Constructal entransy dissipation rate minimization for helm-shaped fin with inner heat sources

A model of three-dimensional helm-shaped body composed of a helm-shaped fin and inner heat sources is built in this paper. For the specified volumes of the body, fin and heat source, the constructal optimizations of the body with single and multiple inner heat sources are implemented. The entransy-dissipation-rate-based equivalent thermal resistance(ETR) is minimized in the optimizations. It shows that for the helm-shaped body with multiple inner heat sources, there exist an optimal ratio of the heat source distance to the radius of the extended fin and a twice optimal radius ratio of the centre fin to the extended fin which lead to the double minimum dimensionless ETR. Comparing the optimal result of the body with helm-shaped fin with that with annular fin, the radius of the centre fin and the distance between the heat source and the center of the body are decreased, and the ETR is decreased by 9.57%. Essentially, the temperature gradient field of the helm-shaped body is more homogenous, and its global heat transfer performance is improved.     

Constructal multidisciplinary optimization of electromagnet based on entransy dissipation minimization

Based on entransy dissipation, the mean temperature difference of solenoid (electromagnet) with high thermal conductivity material inserted is deduced, which can be taken as the fundament for heat transfer optimization using the extremum principle of entransy dissipation. Then, the electromagnet working at steady state (constant magnetic field, constant heat generating rate per unit volume) is optimized for entransy dissipation minimization (i.e. mean temperature difference minimization) with and without vo...     

Constructal entransy dissipation rate minimization of a rectangular body with nonuniform heat generation

Based on construtal theory, a nonuniform heat generation problem in a rectangular body is investigated in this paper. Entransy dissipation rate (EDR) is taken as the optimization objective. The optimal body shapes with constant and variable widths of the high conductivity channel (HCC) are derived. For the rectangular first order assembly (RFOA) with constant cross-section HCC, the shape of the RFOA and width ratio of the HCCs are optimized, and the double minimum EDR is obtained. The heat transfer performance of the RFOA becomes worse when the nonuniform coefficient increases. For the RFOA with variable cross-section HCC, the EDR of the RFOA can be minimized for four times. Compared the optimal construct based on minimum EDR of the RFOA with that based on minimum maximum temperature difference, the shape of the former optimal construct is tubbier, and the average temperature difference is lower. In the practical design of electronic devices, when the thermal safety is ensured, the constructal design scheme of the former optimal construct can be adopted to improve the global heat transfer performance of an electronic device.     

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.     

Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective

The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For two cases (body with heat generation and body heated externally) of a solid conducting wall with an open cavity, a dimensionless equivalent thermal resistance based on entransy dissipation definition was taken as the optimization objective to optimize the model constructal geometry. Numerical results validated the necessity and feasibility of the presented method. Comparisons of the numerical results based on minimization of dimensionless maximum thermal resistance and minimization of dimensionless equivalent thermal resistance, respectively, showed that there was no obvious difference between the two results when the volume fraction Φ occupied by cavity was small, but the difference between the two results increased with the increases of Φ and the body aspect ratio H/L for any model. The optimal cavities for bodies heated externally were more slender than those for bodies with heat generation. Heat origin had obvious effect on the global performance of heat transfer. The entransy dissipation of body heated externally increased 2–3 times than that of body with heat generation, indicating that the global performance of heat transfer weakened. The method presented herein provides some guidelines for some relevant thermal design problems.     

Constructal optimization for H-shaped multi-scale heat exchanger based on entransy theory

Analogizing with the definition of thermal efficiency of a heat exchanger,the entransy dissipation efficiency of a heat exchanger is defined as the ratio of dimensionless entransy dissipation rate to dimensionless pumping power of the heat exchanger.For the constraints of the total tube volume and total tube surface area of the heat exchanger,the constructal optimization of an H-shaped multi-scale heat exchanger is carried out by taking entransy dissipation efficiency maximization as optimization objective,and the optimal construct of the H-shaped multi-scale heat exchanger with maximum entransy dissipation efficiency is obtained.The results show that for the specified total tube volume of the heat exchanger,the optimal constructs of the first order T-shaped heat exchanger based on the maximizations of the thermal efficiency and entransy dissipation efficiency are obviously different with the lower mass flow rates of the cold and hot fluids.For the H-shaped multi-scale heat exchanger,the entransy dissipation efficiency decreases with the increase in mass flow rate when the heat exchanger order is fixed;for the specified dimensionless mass flow rate M(M<32.9),the entransy dissipation efficiency decreases with the increase in the heat exchanger order.The performance of the multi-scale heat exchanger is obviously improved compared with that of the single-scale heat exchanger.Moreover,the heat exchanger subjected to the total tube surface area constraint is also discussed in the paper.The optimization results obtained in this paper can provide a great compromise between the heat transfer and flow performances of the heat exchanger,provide some guidelines for the optimal designs of heat exchangers,and also enrich the connotation of entransy theory.     

