Entransy Dissipation Number Research Articles

OPTIMIZATION ANALYSIS OF PRINTED CIRCUIT HEAT EXCHANGER USED FOR HUMID AIR TURBINE CYCLE BY ECONOMY AND IRREVERSIBLE LOSS EVALUATION

The printed circuit heat exchanger (PCHE) is a prospective candidate with great application potential in humid air turbine cycles due to its high efficiency and compactness. In the present study, a one-dimensional heat transfer and flow resistance model of both straight and zigzag channels was established based on segmental thermal design. The impact of moisture content on thermal hydraulic characteristics, entropy generation, and entransy dissipation of PCHE was evaluated. A two-objective optimization of PCHE for the heat exchange process between flue gas and compressed air was performed. The cost, thermal effectiveness, entropy generation number, and entransy dissipation number were selected as the optimization objectives. The results indicate that as moisture content increases from 0 to 0.15 kg/ kg(d), the j factor decreases by 3%, the effectiveness reduces by 1.6% (straight channel) and 0.9% (zigzag channel), and the entropy generation number and the entransy dissipation number increase by 1.4% and 3.2%, respectively. Therefore, the heat recovery margin in the recuperator design should be amplified to meet the operation conditions of the variable moisture content. The entransy dissipation number of zigzag channels is 1.2 times greater than that of straight channels, which effectively distinguishes the irreversible loss of air in PCHE channels. The criteria to evaluate the optimization of entransy dissipation number is more comprehensive, as the coverage of effectiveness based on entransy dissipation number is broader than that of the entropy generation number, which changes from 0.716-0.788 to 0.769-0.788. The trade-off of cost and irreversible loss needs to be considered in application optimization.

Multi-objective optimization of non-uniform plate heat exchanger with dimples/protrusions for heat recovery of setting machines

The setting machine exhaust gas contains a large number of fiber particles and micro oil droplets, which are adhesive and flammable. This leads to difficulties in waste heat recovery of the exhaust gas. In this article, numerical and experimental studies of a non-uniform plate heat exchanger with dimples/protrusions for waste heat recovery of setting machines are carried out. Based on the three-dimensional fluid-thermal-structural coupling method, the regenerative process between gas and air are investigated numerically with low Reynolds number turbulence model. The effect of the structural parameters (protrusions diameters, protrusions spacing and plate spacing) and operation parameters (air inlet temperature, gas and air flow rate) on the heat transfer performance are discussed. The multi-objective optimization of the plate regenerator is conducted by Box-Behnken Design and Nondominated Sorting Genetic Algorithm II to maximize the thermal performance coefficient and minimize entransy dissipation number. It is found that when D1, H1 S1, D2, H2, S2 are 9 mm, 7 mm, 161 mm, 9 mm, 8 mm and 153 mm respectively, the heat exchanger has the best heat transfer performance. Compared with the original model, the heat transfer rate of the optimized heat exchanger is increased by 3.9%, the thermal performance coefficient of the air side and flue gas side is increased by 5.7% and 5.9% respectively, and the entransy dissipation number is reduced by 24.6%.

Thermodynamic Analysis and Optimization Design of a Molten Salt–Supercritical CO2 Heat Exchanger

The performance of a heat exchanger is directly related to the energy conversion efficiency of the thermal storage system, and its optimal design is an important method to improve the performance of the heat exchanger. This paper uses the distributed parameter method to analyze the effect of the structural parameters and operating parameters of a heat exchanger on the entransy dissipation rate, the entransy dissipation number, the entransy dissipation heat resistance, entropy production rate, and entropy production number in a molten salt–supercritical CO2 concentric tube heat exchanger. The results show that the entransy dissipation rate and entropy production rate have the same trend, with the structural parameters and operating parameters, as well as the changes in the entransy dissipation number and entransy dissipation thermal resistance, jointly affected by the entransy dissipation rate and the heat exchange. Based on the above indicators, single-objective and multi-objective optimization calculations were carried out. The results show that taking the minimum entropy dissipation number, entransy dissipation heat resistance, and improved entropy production number as the objective functions, and using the heat transfer effectiveness as the evaluation index, the optimization effect is better. The ε value is increased by 41.2%, 39.5%, and 40.3% compared with the reference individual. In the multi-objective optimization, taking the minimum number of entransy dissipation and entropy production as the objective function, and using the efficiency of heat transfer and the pressure drop of the working fluid as the evaluation indicators, the optimization effect is better. Compared with the reference individual, the ε value increased by 23.5%, and ΔPh and ΔPc decreased by 51.9% and 32.5%, respectively. This study provides a reference for the optimization of supercritical CO2 heat exchangers by utilizing parameters such as entransy and entropy, which reflect the irreversible loss of the heat transfer process.

