【机械类毕业论文中英文对照文献翻译】在换热情况下减少管与管发生热传递的方法
【机械类毕业论文中英文对照文献翻译】在换热情况下减少管与管发生热传递的方法,机械类毕业论文中英文对照文献翻译,机械类,毕业论文,中英文,对照,对比,比照,文献,翻译,情况,减少,生热,传递,方法,法子
在换热情况下减少管与管发生热传递的方法Somchai WongwisesChi-Chuan Wang著,陈翔译 摘要:这项研究提出了一个新方法,即在换热情况下,分析管板换热器在完全工作情况下管与管之间的工作状态,在公开的文献里很少见到关于传质系数方面的记载,在充满湿空气情形下,人们发现在焓传热性能和传质性能不受进口湿空气的改变而受影响,不象以前的实验都在干燥的情况下完成,在进行换热时,焓传热性能不是依赖于板的设计,传热和传质性能之比在0.61.0范围内,而且这个比率不受板间隔最小雷诺数改变的影响,当雷诺系数足够高的时候,板间距轻微的改变都会影响比率,由于冷凝物被水蒸汽移动所带来的显著影响,金属板构造的热量和质量性能要求被描叙,这些情况表叙如下:Chilton占89%,Colburnj传热因素在15%以内,和Chilton.Colburn相关的81%传质因素在20%以内。关键字:管板换热器 干燥 传热性能 传质性能命名法: 板的表面积 总表面积 管的内部表面积管的外部表面积内外管温度的饱和曲线平均水温和管壁温度 板表面水温度的饱和曲线 管表面水温度的饱和曲线 湿空气定压比热 水定压比热 管的外径管的内径管内水摩擦因素修正因素 最小流程内混合物的最大流速 传热系数 传质系数内部传热系数外部板的总传热系数第一类贝塞耳系数 空气焓 进口空气焓 平均空气焓出口空气焓 平均焓 进口温度空气焓平均水温的空气焓 出口温度的空气焓 板平均水温的空气焓 板表面温度的空气焓 管内平均水温的平均温度焓 管外平均水温的平均温度焓 雾点的焓 板表面的雾点平均焓 传热因素 传质因素 第二类解决方法 第一类解决方法 板的导热性 水的导热性 管的导热性 管长 空气流量 水流量 管排数 压力 管纵向间距 普朗特常数 管的横向间距 传热率 空气边传热率 平均传热率 总传热率 水边传热率 传热特性与传质特性的比率 相对湿度 板底到中心的距离 内径雷诺数 外径雷诺数 施密特常数 板间距 空气温度 水温度 雾点平均温度 内管平均温度 外管平均温度 水平均温度 板厚度 总传热系数 平均速度 湿空气的湿气比率 平均湿气比率 外管平均湿气饱和率 板因素 散热片效率 动态黏度 质量密度 1:介绍:在空调系统与冷藏系统中换热最广泛地采取管板相结合的方式,换热器往往用于冷凝器和蒸发器中,蒸发器的板最广泛的用铝板制作,其表面温度一般在露点温度之下,结果,热量和质量的传递同时发生在板的表面上,总之,在干燥情况下,管板换热器间复杂的的湿空气流程使得做理论模仿非常的困难,所以,它必须在实验中获得。在换热情况下,许多关于管板换热器的研究实验已经完成,例如:关于介绍管板换热器的McQuiston11.12实验数据,大家都了解的湿表面和干燥表面都相关的传热和摩擦影响,Mirth和Ramauhgyani13.14研究关于换热器的热量与质量特性,他们的研究表明。入口露点温度的改变使Nusselt很剧烈的改变,Nusselt减少和露点温度的增加,FU7也提出了在干燥的换热器中有一个板结构,他们的报告提出在合适的温度下,传热系数会随着入口相对湿度增加而明显下降,相比之下,Seshimo的实验数据表明:Nusselt的入口条件是相对独立的,Wang23研究了在干燥情况下,散热片间距.管列数和入口相对湿度对传热的影响,得出合适的传热相对于独立于入口湿度,现有的文献的差别归因于不同的还原方法。虽然对马口铁进行很多的研究,为设计师区分管板换热器提供的信息非常的有限,这可以由报告数据主要集中在对传热特性的研究,而很少对传质系数的研究来解释,因此,现今的研究的目的是提供更多的.系统的有关传质的实验信息,并提出确定在干燥环境下,管板换热器的空气端活动的新的还原方法,管板空间和入口相对湿度对传质特性在研究中也涉及到。 2:实验设备 空气环路实验图如图1所示,它由离心式鼓风机(7.46Kw 10Hp)造成的空气闭环风洞组成,输气管是由渡锌的钢板于850mm*550mm的横截面组成,进气口的干燥球部分和湿部温度是由空气通风筒所控制的,空气流通率 测量是由出口限制和多喷管组成的,这是爱ASHRAE41.2基础上设定的,测量不同的喷管处压力用不同的压力变换装置,在换热器进口与出口区域的空气湿度是在建立在ASHRAE41.1的两个测冷装置测量的。 工作介质和管边都是水,恒温是由提供设置温度的冷水所控制的,水里的水温是由两个RTD装置测量的,水容率是由精度为0.001L/SZ装置测量的,所以温度是由温度阻抗装置测量,其误差为0.05度,在实验中,唯一令人感到满意的是ASHRAE33781,在最后的分析里提到,管板换热器的详细情况被制成表1L型圈和管板换热器测试紧紧相关,进口空气的实验条件如下,不确定性报告,Moffat15分析被制作成表2。 3 数据分析 3.1热传递系数 基本上当前的分析方法是根据Threlkeld20提出的,对于最初的Threlkeld方法的一些重要数据如下:被用语计算总的传热率的平均表达式为: 全部的传热系数是以Vo,w为基础的,依下列如: 依照Bump和Myers16,对于流程结构,平均焓为 在Eq.4里是未混合其他杂物结构的订正因素,全部的传热系数被涉及到抗热性16,如下: 雷诺数被用于Eq.10和Eq.11是基于直径为1的水管上的,在所以的情况下,水边的运动远少于全部运动的10%,在Eq.8中有4个量(bw.p和bw.m和bp和bm)他们包含焓温度的比率,bp和br能被看作 bw.p和bw.m的价值是饱和的焓曲线被外在的低估了,在粗糙的表面和板面,没有bw.p的损失能接近饱和的焓曲线,在低表面温度测量23下,板效率是以焓的不同为基础的,由Threlkeld20得到is.fm是在低的饱和空气焓温度和is.fb是饱和空气焓在以板为基础的温度,焓的使用率一样,单一的板效率如Kandlikar所举例10一样, 然而湿板效率的最初提出是Threlkeld20给的直板结构,对于一个圆板其效率为: 换热器的测试如图3所示 因此,对应板效率被看作圆板来计算,在图中描叙了bw.m需要实验与错误的程序,is.wm必须计算如下: 解决热传递的系数,管与管,排与排的计算方式如下: 1基于测量数据,计算总传热效率 2 所以的ho.c因素 3 计算传热效率的方法 3.1边传热效率 3.2 出口空气焓 3.3 计算ia.m 3.4 Tp.i.m 和 Tp.o.m 3.6 Tw.m 3.7 计算nf.m 3.8 uo 3.9 is.w.m 3.10 Tw. N是is.w.m 3.11 如果Tw.m在3.10是不相等的,那在3.6假设,计算3.5与3.13,将 会于Tw.m重复,直到Tw.m为常数。 3.12 计算部分Q 3.13 计算Tp.i.m和 Tp.o.m对流传热和加强传热效率 3.14 如果Tp.i.m和 Tp.o.m在3.13不相等,在3.4假设,计算3.5和3.13,将会与Tp.i.m和 Tp.o.m一起重复,直到Tp.i.m和 Tp.o.m是持续 的,3.15 计算Eq1空气汗和出口水温 4 如果Q的总和Qtotai不相等,ho.c将会被假定新的值与计算方式直到相等。3.2 传质系数 对于冷而且非常湿的表面同时包括热传递,可以被描叙为Threlkeld20 R对普遍传热特性有可以比较的特性。 