Application of entransy dissipation extremum principle in radiative heat transfer optimization

The concepts of entransy flux and entransy dissipation in radiative heat transfer were introduced based on the analogy with heat conduction and heat convection processes. Entransy will be partially dissipated during the radiative heat transfer processes due to the irreversibility. The extremum principle of entransy dissipation was developed for optimizing radiative heat transfer processes. This principle states that for a fixed boundary temperature the radiative heat transfer is optimized when the entransy dissipation is maximized, while for a fixed boundary heat flux the radiative heat transfer process is optimized when the entransy dissipation is minimized. Finally, examples for the application of the entransy dissipation extremum principle are presented. Supported by the National Basic Research Program of China (“973” Project) (Grant No. 2007CB206901)     

Progress in optimization of mass transfer processes based on mass entransy dissipation extremum principle

The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipation extremum principle are reviewed. Secondly, the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for optimizing the mass transfer processes of one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, and isothermal throttling and isothermal crystallization are summarized. Thirdly, the combination of the mass entransy dissipation extremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized. The scientific features of the mass entransy dissipation extremum principle are emphasized.     

Thermal insulation constructal optimization for steel rolling reheating furnace wall based on entransy dissipation extremum principle

Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the thermal insulation process is optimized when the entransy dissipation is maximized (maximum average temperature difference), while for a fixed boundary temperature, the thermal insulation process is optimized when the entransy dissipation is minimized (minimum average heat loss rate). Based on the constructal theory, the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective. The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained. The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate, the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers; the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers, and can help to improve their global thermal insulation performances. The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems, which will help to extend the application range of the entransy dissipation extremum principle.     

Application of entransy dissipation based thermal resistance to design optimization of a novel finless evaporator

Entransy has been applied and studied in a broad range of heat transfer optimizations recently. Current study proposes the entransy of evaporators to conduct the optimization of heat exchangers in heating, ventilation, air conditioning and refrigeration systems. A novel finless bare tube heat exchanger was studied using a validated heat exchanger modeling tool. The capacity based optimization and entransy dissipation based thermal resistance were used and compared. The applicability of using entransy dissipation based thermal resistance in this type of heat exchanger optimization has been discussed. It has been demonstrated that minimizing entransy dissipation and maximizing capacity are equivalent to optimizing evaporators with fixed flow rates and different when optimizing evaporators with variable flow rates and the deviation is negligible when heat exchanger capacity is small (～1 kW) and more obvious as heat exchanger capacity increases. Thus entransy dissipation based thermal resistance could be used as an alternative optimization index to capacity for evaporators with fixed flow rate and small capacity evaporators with variable flow rates and should be used individually with capacity as an optimization index for evaporators with large capacity and variable flow rates.     

基于火积耗散原理的热网加热器优化设计与分析

为使热网加热器具有最优的换热性能,基于粒子群优化算法,以火积耗散数为目标函数,提出热网加热器优化设计的最小火积耗散优化方法.与传统的热网加热器设计计算不同,本文的优化设计不预先设定热网加热器的结构,通过优化确定热网加热器的最佳尺寸,同时,热网加热器优化设计考虑了工质的相变,以潜热修正值对壳侧蒸汽凝结的对流换热系数进行修正.对一热网加热器优化设计结果表明,通过优化设计,热网加热器的效能增加7.8%,同时热网加热器功率消耗下降19.6%,表明当热网加热器的热力性能最优时,其功耗达最小值.     

Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory

Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory. Three types of 3-D circular disc heat sink models, i.e. without collection microchannels, with center collection microchannels, and with edge collection microchannels, are established respectively. Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels, that of circular disc heat sink with center collection microchannels is the minimum, so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages. Furthermore, the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes. With the mass flow rate increasing, both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease. With the heat flux increasing, the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged. With the same mass flow rate and heat flux, the larger the microchannel branch number, the smaller the maximum thermal resistance. While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.     

换热器新评价标准——火积耗散均匀性系数

定义了火积耗散均匀性系数,选用倾角β=30°～70°的复合人字形板式换热器为研究对象,利用三维CFD数值模拟软件ANSYS-CFX模拟分析换热器的火积耗散率、火用损失率以及系统火积耗散均匀性.结果表明:相同流量时,β=30°的复合人字形板式换热器的火用损失率最少;相同换热量时,β=30°的复合人字形板式换热器的火积耗散率最小;相同传热单元数与有效度时,β=30°的复合人字形板式换热器的火积耗散率最小且系统火积耗散均匀性最优.     

