1.Introduction

The aims of the Experimental Advanced Superconducting Tokamak(EAST)project is to develop a steady-state-capable advanced superconducting tokamak and to establish a scientific and technological basis for nuclear fusion reactors.In the EAST helium liquefaction/refrigeration system,the hot helium gas in the high-pressure channel is cooled by the returning cold vapors through plate- fin heat exchangers(PFHEs)to remove most of the sensible heat[1].PFHEs are efficient and compact heat exchangers that are used in many fields such as chemistry,aerospace,refrigeration and cryogenic industries;they have approximately ten times the surface/volume ratio of conventional tube-shell heat exchangers[2].Unlike room-and high-temperature heat exchangers,cryogenic ones are placed inside the cold box with multilayer insulation and high vacuum to reduce leakage of heat.As the key component in helium lique fiers/refrigerators,the structural size of these PFHEs has great significance for the dimensions of the cold box.Therefore,compactness is an important factor to consider due to space limitations in the cold box.

证明 我们定义由引理2.2可知，f(x)的梯度f(x)的Lipschitz常数L=1且proxg=PC ,proxh=PD。则由三算子分裂

Figure 1.The simplified process flow of the EAST cryogenic system.

The design of heat exchangers is a semi-empirical procedure.The construction type and basic geometries on each fluid side are largely determined by experience,including rules of thumb and Engineering judgments.For various design projects,although the specific performance requirements can be satisfied,the pressure drop,compactness and irreversible heat loss change greatly.Therefore,many studies have recently been dedicated to optimizing the design for different objectives[3].For a series of single objectives,Mishra et al[4],Wen et al[5],Youse fiet al[6–9]and Xie et al[10]used a hybrid genetic algorithm(GA)and other optimization algorithms to optimize PFHEs under various constraints.Additionally,　for　many　multi-objective　optimizations,Babaelahi et al[11],Ahmadi et al[12],Sanaye et al[13],Naja fiet al[14],Youse fiet al[15]and Wen et al[16]provided a set of optimal solutions based on GA and some intelligent approaches to satisfy multiple objectives simultaneously,such as entropy generation,effectiveness,total annual cost,etc.Thus it can be seen that GAs have been widely used for optimizing PFHEs and the optimization capability of this method has been validated by many researchers.

Along with the increase in required cooling capacity for future large-scale refrigerators[17],the size of the cold box will increase accordingly,leading to huge occupied space,high manufacturing costs,high vacuum requirements and long cooling.Therefore,it is necessary to study the thermal hydraulic performance of PFHEs and optimize the volume of these heat exchangers in the refrigerators.Firstly,to reduce the errors caused by the data fitting formula of empirical correlations,a spatial interpolation algorithm based on a few available experimental data is implemented by optimizing the corresponding coefficients.Secondly,strict computational fluid dynamics simulations are carried out to predict the heat transfer and Friction performance in the absence of reliable experimental data.Thirdly,based on hybrid GA,a mathematical model is established to analyze the performance of the heat exchanger and investigate the optimal solutions for the PFHE.Finally,with the model,details of the optimized structural size of the first-stage heat exchanger in the EAST refrigerator are obtained for comparison with the original design size.

真没啥就好了。第二次是我去送小姨。小姨投河死了，我在那儿住了一宿。回来妮儿问我，咋不给她捎包，还是陶大爷好，一来就给她们买糖吃。我问她们陶大爷啥时候走的，两个妮儿争着说，她们还没穿上衣服呢，陶大爷就走了。妮儿小，不知道说瞎话。

2.Thermal modeling

The governing equations for solving the flow and heat transfer problems can be expressed as follows in a uniform format[21]:

一是生活用水带来的污染。生活用水带来的污染主要是生活用水的随意排放造成的，由于水产养殖场周边没有污水处理厂，很多未经处理的生活污水被随意排放在养殖场周边，这就加剧了水污染的程度。