对于管板换热器Eq.18不能正确的表达换热情况,这是因为低的饱和空气焓在板表面不同平均温度为基础的,这方面,程序修改为一个对圆板符合,得出以下各项干燥能源表达式 传热用第二个指示,水的潜热为: 由此得出传热和传质比R被一个运算公式作为Eq.22,可以获得良好的传质性能。3.3 热量和质量传递因素 在换热器中,传热与传质特性被表达如下: 4 结果与讨论板的传热表现和换热器根据叁数 j, 施加给板的影响力的测试的一个典型的情形如图 5所示。在这里, 现在减少管的结果被有 N 一 2 的 Threlkeld 方法所显示。 因为热传递,来自两方法的减少结果的表现几乎是相同的。 这因为现在的管-被-管方式起于 Threlkeld 方法。 从结果所示,板的热传递表现是相对地没有表现出来的。 这一现象相当不同于在完全干的情况先完成的22 和 17, 热传递的表现不依赖板,当 N_4, 在完全干燥的情况操作。 然而, 对于 N 一 1 或 2, 21 显示热传递表现为板间隔的增加而降低。 当雷诺数5,000. 和板的减少的热传递表现增加更加明显。 这一种现象为 N 2, 而且是为 N 一 1 被发现的 espedally. 相反地,现在明显的热传递表现对于 N 一 1 和 2 展现的对于板间隔的变化的没有显著的影响。 显然地,结果被归因于在干燥情况下的浓缩物的出现。这是因为浓缩物为气流式样而改变,粗糙的板表面提供较好的气流的混合效果。结果,板的影响适当地被减少。这一种现象就像是使用可提高的板表面在完全干的情况。 为可提高的表面粗糙程度 ,5 和其他人关于板的报告的可以忽略。因为干燥的 N 一 1 或者 2 移动表现被称如没有限制的j因素, 因为样品 5 和 10 号在图 6 被列举,湿空气对换热器的热传递的影响最初由Threlkeld 方法提出,典型的比较现在的和那之间的特性。 产生使用现在的管与管方法出示 inletrelative 湿气的相对影响较小。 这对1排和2排结构是可以适用的。 相反地,对于最初 Threlkeld 方法的减少的结论,有关热传递表现的20-40%增加到当之前的湿气从 50-90% 被增加的进入物.对于热转移表现, 如之前的所述, 进入物的湿气混合效果几乎可以忽略不计,热传递表现方面的影响也是很小的。 适用于Threlkeld 方法的最初程序和独有的主要表面的效果,结果误差正在略微减少。 现在的管与管之间是更适当的超过在热传递系数方面在完全湿的情况 Threlkeld 方法的最初表现。 Threlkeld 方法和现在的方法之间的结果以热传递率增加表现。 这能从图 7 被清楚地表达出来,由Threlkeld方法和现行方法中样品的入口相对湿度对j的影响正如图7所见的 1000,在这两种方法之间,这个结果偏离较小值,更为重要的是,当 1000时,对现行方法而言,入口湿度的影响可以忽略,尽管如此,我们应该注意到当 1000时,RH=50%时,传质系数的显著上升,这和在水蒸气沿表面冷凝提高更多的空间的较高的下放出冷凝液是分不开的,这个现象随着排除冷凝液管列被随后管列堵塞的树木的上升而消减,干燥过程包含加热和传质之间的类推就比较方便了,这种类推的存在就是因为液体中的传导和扩散是由数字恒等式的自然定律控制的,因此,对空气,水蒸气的混合,的比值通常等于1的,即。在等式19中的形式可近似为像接近大气压的水蒸气一样的稀释单元,等式26的正确性依赖与传质率,Hong和Webb9的实验数据表明这个值在0.7到1.1之间,Seshi等人19给出的是1.1Eckels和Rabas6也得出了相似的值1.1到1.2,因为他们对管板换热器的测试结果有简单的版面几何,已提及的研究都表明了等式26的可用性。在现今研究中,我们应该注意到的值大多在0.6到1.0之间。最初的Threlkeld方法与现行的行列和管列方法有两点不同,首先,当采用Threlkeld方法时会出现较大偏差,这和Threlkeld方法中入口温度的显著影响有关,对现今的简化方法,这个比值在表面全湿时对入口温度的影响不太敏感,其次,简化后的方法说明的比值随雷诺数有微小下降,而原始的方法显示的是相反的趋势,前一节中已提及,随着入口流动惯性的增加,冷凝液可通过进一步的排放提更多空间轻易出除,此状况在板间距减少时更为严重,此条件下,冷凝液的去除在流动惯量较大时,一旦滞留现象消失,有助与大大改善传质。 因此,可见的值随着板间距有微减,如图8所示 管列数为1时的板间距对R的影响值得注意的是此种影响只在雷诺数足够大时才成立,这和较高的流动率会增加蒸汽切应力有关,相反的,板间距对此值的影响在较低雷诺数下相对小,很明显,单一曲线无法描述和的复杂特性,这能从实验的数据 (300 Re5500) 的图 7 被清楚地表达, ih 和 i 的相互关系为: 如图10,11,和12所示, 27 能在 15% ,里面描述 88.9% 的 jh 因素。 28 能使有相互关系 81.2% 的 j 在 20%以内和里面的因素。 29 能使有相互关系 h 的 85.5% 在 20% 里面4. 结论这一项研究是调查管板换热器的传热和传质特性,由以前的结论得出现在的结论:1 分析管的Threlkeld方法在研究中去检验,对于空气完全湿的情况下,它是为两者的传质和传热性能发生改变,即外物对传质性能的影响。2 在完全干燥情况下,板的传热能力是相对独立的,这是因为外物改变空气含量,即更适合换热器的混合特性。3传热和传质性能之比在0.61.0范围内,在版的雷诺数高时,很明显影响传热比。4 相关板的结构为Chilton占89%,Colburnj传热因素在15%以内,和Chilton.Colburn相关的81%传质因素在20%以内。1. 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Wang CC, Lee CJ, Chang CT, Lin SP (1999) Heat transfer and friction correlation for compact louvered fin-and-tube heat exchangers. Int J Heat Mass Transfer 42:1945-1956ORIGINAL Worachest Pirompugd Somchai Wongwises Chi-Chuan Wang A tube-by-tube reduction method for simultaneous heat and mass transfer characteristics for plain fin-and-tube heat exchangers in dehumidifying conditions Received: 19 August 2004/ Accepted: 24 November 2004/Published online: 4 March 2005 C211 Springer-Verlag 2005 Abstract This study proposed a new method, namely a tube-by-tube reduction method to analyze the perfor- mance of fin-and-tube heat exchangers having plain fin configuration under dehumidifying conditions. The mass transfer coecients