Distribution optimization of circulating water in air-cooled heat exchangers for a typical indirect dry cooling system on the basis of entransy dissipation

The flow and heat transfer of air-cooled heat exchangers play important roles in the performance of indirect dry cooling systems in power plants,so it is of benefit to the design and operation of a typical indirect dry cooling system to optimize the thermo-flow characteristics of air-cooled heat exchangers.The entransy dissipation method is applied to the performance optimization of air-cooled heat exchangers in this paper.Two irreversible heat transfer processes in air-cooled heat exchangers,the heat transfer between circulating water and cooling air and the mixing of circulating water,are taken into account and analyzed by means of the entransy dissipation method.The total entransy dissipation rate,which connects the geometrical parameters of air-cooled heat exchanger sectors and the heat capacity rates of the fluids to the heat flow rate in every sector,is obtained.Based on the mathematical relation and the conditional extremum method,an optimization equation group is derived,by which the air-cooled heat exchanger with known air-side parameters is optimized,showing that the entransy dissipation based optimization approach can contribute to the distribution optimization of circulating water in air-cooled heat exchangers of a typical indirect dry cooling system.     

Constructal optimization for a solid-gas reactor based on triangular element

Entropy generation minimization for heat and mass transfer process in a solid-gas reactor is carried out based on constructal theory by using triangular elemental area. The aspect ratio of the triangular elemental area is optimized under constraint conditions. A number of optimal triangular elements are assembled to a new large rectangular area, which is optimised again. The procedure is repeated until the control-volume is covered, and the complete analytical results are obtained. The effects of some parameters on minimum entropy generation are analysed by numerical examples. The results show that smaller entropy generation can be obtained when the optimization for a given volume is carried out on the basis of triangular elements than those obtained on the basis of rectangular elements. Supported by the Program for New Century Excellent Talents in Universities of China (Grant No. NCET-04-1006) and Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)     

倾斜环形空腔内自然对流的实验研究和数值模拟

对大尺寸环形空腔在不同倾斜角度下的自然对流换热进行了实验研究。给出了半径比为2.5,高宽比为38的实验段在0°,22°,45°,67°和90°等角度下的换热关联式,并在水平和竖直情况下进行了数值模拟以便对实验结果进行验证。实验结果表明:在小数下,倾斜角度对自然对流换热的数有较大影响;而在大数下,倾斜角度对数的影响则非常小。最后给出的换热关联式对工程实际中大电流封闭母线的散热设计和校核有重要的参考价值。     

Generalized constructal optimization of strip laminar cooling process based on entransy theory

A strip laminar cooling process is investigated in this paper. Entransy theory and generalized constructal optimization are introduced into the optimization. Total water flow amount(WFA) in the laminar cooling zone(LCZ) and complex function are taken as the constraint and optimization objective, respectively. The entransy dissipation(ED) and maximum temperature different(MTD) of the strip are simultaneously considered in the complex function. WFA distributions of the headers in the LCZ are optimized. The effects of the total WFA, strip thickness and cooling water temperature on the optimal results are analyzed.The optimal cooling scheme is the eleventh cooling mode for the considered total 257 cooling schemes, and the complex function,ED and MTD of the strip are decreased by 11.59%, 5.59% and 17.58% compared with the initial cooling scheme, respectively.The total WFA and strip thickness have the obvious influences on the optimal cooing scheme, but the cooling water temperature has no influence in the parameter analysis range of this paper. The “generalized optimal construct” derived by minimum complex function shows a compromise between the energy retention and quality of the strip.     

Analytical study on coordinative optimization of convection in tubes with variable heat flux

It was certified that the heat transfer between a fluid and a solid wall is closely re-lated to the coordination of the velocity and the temperature gradient/heat flux fields[1,2].When the two fields in a system are fully coordinated, the heat transfer is optimized.Then the highest heat transfer rate is achieved with the least work consumption of fluidflow. Corresponding to the difference of coordination degree, Nusselt number, whichindicates the strength of heat transfer, can change between …     

基于“火积”的喷淋室内气-水热湿交换性能分析

为研究空气饱和程度对换热效果的影响,采用数值模拟方法,计算气体沿等温线、等焓线、等含湿量线向饱和线靠近的过程中全热交换量、"火积"耗散、"火积"耗散热阻、全热交换效率的变化情况。研究发现:气体沿着这三条线逐渐向饱和线靠近时其"火积"耗散热阻始终在减小,全热交换效率在增大。     

空气对水平管内蒸汽强制对流冷凝换热特性的影响

为了研究含空气蒸汽在水平管内强制对流冷凝换热特性,通过实验分析了空气含量及气相流速对局部换热系数的影响;分析了不同空气入口质量分数下,局部换热系数与换热管上、下壁面温度沿换热管轴向的分布规律。结果表明:局部换热系数随空气质量分数的增加而减小,而气相流速的增加会削弱空气对冷凝换热的抑制效果;与纯蒸汽冷凝不同,换热管外下壁面温度会在轴向某一位置后大于上壁面,并且随着入口空气质量分数的增加,该位置逐渐向换热管入口移动;局部换热系数沿轴向变化结果在环状流和波状流条件下存在差异,当空气含量增加时,这种差异会随之减小,使得换热管内局部换热系数轴向变化规律趋于一致。