The first stage of the PFHE is characterized by the maximum temperature difference and the greatest size and largely determines the overall structural size of the cold box.Table 1 shows the operating conditions for a counter- flow four-stream PFHE.For the PFHEs widely used in helium liquefaction/refrigeration systems,the hot and cold streams usually have a different number of passages,which lead to complex heat transfer characteristics.For example,the first stage of the PFHE in the EAST refrigerator has a total 66 passages,of which 22 are assigned to the hot HP helium vapor from the compressor while remaining 20,20 and 4 are assigned to the cold LP,SUB-P helium gas and nitrogen gas,respectively.In this section,the equations for measuring the thermal and hydraulic performance and the design criteria for the multi-stream PFHE are presented.

Table 1.Operating conditions for the first stage of the PFHE in the EAST refrigeration system[19].

Maximum allowable pressure drop(kPa)Hot helium　213.26　300　19.5　90.09　1 Cold helium-1　148.51　77.8　1.1　293　3.5 Cold helium-2　48.24　77.8　0.37　293　1.5 Cold nitrogen　57.4　78.8　1.15　293　1 Working fluid　Mass flow rate(g s–1)Inlet temperature(K)　Inlet pressure(bar)　Outlet temperature(K)

Figure 2.Schematic diagrams of the PFHE core(left)and OSFs(right).

2.1.Heat transfer and pressure drop performance

Offset-strip fins(OSFs)are widely used in PFHEs because of the high compactness and substantial heat transfer enhancement.Schematic diagrams of the PFHE core and OSFs are shown in figure 2.The structural parameters include fin height h, fin space s, fin thickness t and interrupted lengthl.The hydraulic diameter for OSFs can be defined as follows[20]:

(1) 坡体地质条件。桑坪隧道进口位于杂谷脑河右岸突出山脊前部，自然坡度约70°～80°，坡向330°，坡高约130 m，主要由夹结晶灰岩的志留系茂县群(Smx2)绢云母石英千枚岩和变质石英砂岩构成，岩层产状350°∠75°，隧道轴线与岩层走向小角度斜交，洞口区主要发育两组节理：J1：产状105°∠60°，延伸3 m～10 m，间距6 m；J2：产状311°∠82°，延伸2.5 m～8.0 m，间距1 m～2 m。节理面微张，有少量泥质充填物。项目区地震动峰值加速度0.20g，地震基本烈度Ⅷ度。桑坪隧道下半球赤平投影图见图5，桑坪隧道工程地质断面图见图6。

Heat transfer areas for one stream can be defined as

and the flow-free areas can be calculated as

创新管理方法是建立科学有效高校国有资产管理机制的重要途径。高校国有资产管理要跟随时代的形势，逐步完善资产管理方式，利用先进科技手段，如计算机、通讯技术、网络技术等实现国有资产的现代化和创新性管理。

The comprehensive surface Efficiency η0considering the primary and secondary heat transfer is defined as

whereAf(m2)andηfrepresent the secondary fin heat transfer area and fin Efficiency,respectively,which can be calculated by

and

To investigate the possible application of the proposed methods,the counter- flow four-stream aluminum PFHE used in the EAST refrigeration system as the first stage of heat exchanger is analyzed.As a PFHE with maximum temperature difference,its heat load reaches 232.58 kW and the original design size is2.200　×0.600　×0.627m.The thicknesses of the separating plates,cover plates and side bars are designed as 1mm,6mm and 30 mm,respectively.In order to accelerate fluid distribution uniformly in the passage,the length of the distributors is set as 0.3 m on each side.The physical properties of fluids and aluminum are selected at the mean temperature.Considering longitudinal heat conduction,which would flatten the temperature distributions in the wall and thus reduce the effectiveness,the margin has been increased by an additional 50%of the heat transfer length according to the effectiveness,capacity rate ratio and longitudinal conduction parameter[2].