Study on the air-side flow and heat transfer characteristics of corrugated fin under low-pressure environment

ABSTRACT Many troubles appear when vehicles work in the plateau region, and the main reason is that the heat-transfer capability of radiator in the vehicle cooling system reduces under the plateau low air pressure environment. Hence, the research on the flow and heat transfer characteristics of radiators in plateau low air pressure environment is necessary. In this paper, the experimental study on the thermal-hydraulic characteristics of corrugated fin radiator is conducted on a wind tunnel test-bed with low pressure function. The results illustrate that the air-side convective heat transfer coefficient of the corrugated fins decreases with the decrease of the ambient pressure, and the Colburn factor (j) and Friction factor (f) increase simultaneously. When the gauge pressure is −44 kPa, the air-side convective heat transfer coefficient is 34% lower than that under normal pressure on average, and the Colburn factor and Friction factor increase by an average of 21.1% and 55.6%, respectively. On this basis, the entransy dissipation and field synergy angle distribution of the corrugated fin radiator under low-pressure environment are studied. It is showed that the entransy dissipation number at −44 kPa gauge pressure reduces by 65% on average. The air-side field synergy angle increases with the decrease of the ambient pressure. Finally, the experimental correlations of the Colburn factor and Friction factor are performed, and the average deviations of the calculated results are 2.8% and 3.3%, respectively.

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

AbstractA 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.

Effect of surface roughness on the performance of heat exchanger

In this research work, double-pipe counter flow heat exchanger has been analyzed with various roughnesses of steel, aluminum and copper pipes and also with two different cold fluids: water and ammonia at same flow rates. Dimensions of the heat exchanger are inner and outer diameters of inner pipe being 0.034 and 0.042 m, whereas diameters of outer pipe are 0.054 and 0.06 m, respectively, and length of heat exchanger is 1.8 m. In K-ℇ modeling, computational fluid dynamics tool has been used for performance analyses and this computational work has been validated by entropy, exergy and entransy analyses. After computational numerical analyses, this investigation has concluded that maximum rate of heat transfer through heat exchanger has been found with copper–ammonia combination with smooth surface. Minimum rates of entropy generation, exergy destruction, entransy dissipation-based thermal resistance and entransy dissipation number have been obtained with copper–water combination, and minimum entropy generation number and maximum effectiveness have been obtained with copper–ammonia combination. Percentage changes in the parameters/properties have also been calculated at different operating conditions. Copper as inner pipe material with smooth surface and ammonia as cold fluid have been recommended for counter flow double-pipe heat exchanger. Computer software has been developed for hassle-free analyses of heat exchanger.

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.

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.

Application of entropy and entransy concepts to design shell and tube type surface condenser at different 4L/D ratios for Maral Overseas Ltd

ABSTRACTThe optimisation of heat exchanger is an important issue. So, the optimum size of counter flow surface condenser is found in this research work for Maral Overseas Ltd by entropy, exergy and entransy theories. In this work, effectiveness of heat exchanger, number of transfer units, entropy generation, entransy dissipation, entransy dissipation-based thermal resistance, entransy dissipation number and entransy effectiveness for hot/cold fluid sides with outlet temperatures of fluids are found for various 4L/D ratios. And then the optimum value of 4L/D ratio is found for the surface condenser. Entransy dissipation number and entransy-based thermal resistance both must be as low as possible for proper design. It is observed that when 4L/D ratio increases then EDN, entransy dissipation-based thermal resistance, outlet temperature of hot fluid and entropy generation decrease but NTU, effectiveness and outlet temperature of cold fluid increase. This research work is concluded as when 4L/D ratio increases with one unit, EDN values decrease with 0.05–0.02, but after some time, when 4L/D ratio increases with ten units, EDN values decrease with only 0.01. Finally, the optimum condition of 4L/D ratio for surface condenser is found, which is 40. Computer software is also developed to eliminate hectic calculations and human errors for performance analyses of heat exchangers.

Heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks

One-stream heat exchangers and one-stream heat exchanger networks are widely used in engineering. In this paper, the heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks is analyzed with the concepts of entropy generation rate, entropy generation number, revised entropy generation number, entropy resistance, entransy dissipation rate, entransy dissipation number and generalized thermal resistance. For the analyzed one-stream heat exchangers, our numerical results show that the extremum value of the entransy dissipation rate and the minimum values of the entropy resistance and the generalized thermal resistance always lead to the largest heat transfer rate or the lowest temperature of the cooled object, while the minimum values of the other parameters do not always. For the analyzed one-stream heat exchanger networks, the minimizations of entransy dissipation rate, entransy dissipation number and generalized thermal resistance always correspond to the lowest average temperature of the cooled objects, while the minimizations of the other parameters do not. Therefore, only the extremum entransy dissipation principle and the minimum generalized thermal resistance principle are always applicable for the heat transfer performance evaluation of the systems in this paper, while the applicability of the other parameters is conditional.

Design analysis of supercritical carbon dioxide recuperator

The segmental design method is employed to accurately capture the drastic variations of properties in the supercritical carbon dioxide (S-CO2) recuperator. The local heat capacity flow rates of both fluids have drastic changes in sub-heat exchangers even the mass flow rates of both fluids remain unchanged. When the heat duty is given, the local heat conductance, local temperature difference, local effectiveness and local entransy dissipation number have extremums, which appear in the vicinity of the heat capacity rate ratio is one. The heat transfer performance of recuperator improves at the expense of heat conductance. When the total heat conductance is fixed, there exist the maximum local heat flux rates, and the local effectiveness tends to be constant after the local heat capacity rate ratio reaches one, the local entransy dissipation number has the relatively coherent performance behavior in the sub-heat exchangers. The local heat capacity rate ratio has crucial influences on the heat transfer performance of recuperator, and the design parameters must be considered carefully in the design of S-CO2 recuperator.

Coefficient of exergy consumption and its comparison with entropy production number and entransy dissipation number

Coefficient of exergy consumption (CEC) was proposed to characterize the irreversibility degree of irreversible process. The relationships of CEC with the efficiency of thermodynamic system and coefficient of performance of heat pump were developed. The comparisons of CEC with entropy production rate, entropy production number, entransy dissipation rate and entransy dissipation number were illustrated. The results reveal that CEC, entransy dissipation number and modified entropy production number have the same tendency for the irreversible process without power consumption, while entropy production number defined by Bejan falling in entropy production paradox. The reciprocal of CEC can be considered as the efficiency of heat transfer. Therefore, CEC is more universality and applicable to characterize the irreversibility degree of thermal power conversion, thermal conversion and heat transfer processes.

Constructal optimization for “disc-point” vascular networks based on minimum entransy dissipation rate

For the specified total area of the disc and total volume of the vascular network, the constructal optimizations of the first order, second order and third order vascular networks are carried out by taking the minimizations of the entransy dissipation rate and entransy dissipation number, caused by heat transfer with finite temperature difference and flow resistance, as optimization objectives. The optimal constructs for each order vascular network with minimum entransy dissipation rate and entransy dissipation number are obtained. The results show that when the parameter B 1≥10-4, for the same dimensionless mass flow rate M *(1≤ M *≤102), the optimal constructs of the first order vascular network based on the minimizations of entransy dissipation rate and entropy generation rate are obviously different. For the second order vascular network, when the dimensionless mass flow rate locates at the range of 1≤ M *≤102, the magnitude orders of the entransy dissipations caused by heat transfer and flow resistance locate at the same level, and the optimal construct of the vascular network varies obviously with the change of the mass flow rate. For the same total volume of the vascular network and radius of the disc, when the dimensionless mass flow rates of the vascular networks are equal, the first order, second order and third order vascular networks almost exhibit the same performances of the entransy dissipation number; when the dimensionless pumping power satisfies , the minimum entransy dissipation number of the vascular network decreases with the increase in the order of the vascular network, and the performance of the vascular network can be improved by increasing the complexity of the vascular network in this case. Moreover, the performance of the vascular network is also optimized by taking complex index of entransy dissipation rate as optimization objective in this paper. The optimal results obtained in this paper can provide some guidelines for the designs of the vasculature from the point of view of heat transfer optimization.

Optimization principles for two-stream heat exchangers and two-stream heat exchanger networks

This paper presents the relationships for the heat transfer performance of two-stream heat exchangers (THEs) and two-stream heat exchanger networks (THENs) with the entropy generation, the entropy generation number, the revised entropy generation number, the entransy dissipation, the entransy dissipation number and the entransy-dissipation-based (EDB) thermal resistance. The results indicate that the effectiveness only increases with decreasing revised entropy generation number, entransy dissipation number and EDB thermal resistance when the heat capacity flow rates and the inlet temperatures are both fixed. The heat transfer rate increases with decreasing thermal resistance, increasing entropy generation and increasing entransy dissipation for prescribed inlet temperatures and prescribed ratios of the heat transfer rate to the heat capacity flow rates. The effectiveness has monotonic relations with all six parameters if the heat transfer rate is prescribed. Only the EDB thermal resistance has monotonic relation with the heat transfer performances for all the discussed cases. A lower resistance gives a better heat transfer performance. Other heat transfer examples also show that the concept of EDB thermal resistance has a wider suitability to the heat transfer optimizations discussed in the paper than the other five concepts.