which seldom reported in the open literature, are also presented. For fully wet con- ditions, it is found that the reduced results for both sensible heat transfer performance and the mass transfer performance by the present method are insensitive to change of inlet humidity. Unlike those tested in fully dry condition, the sensible heat transfer performance under dehumidification is comparatively independent of fin pitch. The ratio of the heat transfer characteristic to mass transfer characteristic (h c,o /h d,o C p,a ) is in the range of 0.6C241.0, and the ratio is insensitive to change of fin spacing at low Reynolds number. However, a slight drop of the ratio of (h c,o /h d,o C p,a ) is seen with the decrease of fin spacing when the Reynolds number is sucient high. This is associated with the more pronounced influence due to condensate removal by the vapor shear. Corre- lations are proposed to describe the heat and mass performance for the present plate fin configurations. These correlations can describe 89% of the Chilton Colburn j-factor of the heat transfer (j h ) within 15% and can correlate 81% of the Chilton Colburn j-factor of the mass transfer (j m ) within 20%. Keywords Fin-and-tube heat exchanger Dehumidifying Sensible heat transfer performance Mass transfer performance Nomenclature A f Surface area of fin A o Total surface area A p,i Inside surface area of tubes A p,o Outside surface area of tubes b p Slope of the air saturation curved between the outside and inside tube wall temperature b r Slope of the air saturation curved between the mean water temperature and the inside wall temperature b w,m Slope of the air saturation curved at the mean water film temperature of the fin surface b w,p Slope of the air saturation curved at the mean water film temperature of the tube surface C p,a Moist air specific heat at constant pressure C p,w Water specific heat at constant pressure D c Tube outside diameter (include collar) D i Tube inside diameter f i In-tube friction factors of water F Correction factor G max Maximum mass velocity based on minimum flow area h c,o Sensible heat transfer coefficient h d,o Mass transfer coefficient h i Inside heat transfer coefficient h o,w Total heat transfer coefficient for wet external fin I o Modified Bessel function solution of the first kind, order 0 I 1 Modified Bessel function solution of the first kind, order 1 i a Air enthalpy i a,in Inlet air enthalpy i a,m Mean air enthalpy i a,out Outlet air enthalpy i g Saturated water vapor enthalpy W. Pirompugd S. Wongwises ( is less than 0.05, where _ Q w is the water-side heat transfer rate for _ Q w and air-side heat transfer rate _ Q a ), are considered in the final analysis. Detailed geometry used for the present plain fin-and-tube heat exchangers is tabulated in Table 1. The test fin-and-tube heat exchangers are tension wrapped having a L type fin collar. The test conditions of the inlet air are as follows: The test conditions approximate those encountered with typical fan-coils and evaporators of air-condition- ing applications. Uncertainties reported in the present investigation, following the single-sample analysis pro- posed by Moat 15, are tabulated in Table 2. 