2-阴离子聚合形成聚钼酸盐阴离子，控制不同的终点pH值，可得到不同的沉淀物。研究结果表明：当终点pH值为1.5左右时，生成四钼酸铵；当终点pH值为4.5左右时，生成七钼酸铵。其反应式如下：

The heat transfer distance of the fin is revised as follows:

whereA ci(m2)denotes the heat transfer area of cold stream i,Ah(m2)denotes the heat transfer area of the hot stream,Q ci(W)denotes the heat load of cold stream i andQh(W)denotes the heat load of the hot stream.Further,ωis defined as

where α (W m–2K–1)and λf(W m–1K–1)represent the convective heat transfer coefficient and thermal conductivity of the fin,respectively.

The heat transfer coefficient is usually expressed in terms of the Colburn factor,

The fluid–solid coupling model is meshed by the preprocessor GAMBIT v.2.4.6,shown in figure 3.For the commonly used OSFs(95JC1402-05,for which h is 9.5mm,s is 1.4mm,t is 0.2 mm and l is 5mm), figure 4 illustrates the variation trend about j and f in accordance with the grid number.The calculation range covers 0.76,1.22,1.86,3.34,4.04 and 6.01 million grids based on different non-dimensional distances,y+.When the number of grids increases to 4038 300,the deviations compared with the best results(6013 390)are less than 1%for both j and f.Therefore,considering the computational speed and accuracy,the grid numbers of OSFs in this study are determined byy+≤1.5.These simulations have been run on the CentOS 6.7 system,and for each one,248.7 GB of available disk space and the four-node Inter(R)Xeon(R)CPU E5-4620@2.20GHz with 16 cores could be utilized.When the residuals for the flow and energy equations are less than1　×　10-6　and1　×　10-7,respectively,the calculation results are taken as steady.

2.2.Design criteria

The presupposed length of the heat exchanger can be determined by

As is well known,empirical correlations are usually used to measure the performance of PFHEs.However,their prediction errors are not only restricted to the theoretical and experimental measurement errors.Focusing on data fitting processing,a spatial interpolation algorithm based on a kriging approximation model can be constructed through large numbers of reliable experimental data.The fundamental idea of this theory is to use explicit functions to approximate the actual implicit limit state functions[24],which can predict similar features by a kind of linear unbiased and minimum variance estimation in the region covering limited amounts of known information,rather than the complete sample.Therefore,it has a strong ability to forecast information according to limited numbers of available samples.

where the suf fixes,h and ci,denote the hot stream and the other cold streams,respectively.

After the initial dimensions of the heat exchanger are determined,the permitted drop in core pressure can be calculated by

where f denotes the Fanning friction factor.

Generally,it is suggested that the maximum length deviation is set as 10%.The length deviation is expressed by

whereLi(m)represents the length determined by considering the matched heat transfer between the cold stream and hot stream.Lican be worked out using

where(KA)ican be expressed by

When the initial design structure of the PFHE including the length,width and number of stream passages is determined,the original design can be verified by validating the following two criteria:(i)the length deviation is less than 5%;(ii)the pressure drop is lower than the allowed maximum pressure drop.

3.Numerical simulation

Although there are only a few available experimental data appearing in the open literature,simulated results can also provide good performance estimates in the wide range after repeated debugging.

3.1.Numerical model

For the OSF unit,orders of magnitude about the scales between the external structures and inner channels are always meter-scale and millimeter-scale,respectively.To guarantee the flow is fully developed,the studied OSFs have at least 24 rows of periodic fins.

