优化集中供暖散热器毕业论文外文翻译.docx
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优化集中供暖散热器毕业论文外文翻译.docx
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优化集中供暖散热器毕业论文外文翻译
外文文献原文
Optimizationofacentral-heatingradiator
CihatArslanturkandA.FeridunOzguc
DepartmentofMechanicalEngineering,FacultyofEngineering,AtaturkUniversity,25240Erzurum,Turkey
FacultyofMechanicalEngineering,IstanbulTechnicalUniversity,Gumussuyu,80191Istanbul,Turkey
Abstract
Anapproximateanalyticalmodelhasbeenusedtoevaluatetheoptimumdimensionsofacentral-heatingradiator.Theradiatorproblemisdividedintothreeone-dimensionalfinproblemsandthenthetemperaturedistributionswithinthefinsandheat-transferratefromtheradiatorareobtainedanalytically.Theoptimumgeometrymaximizingtheheat-transferrateforagivenradiatorvolumeandthegeometricalconstraintsassociatedwithproductiontechniques,andthermalconstraintshavebeenfound.Theeffectsofgeometricalandthermalparametersontheradiator’sperformancearepresented.
Keywords:
Centralheating;Optimization;Radiators
1.Introduction
Radiatorsarethemostpopularcentral-heatingemitters.Astheradiatorishotterthantheairsurroundingit,acertainamountofheatistransferredtotheairandthusthewaterexistsatalowertemperature.Ofthevariousdesignsavailableusuallyequippedwithconvectionfinstoimprovetheirheatoutput,arecommonindomestic,businessandindustrialenvironments.Theuseofcentral-heatingradiatorsisthemainformofdomesticheatinginthehomes.Althoughradiatorsareknownasradiator,mostoftheiroutputisbynaturalconvection.Sincetheaveragesurfacetemperatureofacentral-heatingradiatorisgenerallylessthan80 °C,thecontributionofradiativetransfertothetotalheattransferissmallerthanthatofthenaturalconvectionheattransfer.Becauseofthelowsurfacetemperatures,radiationheattransfertermintheenergybalanceequationscanbelinearizedinthethermalanalysisofsucharadiator.Inthepresentpaper,assumingthatthepredominantmodesofheattransferareconductionandconvection,andtheeffectoftheradiationisignored,anapproximatemathematicalmodelisconstructedforfindingtemperaturedistributionandheattransferrate.
Thedesignandoptimizationoftheseradiatorsorfinsandfinassembliesaregenerallybasedontwoapproachesand:
oneistominimizethevolumeormassforagivenamountofheatdissipation,andtheotheristomaximizetheheatdissipationforagivenvolumeormass.Theoptimizationproblemconsideredherefocusesonfindingtheoptimumdimensionsofacentral-heatingradiatormaximizingtheheattransferrateforthegivenvolumeoftheradiatormaterialandgeometricalandthermalconstraints.
2.Mathematicalanalysis
ConsideraradiatorwhichisshownschematicallyinFig.1.Consideringsteady-stateconditionsandneglectingthetemperaturechangeacrossthethickness,wemayassumethatthetemperaturedistributionintheradiatorisone-dimensional,angularinthetubeandaxialinthefins.Assumingthatthepredominantmodesofheattransferareconductionandconvectionandtheeffectofradiationisignored,alinearmathematicalmodelisconsidered.Duetothesymmetricconditions,itissufficientthatquarterpartoftheradiatoristakenintoconsiderationasshowninFig.1.Thissuggeststhattheproblembeinvestigatedintermsofthreedomainsformathematicalconvenience.
Full-sizeimage(23K)
Fig.1. Schematicofthemodelledradiator.
Foreachpartoftheradiator,energybalanceequationsaregivenintheformof
(1)
Invokingthecontinuityoftemperatureandheatcurrentatthejunctions,boundaryconditionsofthegoverningequationscanbeexpressedas:
(2a)
θ1(L1)=θ2(0)(2b)
(2c)
(2d)
(2e)
(2f)
(3a)
(3b)
ThesolutionsofthegoverningequationsgiveninEq.