3 Data reduction 3.1 Heat transfer coecient (h c,o ) Basically, the present reduction method is based on the Threlkeld 20 method. Some important reduction pro- Fig. 1 Schematic of experimental setup Dry-bulb temperatures of the air: 270.5C176C Inlet relative humidity for the incoming air: 50% and 90% Inlet air velocity: From 0.3 m/s to 4.5 m/s Inlet water temperature: 70.5C176C Water velocity inside the tube: 1.51.7 m/s 758 cedures for the original Threlkeld method is described as follows. The total heat transfer rate used in the calculation is the mathematical average of _ Q a and _ Q w ; namely, _ Q a _m a (i a;in C0 i a;out ), 1 _ Q w _m w C p;w T w;out C0 T w;in ; 2 _ Q avg _ Q a _ Q w 2 : 3 The overall heat transfer coecient, U o,w , is based on the enthalpy potential and is given as follows: _ Q avg U o;w A o Di m F; 4 where Di m is the mean enthalpy dierence for counter flow coil, Di m i a;m C0 i r;m : 5 According to Bump 4 and Myers 16, for the counter flow configuration, the mean enthalpy is i a;m i a;in i a;in C0i a;out ln i a;in C0 i r;out C0C1C14 i a;out C0i r;in C0C1 C0 i a;in C0 i a;out i a;in C0 i r;out i a;in C0 i r;out C0(i a;out C0 i r;in ; 6 i r;m i r;out i r;out C0 i r;in ln i a;in C0i r;out C0C1C14 i a;out C0 i r;in C0C1 C0 i r;out C0i r;in )(i a;in C0i r;out ) i a;in C0 i r;out )C0i a;out C0i r;in ; 7 where F in Eq. 4 is the correction factor accounting for the present cross-flow unmixed/unmixed configuration. The overall heat transfer coecient is related to the individual heat transfer resistance 16 as follows: 1 U o;w b 0 r A o h i A p;i b 0 p A o ln D c =D i 2pk p L p 1 h o;w A p;o . b 0 w;p A o C16C17 A f g f;wet . b 0 w;m A o C16C17; 8 where h o,w 1 C p;a . b 0 w;m h c;o C16C17 y w =k w ; 9 y w in Eq. 9 is the thickness of the water film. A constant of 0.005 in. was proposed by Myers 16. In practice, (y w /k w ) accounts for only 0.55% compared to (C p,a /b w,m h c,o ), and has often been neglected by previ- ous investigators. As a result, this term is not included in the final analysis. In this study, we had proposed a row-by-row and tube-by-tube reduction method for detailed evaluation of the performance of fin-and-tube heat exchanger in- stead of conventional lump approach. Hence analysis of the fin-and-tube heat exchanger is done by dividing it into many tiny segments (number of tube row number of tube per row number of fin) as shown in Fig. 2.In the analysis, F is the correction factor accounting for a single-pass, cross-flow heat exchanger for one fluid mixed, other fluid unmixed that was shown by Threlkeld 20. The tube-side heat transfer coecient, h i evaluated with the Gnielinski correlation 8, Fig. 2 Dividing of the fin-and-tube heat exchanger into the small pieces Table 2 Summary of estimated uncertainties Primary measurements Derived quantities Parameter Uncertainty Parameter Uncertainty Re Dc =400 Uncertainty Re Dc =5,000 _m a 0.31% Re Dc 1.0% 0.57% _m w 0.5% Re Di 0.73% 0.73% DP 0.5% _ Q w 3.95% 1.22% T w 0.05C176C _ Q a 5.5% 2.4% T a 0.1C176C j 11.4% 5.9% Table 1 Geometric dimensions of the sample plain fin-and-tube heat exchangers No. Fin thickness (mm) Sp (mm) Dc (mm) Pt (mm) Pl (mm) Row no. 1 0.115 1.08 8.51 25.4 19.05 1 2 0.120 1.63 10.34 25.4 22.00 1 3 0.115 1.93 8.51 25.4 19.05 1 4 0.115 2.12 10.23 25.4 19.05 1 5 0.120 2.38 10.34 25.4 22.00 1 6 0.115 1.12 8.51 25.4 19.05 2 7 0.120 1.58 8.62 25.4 19.05 2 8 0.115 1.95 8.51 25.4 19.05 2 9 0.120 3.01 8.62 25.4 19.05 2 10 0.130 2.11 10.23 25.4 22.00 2 11 0.115 1.12 10.23 25.4 19.05 4 12 0.115 1.44 10.23 25.4 19.05 4 13 0.115 2.20 10.23 25.4 19.05 4 14 0.130 2.10 10.23 25.4 22.00 4 15 0.130 1.72 10.23 25.4 22.00 6 16 0.130 2.08 10.23 25.4 22.00 6 17 0.130 3.03 10.23 25.4 22.00 6 759 h i f i =2Re Di C01000Pr 1:0712:7 f i =2 p Pr 2=3 C01 C1 k i D i ; 10 and the friction factor, f i is f i 1 1:58ln Re Di C03:28 2 : 11 The Reynolds number used in Eqs. 10 and 11 is based on the inside diameter of the tube and Re Di qVD i =l: In all case, the water side resistance is less than 10% of the overall resistance. In Eq. 8 there are four quantities (b w,m , b w,p , b p and b r ) involving enthalpy-temperature ratios that must be evaluated. The quantities of b p and b r can be calculated as b 0 r i s;p;i;m C0 i r;m T p;i;m C0T r;m ; 12 b 0 p i s;p;o;m C0 i s;p;i;m T p;o;m C0 T p;i;m : 13 The values of b w,p and b w,m are the slopes of satu- rated enthalpy curve evaluated at the outer mean water film temperature at the base surface and at the fin sur- face. Without loss of generality, b w,p can be approxi- mated by the slope of saturated enthalpy curve evaluated at the base surface temperature 23. The wet fin eciency (g f,wet ) is based on the enthalpy dierence proposed by Threlkeld 20. i.e., g f,wet i C0 i s,fm i C0i s,fb ; 14 where i s,fm is the saturated air enthalpy at the mean temperature of fin and i s,fb is the saturated air enthalpy at the fin base temperature. The use of the enthalpy potential equation, greatly simplifies the fin eciency calculation as illustrated by Kandlikar 10. However, the original formulation of the wet fin eciency by Threlkeld 20 was for straight fin configuration (Fig. 2a). For a circular fin (Fig. 2b), the wet fin eciency is 23, g f;wet 2r i M T (r 2 o C0r 2 i ) C2 K 1 (M T r i )I 1 (M T r o )C0K 1 (M T r o )I 1 (M T r i ) K 1 (M T r o )I 0 (M T r i )K 0 (M T r i )I 1 (M T r o ) C20C21 ; 15 where M T 2h o;w k f t r ; 16 The test heat exchangers are of Fig. 3c configura- tion. Hence, the corresponding fin eciency is calcu- lated by the equivalent circular area method as depicted in Fig. 4. Evaluation of b w,m requires a trial and error proce- dure. For the trial and error procedure, i s,w,m must be calculated using the following equation: i s;w;m i a;m C0 C p;a h o;w g f;wet b 0 w;m h c;o C2 1C0 U o;w A o b 0 r h i A p;i b 0 p ln D c =D i 2pk p L p # ! C2i a;m C0i r;m : 17 An algorithm for solving the sensible heat transfer coecient h c,o for the present row-by-row and tube-by- tube approach is given as follows: 1. Based on the measurement information, calculate the total heat transfer rate _ Q total using Eq. (3). 2. Assume a h c,o for all elements. 3. Calculate the heat transfer performance for each segment with the following procedures. 3.1. Calculate the tube side heat transfer coecient of h i using Eq. 10. 