只有老于世故的老太医，久在京城，品级不低，熟悉官场那一套，将赵凤洲一干人的对话一句句听在耳里，记在心中。

As shown in figure 1,the EAST helium cryogenic system mainly consists of a compressor station,cryogenic distribution system and cold box[18].Seven stages of the PFHE—three turbine expanders,cryogenic absorber and filter,cryogenic valves,etc—are installed in the vertical cold box.In the figure,‘HP’stands for high pressure,‘LP’for low pressure,‘SUB-P’forsub-atmosphericpressure, ‘EX’forheat exchanger,‘LN2’for liquid nitrogen,‘LHe’for liquid helium,‘THS’for thermal shield, ‘HTS CL’for high temperature superconducting current leads and ‘PF coils’for poloidal field coils.

whereφrepresents different variables in conservation equations for mass,momentum and energy,respectively.After repeated commissioning,a lowk-εmodel developed by Abid[22]is employed.

In order to obtain solutions from these partial differential equations,commercial software based on the finite-volume method,FLUENT v.15.0,is adopted.A second-order upwind scheme and SIMPLE velocity–pressure combined algorithm is selected to discretize and solve these equations.The mass flow inlet and pressure outlet condition are set as inlet and outlet conditions,respectively.The condition of uniform heat flux boundary is employed on the bottom surface of the upper and lower separating plates.In order to simulate the actual performance of OSFs,periodic boundary conditions are applied to both sides in the physical model,as shown in figure 3.On the interface between solid and fluid,non-slip and coupled thermal boundary conditions are set as the velocity and temperature boundary conditions,respectively.

G(kg m–2s–1),the mass flux,and Reynolds number can be calculated as follows:

3.2.Model validation

A type of OSF(65JC2503-05)from Peng[23]is selected to validate the reliability of the numerical method,as displayed in figure 5.The temperature distribution contour of the fluid flowing through the fin channel is depicted in figure 6 when the Reynolds number reaches 1342.5.In order to evaluate the performance of numerical simulation results,the　root mean　squared　errors(RMSEs),RMSEs=can be used.The RMSEs between the simulated results and experimental data are 3.97%and 5.26%,respectively for factors j and f.Therefore,the numerical method could be used to calculate the heat transfer and friction performance reliably.

Figure 3.Mesh generation of a partial region containing OSF fins and plates.

Figure 4.Grid independence test.

4.Optimization method

4.1.Data fitting based on kriging approximation

Figure 5.Comparison between the experimental and simulated results.

whereQ(W)represents the total heat load,ΔTlog(K)represents the logarithmic mean temperature difference andKA denotes the thermal conductivity of the heat exchanger,which can be expressed by

It can be observed from the curves of the performance characteristics that the trend between the input and output values shows a similar linear behavior near the origin.Hence,available　exponential function scan　better predict the relationship,which can be represented as

Figure 6.Temperature distribution contour.

Figure 7.Flowchart of the optimization method.

wherewjandxjare the jth coordinates of the sample point w and x.θjgives the multiplicative inverse of the correlation length in the jth direction.The accuracy of this model is greatly affected by unknown different coefficient sθjin n dimensions.Lophaven[25]compiled a program to optimize　θj,but its overwhelming dependence on initial values makes it extremely vulnerable to bad results when estimating the range of coefficients improperly.Considering that the choice of coefficientsθjdirectly affects the reliability of the model,the optimalθjcorresponding to maximum likelihood estimation can be obtained by a hybrid GA according to the following minimum optimization function:

where∣R∣is the determinant of R and　2σ　is the process variance.

4.2.Hybrid genetic algorithm

另有研究显示，CgA在NEN细胞的胞质中表达不一致，在某些器官或组织，例如肺、直肠、阑尾等不表达[10]，因此在2013年的美国国立综合癌症网络(NCCN)指南中将其列为诊断NEN的3类证据[11]。而SCGN在直肠、阑尾等部位的NEN中表达，在肺NEN中也呈阳性表达，阳性表达率几乎达到100%。本研究结果显示，在胃和胰腺NEN，SCGN和CgA均高表达，但在肠道NEN中9例SCGN阳性，而CgA均呈阴性表达，提示SCGN联合CgA诊断GEP-NEN可更好地提高检出率。

GAs are a self-organizing,adaptive artificial intelligence technology based on the principle of the process of biological evolution.Because it uses three operators,reproduction,mutation and crossover,GA has been found to have a strong global search ability but a weak local search ability[26].Therefore,in many cases,a suboptimal solution to the problem is likely to be obtained,rather than the optimal solution.

