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在換熱情況下減少管與管發(fā)生熱傳遞的方法 Somchai WongwisesChi-Chuan Wang著，陳翔譯 摘要：這項研究提出了一個新方法，即在換熱情況下，分析管板換熱器在完全工作情況下管與管之間的工作狀態(tài)，在公開的文獻里很少見到關(guān)于傳質(zhì)系數(shù)方面的記載，在充滿濕空氣情形下，人們發(fā)現(xiàn)在焓傳熱性能和傳質(zhì)性能不受進口濕空氣的改變而受影響，不象以前的實驗都在干燥的情況下完成，在進行換熱時，焓傳熱性能不是依賴于板的設(shè)計，傳熱和傳質(zhì)性能之比在0.6~1.0范圍內(nèi)，而且這個比率不受板間隔最小雷諾數(shù)改變的影響，當雷諾系數(shù)足夠高的時候，板間距輕微的改變都會影響比率，由于冷凝物被水蒸汽移動所帶來的顯著影響，金屬板構(gòu)造的熱量和質(zhì)量性能要求被描敘，這些情況表敘如下：Chilton占89%，Colburnj傳熱因素在15%以內(nèi)，和Chilton.Colburn相關(guān)的81%傳質(zhì)因素在20%以內(nèi)。 關(guān)鍵字：管板換熱器 干燥 傳熱性能 傳質(zhì)性能 命名法： 板的表面積 總表面積 · 管的內(nèi)部表面積 管的外部表面積 內(nèi)外管溫度的飽和曲線 平均水溫和管壁溫度 板表面水溫度的飽和曲線 管表面水溫度的飽和曲線 濕空氣定壓比熱 水定壓比熱 管的外徑 管的內(nèi)徑 管內(nèi)水摩擦因素 修正因素 最小流程內(nèi)混合物的最大流速 傳熱系數(shù) 傳質(zhì)系數(shù) 內(nèi)部傳熱系數(shù) 外部板的總傳熱系數(shù) 第一類貝塞耳系數(shù) 空氣焓 進口空氣焓 平均空氣焓 出口空氣焓 平均焓 進口溫度空氣焓 平均水溫的空氣焓 出口溫度的空氣焓 板平均水溫的空氣焓 板表面溫度的空氣焓 管內(nèi)平均水溫的平均溫度焓 管外平均水溫的平均溫度焓 霧點的焓 板表面的霧點平均焓 傳熱因素 傳質(zhì)因素 第二類解決方法 第一類解決方法 板的導熱性 水的導熱性 管的導熱性 管長 空氣流量 水流量 管排數(shù) 壓力 管縱向間距 普朗特常數(shù) 管的橫向間距 傳熱率 空氣邊傳熱率 平均傳熱率 總傳熱率 水邊傳熱率 傳熱特性與傳質(zhì)特性的比率 相對濕度 板底到中心的距離 內(nèi)徑雷諾數(shù) 外徑雷諾數(shù) 施密特常數(shù) 板間距 空氣溫度 水溫度 霧點平均溫度 內(nèi)管平均溫度 外管平均溫度 水平均溫度 板厚度 總傳熱系數(shù) 平均速度 濕空氣的濕氣比率 平均濕氣比率 外管平均濕氣飽和率 板因素 散熱片效率 動態(tài)黏度 質(zhì)量密度 1：介紹：在空調(diào)系統(tǒng)與冷藏系統(tǒng)中換熱最廣泛地采取管板相結(jié)合的方式，換熱器 往往用于冷凝器和蒸發(fā)器中，蒸發(fā)器的板最廣泛的用鋁板制作，其表面溫度一般在露 點溫度之下，結(jié)果，熱量和質(zhì)量的傳遞同時發(fā)生在板的表面上，總之，在干燥情況下， 管板換熱器間復雜的的濕空氣流程使得做理論模仿非常的困難，所以，它必須在實驗 中獲得。在換熱情況下，許多關(guān)于管板換熱器的研究實驗已經(jīng)完成，例如：關(guān)于介紹 管板換熱器的McQuiston[11.12]實驗數(shù)據(jù)，大家都了解的濕表面和干燥表面都相關(guān)的 傳熱和摩擦影響，Mirth和Ramauhgyani[13.14]研究關(guān)于換熱器的熱量與質(zhì)量特性， 他們的研究表明。