3.2. Assume an outlet air enthalpy of the calculated segment. 3.3. Calculate i a,m by Eq. 6 and i r,m by Eq. 7. 3.4. Assume T p,i,m and T p,o,m . 3.5. Calculate b 0 r A o C0C1 = h i A p;i C0C1 and b 0 p A o ln D c =D i hi = h 2pk p L p C138. 3.6. Assume a T w,m . 3.7. Calculate the g f,wet using Eq. 15. 3.8. Calculate U o,w from Eq. 8. 3.9. Calculate i s,w,m by Eq. 17. 3.10. Calculate T w,m from i s,w,m . Fig. 3 Type of fin configuration Fig. 4 Approximation method for treating a plate fin of uniform thickness 760 3.11. If T w,m derived in step 3.10 is not equal that is assumed in step 3.6, the calculation step 3.7 3.10 will be repeated with T w,m derived in step 3.10 until T w,m is constant. 3.12. Calculate _ Q of this segment. 3.13. Calculate T p,i,m and T p,o,m from the inside convection heat transfer and the conduction heat transfer of tube and collar. 3.14. If T p,i,m and T p,o,m derived in step 3.13 are not equal that is assumed in step 3.4, the calculation step 3.53.13 will be repeated with T p,i,m and T p,o,m derived in step 3.13 until T p,i,m and T p,o,m are constant. 3.15. Calculate the outlet air enthalpy by Eq. 1 and the outlet water temperature by Eq. 2. 3.16. If the outlet air enthalpy derived in step 3.15 is not equal that is assumed in step 3.2, the cal- culation step 3.33.15 will be repeated with the outlet air enthalpy derived in step 3.15 until the outlet air enthalpy is constant. 4. If the summation of _ Q for all elements is not equal _ Q total , h c,o will be assumed a new value and the cal- culation step 3 will be repeated until the summation of _ Q for all elements is equal _ Q total . 3.2 Mass transfer coecient (h d,o ) For the cooling and dehumidifying of moist air by a cold surface involves simultaneously heat and mass transfer, and can be described by the process line equation from Threlkeld 20: di a dW a R i a C0 i s;w W a C0 W s;w i g C02;501R; 18 Where R represent the ratio of sensible heat transfer characteristics to the mass transfer performance. R h c;o h d;o C p;a : 19 However, for the present fin-and-tube heat ex- changer, Eq. 18 did not correctly describe the dehu- midification process on the psychrometric chart. This is because the saturated air enthalpy (i s,w ) at the mean temperature at the fin surface is dierent from that at the fin base. In this regard, a modification of the process line on the psychrometricchart corresponding to the fin-and- tube heat exchanger is made. The derivation is as fol- lows. From the energy balance of the dehumidification one can arrive at the following expression: _m a di a h c;o C p;a dA p;o i a;m C0i s;p;o;m h c;o C p;a dA f i a;m C0 i s;w;m : 20 Note that the first term on the right-hand side de- notes the sensible heat transfer whereas the second term is the latent heat transfer. Conservation of the water condensate gives: _m a dW a h d;o dA p;o W a;m C0 W s;p;o;m h d;o dA f W a;m C0 W s;w;m : 21 Dividing Eq. 20 by Eq. 21 yields di a dW a R C1i a;m C0 i s;p;o;m R C1e C01C1i a;m C0 i s;w;m W a;m C0 W s;p;o;m e C01C1W a;m C0 W s;w;m ; 22 where e A o A p;o : 23 By assuming a value of the ratio of heat transfer to mass transfer, R and by integrating Eq. 22 with an iterative algorithm, the mass transfer coecient can be obtained. Analogous procedures for obtaining the mass transfer coecients are given as: 1. Obtain W s,p,o,m and W s,w,m from i s,p,o,m and i s,w,m from those calculation of heat transfer. 