Figure 8.Iteration process for optimizing θ.

Figure 9.Comparison of j and f values from simulations,kriging predictions and empirical correlations.

Table 2.Range of decision variables.

Parameters　Range Total width,L,1(m)　0.26–0.86 Total length,L,2(m)　0–3.6 Fin height,h,i(mm)　[4.7 6.5 9.5]Fin space,s,i(mm)　[1.4 1.7 2]Fin thickness,t,i(mm)　[0.2 0.3 0.4 0.5]Interrupted length,l,i(mm)　[3 4 5]Number of layers,Ni　1–100

A hybrid GA,based on a mature GA and another optimization algorithm,is designed to seek the optimal solution for global performance relatively quickly.In this study,the genetic operators are used to search the population with good performance on a global scale.When the number of evolutions is a multiple of a fixed value N(e.g.10),nonlinear programming would be used to find the optimal solution according to current chromosomes on a local scale.Figure 7 brie fly shows the flowchart of the optimization process.

5.Results and discussion

5.1.Examination of the reliability of the approximation model

To construct an accurate kriging approximation model,264 available data points for factors j and f with 25 types of OSF are collected from Kays[27]and Peng[23].After iterative calculations by hybrid GA,coefficientsθjcorresponding to maximum likelihood estimation are determined as illustrated in figure 8.To further verify the forecasting ability of this model,a type of OSF(65JC1703-05)is used to test the accuracy of the estimation model.Figure 9 shows a comparison of the results of numerical simulations,predictions and empirical correlations[20].The RMSEs between the simulated and predicted results are 4.53%for factor j and 6.17%for factor f,while the errors of j and f values compared with empirical correlations are 6.42%and 15.1%,respectively.Therefore,a kriging model can be used as a more accurate data fitting tool than the typical empirical correlations to forecast results.

5.2.Optimization results

2.1.3 金芪降糖片供试品溶液的制备 精密称取金芪降糖片粉末0.5 g，甲醇定容至50 mL容量瓶，超声提取1 h，称质量，补足质量，进样前0.45 μm微孔滤膜过滤。

Figure 10.Iteration process for minimization of V.

Table 3.Optimization results(mm).

Parameters　L1　L2　h1　s1　t1　l1　N1　h2　s2　t2　l2 Original　600　2200　4.7　2.0　0.3　3　22　9.5　1.4　0.2　3 Optimized　420　1854　4.7　1.7　0.3　4　30　6.5　1.7　0.4　4 Parameters　N2　h3　s3　t3　l3　N3　h4　s4　t4　l4　N4 Original　209.5　2.00.3–　209.51.40.23　4 Optimized　12　6.5　2.0　0.2　4　7　6.5　2.0　0.3　4　2

Table 4.Comparisons of performance parameters from two design schemes.

Original design　Optimized design Parameters Cold nitrogen Heat transfer coefficient(W m–2K–1)　470.58　230.28　103.05　67.05　316.11　490.25　214.05　163.70 Fin Efficiency　0.97　0.57　0.48　0.43　0.98　0.97　0.94　0.95 Heat transfer area(m2)　135.40　302.67　219.94　60.53　78.87　41.74　22.44　6.23 Inlet Reynolds number　741.96　241.41　107.91　553.92　154.94　200.61　152.41　699.91 Pressure drop(kPa)　0.44　2.33　0.56　0.66　0.11　3.47　1.50　0.76 Hot helium Cold helium-1 Cold helium-2 Cold nitrogen Hot helium Cold helium-1 Cold helium-2