(1)areexpressedasfollows:
(4)
Usingthewell-knownDittus–Boeltercorrelation,theheat-transfercoefficient,hi,insidethetubeisexpressedintermsofpiperadiusforselectedinnerfluidvelocity.
hi=A(U)0.8(R)0.2(5)
ThecoefficientAinEq.(5)canbecalculatedusingthermo-physicalpropertiesoftheinnerfluid.
ApplyingtheboundaryconditionsgiveninEqs.(2a),(2b),(2c),(2d),(2e)and(2f),theunknowncoefficientsCj,1andCj,2inEq.(4)canbesymbolicallycalculated.
3.Optimizationprocedure
Theobjectivehereistomaximizetheheattransferrateforattainingtheradiatorvolumefractionandheldfixallotherthermalparameters.Thetotalheattransferrate,i.e.objectivefunction,isreadilycalculatedbyapplyingNewton’slawofcoolingbetweenthetubeandtheinnerfluidas:
(6)
Theradiator’svolume-fractionisexpressedasanequalityconstraint.
(7)
Sincetheradiator’sfrontaldimensions,whichmustbeequalorlessthanℓduetotheproductiontechnique,arerestrictedascanbeseeninFig.1,thefollowingequalityconstraintscanbewritten:
(8)
Forsimplicity,selectingδ1 = δ2 = δ3 = δandemployingtheequalityconstraintsgiveninEqs,anobjectivefunctioncanbefoundwithoneindependentvariableofradiatortuberadius,R.ThevalueofRwhichmaximizesthefunctionisobtainedbydifferentiatingthefunctionwithrespecttoRandsettingtheresultequaltozeroandthensolvingthenewresultingequation.
4.Resultsanddiscussion
Itwouldbeofinteresttoexaminetheeffectsofdifferentparameters(suchastuberadius,thicknessesofthefins,heattransferandcoefficients)onthetemperaturedistributions.However,thiswouldrequireprovidingtoomanyexamples.Therefore,onlyoneexampleispresentedthatwillshowthetemperaturedistributionwithinthefinsandthetubewall.Fig.2showsthetemperaturedistributionsforasetofgiventhermalandgeometricalparameters.
Full-sizeimage(36K)
Fig.2. Temperaturedistributionofthethreeradiatorsections.
Theoptimizationprocedurecanbeconductedbylocatingthegeometricalandthermalconditionsthatyieldthetotalheattransferrate.However,theexistenceofsuchavalueshouldfirstbechecked.InFig.3,thedimensionlessheattransferrateisplottedversustuberadiusforthreeinnerfluidvelocities.AclearmaximumheattransferrateisshowninFig.3.Notealsothatforhigherinnerfluidvelocities,themaximumappearsathigherradiuses.
Full-sizeimage(58K)
Fig.3. Heattransferrateversusradiatortuberadiusforthegivenvolumefractionandinnerfluidvelocity.
ThevariationsofmaximumheattransferrateandoptimumdimensionsasafunctionofradiatorvolumefractionareshowninFig.4forthreedifferentenvironmenttemperatures.Asexpected,theincreaseofradiatorvolumefractionincreasesthemaximumheattransferrateandoptimumtubediameter.Assumingthattheflowinsidethetubeisturbulentflow,thewell-knownDittus–Boelterequationwasusedinoptimizationcalculations.ThevaluesoftheoptimumtubediameterspresentedinFig.4havebeenusedforcheckingthevalidityoftheaforesaidassumption.IthasbeenseenthattheinnerfluidflowisturbulentforallcasesinFig.4.
Full-sizeimage(42K)
Fig.4. Theeffectstheinnerfluidtemperatureonoptimumdimensionsandmaximumheattransferrate.
ThevariationsofmaximumheattransferrateandoptimumtuberadiusasafunctionofradiatorvolumefractionforthreedifferentambientfluidtemperaturesareshowninFig.5.ItcanbeseenthatthecurvesshowninFig.5approachanasymptoticvalueoftheheattransferrateatthelargevaluesofradiatorvolumefraction.ThatthemaximumheattransferratedependsonambientfluidtemperaturebutthecorrespondingoptimumtuberadiusdoesnotdependonthisparameterisalsoshowninFig.5.