2. Assume a value of R. 3. Calculations is performed from the first element to the last element, employing the following procedures: 3.1. Assume an outlet air humidity ratio. 3.2. Calculate the outlet air humidity ratio of each element by Eq. 22. 3.3. If the outlet air humidity ratio obtained from step 3.2 is not equal to the assumed value of step 3.1, the calculation steps 3.1 and 3.2 will be re- peated. 4. If the summation of the outlet air humidity ratio for each element of the last row is not equal to the measured outlet air humidity ratio, assuming a new R value and the calculation step 3 will be repeated until the summation of the outlet air humidity ratio of the last row is equal to the measured outlet air humidity ratio. 3.3 Chilton-Colburn j-factor for heat and mass transfer (j h and j m ) The heat and mass transfer characteristics of the heat exchanger is presented by the following non-dimensional group: j h h c;o G max C p;a Pr 2=3 ; 24 j m h d;o G max Sc 2=3 : 25 761 4 Results and discussions Heat transfer performance of the fin-and-tube heat exchangers is in terms of dimensionless parameter j h .A typical plot for examination of the influence of fin pitch is shown in Fig. 5. In this figure, the reduced results by the present tube-by-tube method and those by the ori- ginal Threlkeld method having N=2 is shown. For heat transfer performance, reduced results from both meth- ods are nearly the same. This is somehow expected be- cause the present tube-by-tube approach is originated from the Threlkeld method. From the results, one can see that the heat transfer performance is relatively insensitive to the fin pitch. Notice that this phenomenon is quite dierent from that tested in fully dry conditions. As reported by Wang et al. 22 and Rich 17, the heat transfer performance is independent of fin pitch when N 4 operated at fully dry conditions. However, for N=1 or 2, Wang and Chi 21 reported that the heat transfer performance drops with the increase of fin spacing. This is especially pronounced when Re Dc 5,000. For Re Dc 5,000, the heat transfer performance increases with decrease of fin pitch. This phenomenon is seen for N 2, and is espe- cially pronounced for N=1. By contrast, the present sensible heat transfer performance exhibits a compara- tively insensitive influence to the change of fin spacing for N=1 and 2. Apparently, the results are attributed to the presence of condensate under dehumidification. This is because the appearance of condensate plays a role to alter the airflow pattern, roughening the fin surface and providing a better mixing of the airflow. As a conse- quence, the influence of fin pitch is reduced accordingly. This phenomenon is analogous to using the enhanced fin surface in fully dry condition. For enhanced surfaces such as slit and louver fin geometry, Du and Wang 5 and Wang et al. 24, 25 reported a negligible eect of fin pitch even for N=1 or 2. Mass transfer performance of the