Optimization design of recuperator in a chemical heat pump system based on entransy dissipation theory

Based on the entransy dissipation theory, the multi-parameter optimization design of recuperator is conducted in an Isopropanol–Acetone–Hydrogen (IAH) chemical heat pump system. The performance of the heat pump system can be improved significantly through the multi-parameter optimization, when the main operation parameters of chemical heat pump remain unchanged. When the main operation parameters of chemical heat pump and the heat transfer area of recuperator remain unchanged, the heat transfer rate of recuperator, the high-temperature heat released from the exothermic reactor, and the coefficient of performance (COP) and exergy efficiency of IAH heat pump system greatly increase while the compressor power decreases remarkably as entransy dissipation number decreases. This is done only by optimizing the combination of design parameters of recuperator taking entransy dissipation number as the objective function under certain constraint conditions, and the cost is no more than the low-temperature waste heat having no practical value.

Analysis of a new cross flow heat exchanger flow arrangement – Extension to several rows

The present paper presents a theoretical analysis of a cross flow heat exchanger with a new flow arrangement comprehending several tube rows. The thermal performance of the proposed flow arrangement is compared with the thermal performance of a typical counter cross flow arrangement that is used in chemical, refrigeration, automotive and air conditioning industries. The thermal performance comparison has been performed in terms of the following parameters: heat exchanger effectiveness and efficiency, dimensionless entropy generation, entransy dissipation number, and dimensionless local temperature differences. It is also shown that the uniformity of the temperature difference field leads to a higher thermal performance of the heat exchanger. In the present case this is accomplished thorough a different organization of the in-tube fluid circuits in the heat exchanger. The relation between the recently introduced “entransy dissipation number” and the conventional thermal effectiveness has been obtained in terms of the “number of transfer units”. A case study has been solved to quantitatively to obtain the temperature difference distribution over two rows units involving the proposed arrangement and the counter cross flow one. It has been shown that the proposed arrangement presents better thermal performance regardless the comparison parameter.

Principle of equipartition of entransy dissipation for heat exchanger design

In the present work, a principle of equipartition of entransy dissipation (EoED) for heat exchanger design is established, which says that for a heat exchanger design with given heat duty and heat transfer area, the total entransy dissipation rate reaches the minimum when the local entransy dissipation rate is uniformly distributed along the heat exchanger. When the heat transfer coefficient is unfixed, the total entransy dissipation obtained by the EoED principle is less than that obtained by the principle of equipartition of temperature difference (EoTD). Furthermore, the exchanger effectiveness obtained by the EoED principle is larger than that obtained by the EoTD principle. When the heat transfer coefficient is fixed, the EoED principle is equivalent to the EoTD principle. We show that the equipartition of entropy production (EoEP) and EoED principles give rise to difference in entropy generation and entransy dissipation for a heat exchanger optimization design. The discrepancies are caused by distinct features of entropy production minimization and entransy dissipation minimization principles, the former is to optimize the design of heat exchanger by making the lost available work minimum, while the latter is not involved with heat-work conversion. It is found that the entropy generation number is not suitable for evaluating heat exchanger performance, since it directly depends on the inlet and outlet temperatures of working fluids. On the contrary, the entransy dissipation number is not directly related to the inlet and outlet temperatures of working fluids. Therefore, the entransy dissipation number is more suitable for serving as a criterion to evaluate heat exchanger performance.

Entransy dissipation number and its application to heat exchanger performance evaluation

Based on the concept of the entransy which characterizes heat transfer ability, a new heat exchanger performance evaluation criterion termed the entransy dissipation number is established. Our analysis shows that the decrease of the entransy dissipation number always increases the heat exchanger effectiveness for fixed heat capacity rate ratio. Therefore, the smaller the entransy dissipation number, the better the heat exchanger performance is. The entransy dissipation number in terms of the number of exchanger heat transfer units or heat capacity rate ratio correctly exhibits the global performance of the counter-, cross- and parallel-flow heat exchangers. In comparison with the heat exchanger performance evaluation criteria based on entropy generation, the entransy dissipation number demonstrates some distinct advantages. Furthermore, the entransy dissipation number reflects the degree of irreversibility caused by flow imbalance.