As the first stage of the heat exchanger is characterized by the maximum heat load its structure has a huge influence on the size of the cold box in EAST.Therefore,under the constraints of performance requirements,existing manufacturing techniques and structural strength,minimizing the volume of the PFHE is set as the optimization goal;this can be expressed mathematically as follows:

where

为了确保基层农村河道清淤施工的质量，在确定清淤施工所用施工技术的基础上，需要做好必要的施工准备工作，为后续的施工奠定良好条件。具体准备工作要点如下，一是做好施工布置。要本着因地制宜、经济合理和可靠安全等原则，立足于基层农村河道清淤的实际情况，严格依据施工招标文件等来做好施工布置工作。二是组织设计单位、建设单位及监理单位等做好水准点和控制点等的施工测量与放样工作，确保相关淤泥清除表面标高等控制的准确性。三是要做好河道清淤施工中所用设备的良好运行和维护管理，确保设备运行状态良好，为后续的河道清淤奠定良好的施工基础。

面汤清亮，面型整齐，配菜青翠，入口筋道爽滑，面香浓郁挂齿，实乃面中极品。还可以依据自己的口味，酌量添加肉酱、鸡蛋酱、蘑菇酱等卤子调味，一碗下肚，既可饱腹，又能暖身。热乎乎的一碗刀削面，里面蕴含着厚重的山西地域文化，2000多年的削面发展史，在吞咽之间瞬时升华，仿若唇齿之间，都沾染着三晋大地的文化气息。

In order to avoid structural deformation due to the extreme aspect ratio in cross section,the aspect ratio is also constrained in equation(21).Table 2 shows the ranges of independent variables based on the space left in the cold box and existing manufacturing techniques.Additionally,to avoid too high pressure drops dominated by the viscous force and guarantee the prediction accuracy of the thermal hydraulic performance of OSFs,the Reynolds numbers for every stream are constrained above 100.

To handle the constraints in the optimization algorithm,the method of penalty functions is used to let the objective function convert from the constrained problem to an unconstrained one[28].The population size and crossover rate are originally set as 200 and 0.95,respectively.When the tolerance of penalty values is less than 1 × 10–6,the results are considered to have converged.As illustrated in figure 10,the best penalty values are found to be steady at 0.264 after 358 generations.Table 3 provides the detailed parameters.It can be observed　that the structural size is reduced　from 2.200　×0.600　×0.627(m3)to1.854×0.420×0.340(m3)with a large reduction in volume.Unlike the empirical selections of several types of common OSFs and perforated fins,the optimization process considers a database that includes a wide range of OSFs characterized by excellent structural strength.A comparison of performance parameters from two design schemes is illustrated in table 4.The results show that,due to the more accurate performance data fitting tool and global optimization,the heat transfer coefficients of three cold fluids have been greatly improved,thereby causing higher fin heat transfer efficiencies,smaller heat transfer areas and larger core pressure drops.

6.Conclusions

In this study,an approximation model coupled with a hybrid GA is developed to investigate the thermal hydraulic performance of counter- flow FPHEs and optimize the volume of the first stage of the heat exchanger in the EAST refrigerator within the constraints of heat exchange requirements,maximum allowable pressure drop,existing manufacturing techniques　and　sufficient　structural　strength.　The　main conclusions are as follows:

(i)Through optimization of the corresponding coefficients,θ　j,the kriging approximation model can be used as a more accurate data fitting tool than the typical empirical correlations with forecast j and f factors of OSFs,which is also validated by computational fluid dynamics simulations.

星光村现有整栋闲置房屋共32幢，已出租10幢用于改造成新业态。已建成的有星光里咖啡屋、金慧私房菜、成都静纯净文化传播有限公司培训活动室和民宿、DIY巧克力体验馆、罗江组织部两新组织活动阵地、汉文化体验馆、岭上花开文化发展有限公司；在建的有国学培训馆、湖南电视台四川办事处、茶文化体验馆等。

(ii)Based on a hybrid GA,a concrete scheme for optimizing the volume of the multi-stream plate- fin heat exchanger is proposed.By carrying out the optimization,the size of the structure is reduced from 2.200 × 0.600 × 0.627(m3)to 1.854 × 0.420 × 0.340(m3),indicating a large reduction in volume under the constraints of performance requirements,existing manufacturing techniques and structural strength.