入口露點溫度的改變使Nusselt很劇烈的改變，Nusselt減少和露點 溫度的增加，F(xiàn)U[7]也提出了在干燥的換熱器中有一個板結(jié)構(gòu)，他們的報告提出在合 適的溫度下，傳熱系數(shù)會隨著入口相對濕度增加而明顯下降，相比之下，Seshimo的 實驗數(shù)據(jù)表明：Nusselt的入口條件是相對獨立的，Wang[23]研究了在干燥情況下， 散熱片間距.管列數(shù)和入口相對濕度對傳熱的影響，得出合適的傳熱相對于獨立于入 口濕度，現(xiàn)有的文獻的差別歸因于不同的還原方法。雖然對馬口鐵進行很多的研究， 為設(shè)計師區(qū)分管板換熱器提供的信息非常的有限，這可以由報告數(shù)據(jù)主要集中在對傳 熱特性的研究，而很少對傳質(zhì)系數(shù)的研究來解釋，因此，現(xiàn)今的研究的目的是提供更 多的.系統(tǒng)的有關(guān)傳質(zhì)的實驗信息，并提出確定在干燥環(huán)境下，管板換熱器的空氣端 活動的新的還原方法，管板空間和入口相對濕度對傳質(zhì)特性在研究中也涉及到。 2：實驗設(shè)備 空氣環(huán)路實驗圖如圖1所示，它由離心式鼓風機（7.46Kw 10Hp）造成的空氣閉環(huán) 風洞組成，輸氣管是由渡鋅的鋼板于850mm*550mm的橫截面組成，進氣口的干燥球部分和濕部溫度是由空氣通風筒所控制的，空氣流通率 測量是由出口限制和多噴管組成的，這是愛ASHRAE41.2基礎(chǔ)上設(shè)定的，測量不同的噴管處壓力用不同的壓力變換裝置，在換熱器進口與出口區(qū)域的空氣濕度是在建立在ASHRAE41.1的兩個測冷裝置測量的。 工作介質(zhì)和管邊都是水，恒溫是由提供設(shè)置溫度的冷水所控制的，水里的水溫是 由兩個RTD裝置測量的，水容率是由精度為0.001L/SZ裝置測量的，所以溫度是 由溫度阻抗裝置測量，其誤差為0.05度，在實驗中，唯一令人感到滿意的是 ASHRAE33~78[1]，在最后的分析里提到，管板換熱器的詳細情況被制成表1L型 圈和管板換熱器測試緊緊相關(guān)，進口空氣的實驗條件如下，不確定性報告， Moffat[15]分析被制作成表2。 3 數(shù)據(jù)分析 3.1熱傳遞系數(shù) 基本上當前的分析方法是根據(jù)Threlkeld[20]提出的，對于最初的Threlkeld方法的一些重要數(shù)據(jù)如下：被用語計算總的傳熱率的平均表達式為： 全部的傳熱系數(shù)是以Vo,w為基礎(chǔ)的，依下列如： 依照Bump和Myers[16]，對于流程結(jié)構(gòu)，平均焓為 在Eq.4里是未混合其他雜物結(jié)構(gòu)的訂正因素，全部的傳熱系數(shù)被涉及到抗熱性[16]，如下： 雷諾數(shù)被用于Eq.10和Eq.11是基于直徑為1的水管上的，在所以的情況下，水邊的運 動遠少于全部運動的10%，在Eq.8中有4個量（b`w.p和b`w.m和b`p和b`m）他們包含焓 ——溫度的比率，b`p和b`r能被看作 b`w.p和b`w.m的價值是飽和的焓曲線被外在的低估了，在粗糙的表面和板面，沒有 b`w.p的損失能接近飽和的焓曲線，在低表面溫度測量[23]下，板效率是以焓的不同為 基礎(chǔ)的，由Threlkeld[20]得到is.fm是在低的飽和空氣焓溫度和is.fb是飽和空氣焓在以 板為基礎(chǔ)的溫度，焓的使用率一樣，單一的板效率如Kandlikar所舉例[10]一樣， 然 而濕板效率的最初提出是Threlkeld[20]給的直板結(jié)構(gòu)，對于一個圓板其效率為： 換熱器的測試如圖3所示 