a heat exchanger. Both parallel- and counter-flow heat exchangers were considered. Fluid temperature variations of these two flow arrangements were found to be quite different, but the efficiencies and cold fluid exit temperatures differed only slightly when a uniform current was used for all TE elements. If the length of the heat exchanger exceeds an optimal value, the cold fluid temperature begins to rise and the efficiency drops for both parallel- and counter-flow arrangements. The second law of thermodynamics was applied to the optimization of TE refrigerators operating between two constant-temperature reservoirs and between two flowing fluids. It was found that if a TE cooling system incorporates a heat exchanger, a nonuniform current distribution should be used to achieve the maximum efficiency and the lowest cold fluid temperature. The optimization results for TE refrigerators operating between two constant-temperature reservoirs are not applicable to TE cooling systems between two flowing fluids. The most energy-efficient current distribution for the parallel-flow arrangement is the one which increase in the direction of the cold fluid.     

Optimum design of double pipe heat exchanger

Heat exchangers are used in industrial processes to recover heat between two process fluids. Although the necessary equations for heat transfer and the pressure drop in a double pipe heat exchanger are available, using these equations the optimization of the system cost is laborious. In this paper the optimal design of the exchanger has been formulated as a geometric programming with a single degree of difficulty. The solution of the problem yields the optimum values of inner pipe diameter, outer pipe diameter and utility flow rate to be used for a double pipe heat exchanger of a given length, when a specified flow rate of process stream is to be treated for a given inlet to outlet temperature.     

新型高效紧凑式换热器仿真及热力分析

为了提高新型高效紧凑式换热器设计的功能性,并使其满足热力学性能需求,对绕管的结构参数及桥接布管方式进行设计。采用一种新型的变径变线桥接方式,在体积有限的情况下实现密集的管束布置形式;对该新型换热器设计进行全尺寸流域建模及CFD数值模拟;并将三维建模结果与一维程序计算结果对比,进行可靠性验证。计算结果表明：三维计算的各项热力学性能结果与一维计算仅有较小偏差,总传热系数相对误差仅为3.74%,总传热量相对误差仅为1.04%,验证了该三维计算模型具有较好的准确性;结合温度云图证明了换热区域基本集中在绕管段,为简化复杂换热器的计算提供了思路;该新型高效紧凑式换热器设计实现了管侧双股流可独立运行且同层间不存在无效换热区,整体换热平顺进行,壳侧流阻较小,换热能力保持较好;在工况范围内整机换热体积功率达到4.67 MW。     

SECOND LAW ANALYSIS OF A SOLAR THERMAL POWER SYSTEM

This communication presents second law analysis based on exergy concept for a solar thermal power system. Basic energy and exergy analysis for the system components (viz. parabolic trough collector/receiver and Rankine heat engine etc.) are carried out for evaluating the energy and exergy losses as well as exergetic efficiency for typical solar thermal power system under given operating conditions. Relevant energy flow and exergy flow diagrams are drawn to show the various thermodynamic and thermal losses. It is found that the main energy loss takes place at the condenser of the heat engine part whereas the exergy analysis shows that the collector-receiver assembly is the part where the losses are maximum. The analysis and results can be used for evaluating the component irreversibilities which can also explain the deviation between the actual efficiency and ideal efficiency of solar thermal power system.     

Thermodynamic optimisation of the integrated design of a small‐scale solar thermal Brayton cycle

The Brayton cycle's heat source does not need to be from combustion but can be extracted from solar energy. When a black cavity receiver is mounted at the focus of a parabolic dish concentrator, the reflected light is absorbed and converted into a heat source. The second law of thermodynamics and entropy generation minimisation are applied to optimise the geometries of the recuperator and receiver. The irreversibilities in the recuperative solar thermal Brayton cycle are mainly due to heat transfer across a finite temperature difference and fluid friction. In a small‐scale open and direct solar thermal Brayton cycle with a micro‐turbine operating at its highest compressor efficiency, the geometries of a cavity receiver and counterflow‐plated recuperator can be optimised in such a way that the system produces maximum net power output. A modified cavity receiver is used in the analysis, and parabolic dish concentrator diameters of 6 to 18 m are considered. Two cavity construction methods are compared. Results show that the maximum thermal efficiency of the system is a function of the solar concentrator diameter and choice of micro‐turbine. The optimum receiver tube diameter is relatively large when compared with the receiver size. The optimum recuperator channel aspect ratio for the highest maximum net power output of a micro‐turbine is a linear function of the system mass flow rate for a constant recuperator height. For a system operating at a relatively small mass flow rate, with a specific concentrator size, the optimum recuperator length is small. For the systems with the highest maximum net power output, the irreversibilities are spread throughout the system in such a way that the internal irreversibility rate is almost three times the external irreversibility rate. Copyright © 2011 John Wiley & Sons, Ltd.     