Full-sizeimage(42K)
Fig.5. Theeffectstheroomtemperatureonoptimumdimensionsandmaximumheattransferrate.
5.Conclusions
Anapproximateanalyticalmodelhasbeenproposedfortheoptimumdesignofcentral-heatingradiatorsinthepresentpaper.Theradiatorproblemhasbeendividedintothreeone-dimensionalfinproblems.Theproblemshavebeensolvedtoevaluatethetemperaturedistributionswithinthefinsusingtheboundaryconditionsoftheradiatorandthecontinuityoftemperatureandheatcurrentatthejunctionsofthefins.Thetemperaturedifferenceshavebeenusedwithintheheattransferratefromtheradiatortotheenvironment.Theoptimumradiatorgeometrymaximizingtheheattransferratehasbeenobtainedbyusingtheapproximateanalyticalmodel.Thepresentoptimizationtechniquecanbeextendedtocentral-heatingradiatorwithmorecomplexgeometry.
中文译文:
优化集中供暖散热器
阿尔斯兰蒂尔克和厄兹居奇
机械工程学院,阿塔图尔克大学,25240埃尔祖鲁姆,土耳其
学院:
机械工程,伊斯坦布尔技术大学,Gumussuyu,80191伊斯坦布尔,土耳其
摘要:
近似解析模型已经被用来评估集中供暖散热器的最佳尺寸。
散热器的问题是被分为三个一维的问题,然后温度分布和来自散热器的热传输速率,得到了很好分析。
优化热传输速率的几何最大限度,是为了给定散热器的数量和与生产技术相关的几何约束。
并且对于热的限制,已经被发现。
现在介绍几何和热参数对散热器的性能的影响。
关键词:
集中供热;优化;散热器
1导言
散热器是最受欢迎的集中采暖设备。
作为散热器,它比周围的空气热,此时一定数额的热量转移到空气,从而水在较低的温度下存在。
对各种可用的设计通常配备对流散热,以改善其热输出,这些设计普遍应用于国内商业、工业领域。
对于集中供暖散热器的使用
主要形式是国内的家居采暖。
尽管散热器被称为散热器,但他们中的大部分是以自然对流的形式输出的。
由于集中采暖散热器的平均表面温度一般情况下低于80℃,所以辐射传热对于总热量的传输的贡献小于自然对流换热。
由于表面温度较低,在对这种散热器的热分析中,对于辐射传热来说,在能量平衡方程中可以线性化。
在本文中,假设的主要模型,传热是传导和对流,辐射对其的影响可以被忽略。
为了测量温度分布和传热率,一种近似的数学模型被构建出来。
设计和优化这些散热器或散热器片,一般是基于两种方法,一种是为了某一特定数量的散热,尽量减少其数量或质量;另一种是为了某一特定的数量或质量,最大限度的增大热耗散。
这里考虑的优化问题的重点是:
根据给定的散热器材料的数量和几何限制、热限制,以找到能最大限度的发挥热传递的集中采暖散热器的最佳尺寸。
2数学分析
在图1中所显示的散热器,考虑到稳定状态的条件和忽略温度在整个厚度边界层上的变化,我们可以假定温度在散热器管的中心线上的分布是一维的。
假设关于传热是传导和对流,以及可以忽略辐射对其的影响,这个结论是正确的。
那么线性数学模型即被认可。
由于平衡的条件,散热器的一部分显示在图1中已经足够了。
这表明,为了数学方便,这个问题在条款的三个领域内会被调查。
Full-sizeimage(23K)
图1散热器示意图
对于散热器的每个部分,能量平衡方程都以以下形式给出
(1)
目前在联结点对温度和热的连续性的引用,边界条件的方程可表示为:
(2a)
θ1(L1)=θ2(0)(2b)
(2c)
(2d)
(2e)
(2f)
(3a)
(3b)
该方程给出了均衡器,
(1)表示如下:
(4)
使用著名的Dittus-Boelter的相关性,为了选定内流速,传热系数、内管都以管半径的形式表示。
hi=A(U)0.8(R)0.2(5)
在如(
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