因此，對應(yīng)板效率被看作圓板來計算，在圖中描敘了b`w.m需要實驗與錯誤的程序， is.wm必須計算如下： 解決熱傳遞的系數(shù)，管與管，排與排的計算方式如下： 1基于測量數(shù)據(jù)，計算總傳熱效率 2 所以的ho.c因素 3 計算傳熱效率的方法 3.1邊傳熱效率 3.2 出口空氣焓 3.3 計算ia.m 3.4 Tp.i.m 和 Tp.o.m 3.6 Tw.m 3.7 計算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假設(shè)，計算3.5與3.13，將 會于Tw.m重復，直到Tw.m為常數(shù)。 3.12 計算部分Q 3.13 計算Tp.i.m和 Tp.o.m對流傳熱和加強傳熱效率 3.14 如果Tp.i.m和 Tp.o.m在3.13不相等，在3.4假設(shè)，計算3.5和 3.13，將會與Tp.i.m和 Tp.o.m一起重復，直到Tp.i.m和 Tp.o.m是持續(xù) 的， 3.15 計算Eq1空氣汗和出口水溫 4 如果Q的總和Qtotai不相等，ho.c將會被假定新的值與計算方式直到相等。 3.2 傳質(zhì)系數(shù) 對于冷而且非常濕的表面同時包括熱傳遞，可以被描敘為Threlkeld[20] R對普遍傳熱特性有可以比較的特性。 對于管板換熱器Eq.18不能正確的表達換熱情況，這是因為低的飽和空氣焓在板表面不同平均溫度為基礎(chǔ)的，這方面，程序修改為一個對圓板符合，得出以下各項干燥能源表達式 傳熱用第二個指示，水的潛熱為： 由此得出傳熱和傳質(zhì)比R被一個運算公式作為Eq.22，可以獲得良好的傳質(zhì)性能。 3.3 熱量和質(zhì)量傳遞因素 在換熱器中，傳熱與傳質(zhì)特性被表達如下： 4 結(jié)果與討論 板的傳熱表現(xiàn)和換熱器根據(jù)叁數(shù) j, 施加給板的影響力的測試的一個典型的情形如圖 5所示。 在這里, 現(xiàn)在減少管的結(jié)果被有 N 一 2 的 Threlkeld 方法所顯示。 因為熱傳遞，來自兩方法的減少結(jié)果的表現(xiàn)幾乎是相同的。 這因為現(xiàn)在的管-被-管方式起于 Threlkeld 方法。 從結(jié)果所示，板的熱傳遞表現(xiàn)是相對地沒有表現(xiàn)出來的。 這一現(xiàn)象相當不同于在完全干的情況先完成的[22] 和 [17], 熱傳遞的表現(xiàn)不依賴板，當 N>_4， 在完全干燥的情況操作。 然而, 對于 N 一 1 或 2, [21] 顯示熱傳遞表現(xiàn)為板間隔的增加而降低。 當雷諾數(shù)<5,000. [21] 解釋為 Saboya 和實驗觀察為基礎(chǔ)的結(jié)果 naphthalene 實驗 18]和換熱器。 他們的結(jié)果指出邊界是最重要的因素, 然而流程慣性的效果發(fā)生是由較高的雷諾數(shù)字控制。 因此, 對于完全干的表面, 板的效果減少為雷諾數(shù)>5,000. 和板的減少的熱傳遞表現(xiàn)增加更加明顯。 這一種現(xiàn)象為 N <2, 而且是為 N 一 1 被發(fā)現(xiàn)的 espedally. 相反地，現(xiàn)在明顯的熱傳遞表現(xiàn)對于 N 一 1 和 2 展現(xiàn)的對于板間隔的變化的沒有顯著的影響。 顯然地，結(jié)果被歸因于在干燥情況下的濃縮物的出現(xiàn)。這是因為濃縮物為氣流式樣而改變,粗糙的板表面提供較好的氣流的混合效果。結(jié)果，板的影響適當?shù)乇粶p少。這一種現(xiàn)象就像是使用可提高的板表面在完全干的情況。 