Costs of Irreversibilities in Heat Exchanger Design

Abstract

An operationally convenient methodology is presented for relating economic costs to entropy generation. This methodology, in the hands of the heat exchanger designer, allows an interaction with the system designer to gain insights into the trade-offs allowed between the thermodynamic irreversibilities of flow friction, heat transfer, heat leakage, and mixing. The methodology starts with a recognition of the appropriate individual irreversibilities, then relates the individual costs to system rating and energy penalties by thermodynamic arguments. The analysis loop is closed by considerations related to reduction of the individual irreversibilities in a cost-effective way. In contrast, the usual energy or “exergy” analysis provides an answer for the overall costs of the collective irreversibilities. This does not provide the engineer with the insight needed to minimize the individual irreversibilities in a cost-effective manner,     

Numerical research on heat transfer and flow resistance performance of specially‐shaped rod baffle heat exchangers

In order to overcome the disadvantages of heat transfer performance in the shell side of the common circular cross section rod baffle heat exchanger with a low Reynolds number, a numerical simulation on fluid flow and heat transfer in the shell side with different types of rod baffles is carried out. The rod baffles include the circular cross section, trigonal cross section, and rhombic cross section. The influence of heat transfer enhancement and flow resistance reduction affected by baffles is summarized. It is indicated that the trigonal and rhombic cross section rod baffles present the better performance of heat transfer enhancement and flow resistance reduction. With the rhombic cross section rod baffles in the shell side, the higher heat transfer coefficient and overall property in the shell side are achieved when Re is lower, and the heat transfer coefficient in the shell side is 10% higher than that of a circular cross section rod baffle at the same Reynolds number. The trigonal and rhombic cross section rod baffles in the shell side give more optional structure forms for expanding the application scope of rod baffle heat exchangers. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20388     

Design and optimization of a downhole coaxial heat exchanger for an enhanced geothermal system (EGS)

The present study considers the design, performance analysis and optimization of a downhole coaxial heat exchanger for an enhanced geothermal system (EGS). The optimum mass flow rate of the geothermal fluid for minimum pumping power and maximum extracted heat energy was determined. In addition, the coaxial pipes of the downhole heat exchanger were sized based on the optimum geothermal mass flow rate and steady-state operation. Transient effect or time-dependent cooling of the Earth underground, and the optimum amount and size of perforations at the inner pipe entrance region to regulate the flow of the geothermal fluid were disregarded to simplify the analysis. The paper consists of an analytical and numerical thermodynamic optimization of a downhole coaxial heat exchanger used to extract the maximum possible energy from the Earth's deep underground (2 km and deeper below the surface) for direct usage, and subject to a nearly linear increase in geothermal gradient with depth. The thermodynamic optimization process and entropy generation minimization (EGM) analysis were performed to minimize heat transfer and fluid friction irreversibilities. An optimum diameter ratio of the coaxial pipes for minimum pressure drop in both limits of the fully turbulent and laminar fully-developed flow regime was determined and observed to be nearly the same irrespective of the flow regime. Furthermore, an optimum geothermal mass flow rate and an optimum geometry of the downhole coaxial heat exchanger were determined for maximum net power output. Conducting an energetic and exergetic analysis to evaluate the performance of binary power cycle, higher Earth's temperature gradient and lower geofluid rejection temperatures were observed to yield maximum first- and second-law efficiencies.     

Irreversibility minimization of heat exchangers for transcritical CO2 systems

Irreversibility analyses of both evaporator and gas cooler of a CO₂ based transcritical heat pump for combined cooling and heating, employing water as the secondary fluid, have been reported. The analysis includes both operational and material associated irreversibilities. Optimization of heat exchanger tube diameter and length and effect of design parameters on overall system performance is also presented. Results clearly show that higher heat transfer coefficient can be achieved by reducing the diameter only to a limited extent due to rapid increase in pressure drop. The minimum possible diameter depends on mass flow rate (capacity) and division of flow path. The right combination of optimum diameter and length depends on the number of passes, capacity and operating parameters. It is noteworthy that due to higher pressure drop occurring in the evaporator compared to the gas cooler, zero temperature approach is attained before the optimum length is reached in case of the evaporator. Presented results are expected to help choose effective heat exchanger size in terms of diameter, length and number of passes.     