present dehumidi- fying coils is termed as dimensionless j m factor. For examination of the influence of inlet humidity on the mass transfer characteristics between the present method and that of original Threlkeld method, a typical com- parison for sample no. 5 and 10 is illustrated in Fig. 6. As seen in the figure, results using the present tube-by- tube method show relatively small influence of the inlet relative humidity. This is applicable for both 1-row and 2-row configuration. By contrast, for the reduced results by the original Threlkeld method, one can see about 20 40% increase of mass transfer performance when the inlet relative humidity is increased from 50% to 90%. For the heat transfer performance, as aforementioned previously, the eect of inlet relative humidity is almost negligible regardless the reduction method is chosen. Hence, it is expected that the associated influence on the mass transfer performance is also small. With the ori- ginal procedures of Threlkeld method that was appli- cable to the counter-cross flow arrangement and of exclusive of the eect of primary surface, the reduced results are somewhat misleading. Hence the present tube-by-tube method is more appropriate than the ori- ginal procedures of Threlkeld method in reducing the mass transfer coecient under fully wet conditions. The departure of the reduced results between Threlkeld method and the present method increases with the mass transfer rate. This can be made clear from Fig. 7 with a Fig. 5 Eect of the fin pitch on j h between those derived by Threlkeld method and by present method Fig. 6 Eect of the inlet relative humidity on j m between those derived by Threlkeld method and by present method for samples no. 5 and 10 762 very close fin spacing of 1.08 mm. As seen in Fig. 7 at Re Dc 1,000, the results indicate a departure of the re- duced results for more than 50% between these two methods. Moreover, there is negligible influence of inlet humidity for the present method when Re Dc 1,000 when RH=50%. This is in connection with the blow-o of condensate at larger Re Dc which make more zoom for water vapor to condensate along the surface and even resultis in a partially dry consitions due to the rise of dew point temperature. This phenomenon becomes less pro- nounced with the rise of the number of tube row for condensate blow-o may be blocked by the subsequent tube row. The dehumidifying process involves heat and mass transfer simultaneously, if mass transfer data are unavailable, it is convenient to employ the analogy be- tween heat and mass transfer. The existence of the heat and mass analogy is because the fact that conduction and diusion in a liquid are governed by physical laws of identical mathematical form. Therefore, for air-water vapor mixture, the ratio of h c,o /h d,o C p,a is generally around unity, i.e., h c;o h d;o C p;a C25 1: 26 The term in Eq. 19 approximately equals to unity for dilute mixtures like water vapor in air near the atmo- spheric pressure (temperature well-below corresponding boiling point). The validity of Eq. 26 relies heavily on the mass transfer rate. The experim
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