(iii)The optimization procedure can be taken as a guidance for practical design.Moreover,the offered design process for PFHEs can be analogized for other types of heat exchanger.

对建立的输电塔有限元模型进行模态分析,可以确定结构的振动特性,得到反映结构动力特性的自振频率和振型.进行模态分析得到钢管塔的前12阶自振频率和振型特征如表1所示,前3阶模态振型如图2所示.由表1和图2可以看出:该钢管塔的1阶、2阶模态振型分别为横向和纵向的弯曲,模态频率相差不大,说明该钢管塔的横向、纵向刚度相差不大;第3阶振型为扭转振型,扭转振型出现在弯曲振型之后.

This work was supported by funds of the Science Foundation within the Institute of Plasma Physics,Chinese Academy of Sciences(No.Y32ETY130B).The authors express their great appreciation to the EAST cryogenic group for their help.

References

[1]Qiu L L et al 2012 Plasma Sci.Technol.14 1030

[2]Hesselgreaves J E 2001 Compact Heat Exchangers,Selection,Design,Operation(Oxford:Pergamon)

[3]Youse fiM et al 2015 Int.Rev.Mech.Eng.9 81

[4]Mishra M,Das P K and Sarangi S 2009 Appl.Therm.Eng.29 2983

[5]Wen J et al 2016 Int.J.Therm.Sci.101 116

[6]Youse fiM,Enayatifar R and Darus A N 2012 Int.Commun.Heat Mass 39 258

[7]Youse fiM,Youse fiM and Darus A N 2012 Proc.Inst.Mech.Eng.A 226 1050

[8]Youse fiM et al 2015 Appl.Therm.Eng.83 71

[9]Youse fiM and Darus A N 2012 Optimal design of plate- fin heat exchangers by particle swarm optimization Proc.SPIE 8350 26

[10]Xie G N,Sunden B and Wang Q W 2008 Appl.Therm.Eng.28 895

[11]Babaelahi M,Sadri S and Sayyaadi H 2014 Chem.Eng.Technol.37 87

[12]Ahmadi P,Hajabdollahi H and Dincer I 2010 J.Heat Trans.133 021801

[13]Sanaye S and Hajabdollahi H 2010 Appl.Energy 87 1893

[14]Naja fiH,Naja fiB and Hoseinpoori P 2011 Appl.Therm.Eng.31 1839

[15]Youse fiM et al 2015 Proc.Inst.Mech.Eng.E 231 164

[16]Wen J et al 2016 Energy Convers.Manage.117

[17]Cheng A Y et al 2016 Plasma Sci.Technol.18 202

[18]Zhu Z G et al 2017 Plasma Sci.Technol.19 055603

[19]Bai H et al 2006 Fusion Eng.Des.81 2597

[20]Manglik R M and Bergles A E 1995 Exp.Therm.Fluid Sci.10 171

[21]Patankar S V 1980 Numerical Heat Transfer and Fluid Flow(New York:McGraw-Hill)

[22]Abid R 1993 Int.J.Eng.Sci.31 831

[23]Peng H and Ling X 2009 Appl.Therm.Eng.29 2251

[24]Sacks J,Schiller S B and Welch W J 1989 Technometrics 31 41

[25]DACE—a Matlab kriging toolbox(http://www2.imm.dtu.dk/projects/dace/)

[26]Holland J H 1976 Adaptation Progress in Theoretical Biology ed R Rosen and F M Snell(New York:Academic)263–93

[27]Kays W M and London A L 1984 Compact Heat Exchangers 3rd edn(New York:McGraw-Hill)

[28]Youse fiM et al 2015 Int.Rev.Model.Simul 8 75