A dynamic model for the efficiency optimization of an oscillatory low grade heat engine

A simple approach is presented for the modeling of complex oscillatory thermal-fluid systems capable of converting low grade heat into useful work. This approach is applied to the NIFTE, a novel low temperature difference heat utilization technology currently under development. Starting from a first-order linear dynamic model of the NIFTE that consists of a network of interconnected spatially lumped components, the effects of various device parameters (geometric and other) on the thermodynamic efficiencies of the device are investigated parametrically. Critical components are highlighted that require careful design for the optimization of the device, namely the feedback valve, the power cylinder, the adiabatic volume and the thermal resistance in the heat exchangers. An efficient NIFTE design would feature a lower feedback valve resistance, with a shorter connection length and larger connection diameter; a smaller diameter but taller power cylinder; a larger (time-mean) combined vapor volume at the top part of the device; as well as improved heat transfer behavior (i.e. reduced thermal resistance) in the hot and cold heat exchanger blocks. These modifications have the potential of increasing the relevant form of the second law efficiency of the device by 50% points, corresponding to a 3.8% point increase in thermal efficiency.     

The Finite Difference Method and the Numerical Approach for Modeling the Maldistribution of the Flow of Media in Tube-and-Fin Cross-flow Heat Exchangers

The work deals with thermal and hydraulic modeling of fin-and-tube cross-flow heat exchangers with a non-uniform flow of media. A maldistribution of media flow is not considered in the standard thermodynamic analysis, and the results of such analysis may be too optimistic. The authors applied two modeling methods to include the information about a non-uniform flow of media through the heat exchangers. The finite difference method and the numerical approach are applied in the first and in the second stage of the analysis, respectively. The general assumption is that the real device can be divided into repetitive elements, thus allowing to consider the media flow non-uniformity. The two methods are used for simulations of selected experiments carried out for a single-row fin-and-tube cross-flow heat exchanger. A traditional computational analysis is also performed and a comparison of the results is made. The results confirmed the applicability of the proposed methods.     

A parametric study of refrigerant flow in non-adiabatic capillary tubes

This paper presents a parametric analysis of refrigerant flow through capillary tube–suction line heat exchangers, used in domestic refrigeration systems. The analysis is based on a homogeneous model developed by the authors. The model is based on the numerical solution of fundamental equations of conservation of mass, momentum and energy of refrigerant flow. The refrigerant flow characteristics are investigated by varying thermodynamic (e.g. condensing temperature, evaporating temperature, inlet sub-cooling, suction line superheat) and geometric parameters (e.g. inlet adiabatic length, heat exchanger length and internal diameter of the capillary tube) of the capillary flow. The source of divergence in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the capillary heat exchanger.     

A Correction Factor-Based General Thermal Resistance Formula for Heat Exchanger Design and Performance Analysis

Methods for the analysis of heat exchangers with various flow arrangements modeling, design, and performance are essential for heat transfer system modeling and its integration with other energy system models. This paper proposes the use of the linear-transfer law for the heat exchanger design and performance analysis as a function of the thermal resistance related to the ratio of a linear temperature difference to the total heat transfer rate. Additionally, we derived a correction factor that represents the influence of the flow arrangement on the heat transfer performance by the effective thermal conductance, as a function of correction factor, heat transfer coefficient, and surface area. Based on the effective thermal conductance, we propose the hot-end NTU and cold-end NTU for deriving a standardized and general thermal resistance formula for different types of heat exchangers by the combination of the correction factor with linear-transfer law. Moreover, for parallel-flow, cross-flow, and 1-2 Tubular Exchanger Manufacturers Association(TEMA) E shell-and-tube heat exchangers, we derived and obtained alternative correction factor expressions without introducing any temperatures. Two cases about heat exchanger design and performance analysis show that the calculation processes using the correction factor-based general thermal resistance are straightforward without any iteration and the calculation results are accurate. Finally, the experimental validation shows that the general thermal resistance formula is appropriate for analyzing the heat transfer performance. That is, the correction factor-based general thermal resistance formula provides a standardized model for heat exchanger analysis and heat transfer/integrated energy system modeling using the heat current method.