為可提高的表面粗糙程度 ,[5] 和其他人關(guān)于板的報告的可以忽略。 因為干燥的 N 一 1 或者 2 移動表現(xiàn)被稱如沒有限制的j因素， 因為樣品 5 和 10 號在圖 6 被列舉， 濕空氣對換熱器的熱傳遞的影響最初由Threlkeld 方法提出，典型的比較現(xiàn)在的和那之間的特性。 產(chǎn)生使用現(xiàn)在的管與管方法出示 inletrelative 濕氣的相對影響較小。 這對1排和2排結(jié)構(gòu)是可以適用的。 相反地，對于最初 Threlkeld 方法的減少的結(jié)論，有關(guān)熱傳遞表現(xiàn)的20-40%增加到當之前的濕氣從 50-90% 被增加的進入物.對于熱轉(zhuǎn)移表現(xiàn), 如之前的所述, 進入物的濕氣混合效果幾乎可以忽略不計，熱傳遞表現(xiàn)方面的影響也是很小的。 適用于Threlkeld 方法的最初程序和獨有的主要表面的效果，結(jié)果誤差正在略微減少。 現(xiàn)在的管與管之間是更適當?shù)某^在熱傳遞系數(shù)方面在完全濕的情況 Threlkeld 方法的最初表現(xiàn)。 Threlkeld 方法和現(xiàn)在的方法之間的結(jié)果以熱傳遞率增加表現(xiàn)。 這能從圖 7 被清楚地表達出來， 由Threlkeld方法和現(xiàn)行方法中樣品的入口相對濕度對j的影響 正如圖7所見的 1000，在這兩種方法之間，這個結(jié)果偏離較小值，更為重要的是，當 1000時，對現(xiàn)行方法而言，入口濕度的影響可以忽略，盡管如此，我們應(yīng)該注意到當 1000時，RH=50%時，傳質(zhì)系數(shù)的顯著上升，這和在水蒸氣沿表面冷凝提高更多的空間的較高的下放出冷凝液是分不開的，這個現(xiàn)象隨著排除冷凝液管列被隨后管列堵塞的樹木的上升而消減，干燥過程包含加熱和傳質(zhì)之間的類推就比較方便了，這種類推的存在就是因為液體中的傳導和擴散是由數(shù)字恒等式的自然定律控制的，因此，對空氣，水蒸氣的混合，的比值通常等于1的，即。 在等式19中的形式可近似為像接近大氣壓的水蒸氣一樣的稀釋單元，等式26的正確性依賴與傳質(zhì)率，Hong和Webb[9]的實驗數(shù)據(jù)表明這個值在0.7到1.1之間，Seshi等人[19]給出的是1.1Eckels和Rabas[6]也得出了相似的值1.1到1.2，因為他們對管板換熱器的測試結(jié)果有簡單的版面幾何，已提及的研究都表明了等式26的可用性。在現(xiàn)今研究中，我們應(yīng)該注意到的值大多在0.6到1.0之間。 最初的Threlkeld方法與現(xiàn)行的行列和管列方法有兩點不同， 首先，當采用Threlkeld方法時會出現(xiàn)較大偏差，這和Threlkeld方法中入口溫度的顯 著影響有關(guān)，對現(xiàn)今的簡化方法，這個比值在表面全濕時對入口溫度的影響不太敏感， 其次，簡化后的方法說明的比值隨雷諾數(shù)有微小下降，而原始的方法 顯示的是相反的趨勢，前一節(jié)中已提及，隨著入口流動慣性的增加，冷凝液可通過進 一步的排放提更多空間輕易出除，此狀況在板間距減少時更為嚴重，此條件下，冷凝 液的去除在流動慣量較大時，一旦滯留現(xiàn)象消失，有助與大大改善傳質(zhì)。 因此，可見的值隨著板間距有微減，如圖8所示 管列數(shù)為1時的板間距對R的影響 值得注意的是此種影響只在雷諾數(shù)足夠大時才成立，這和較高的流動率會增加蒸汽切應(yīng)力有關(guān)，相反的，板間距對此值的影響在較低雷諾數(shù)下相對小，很明顯，單一曲線無法描述和的復雜特性，這能從實驗的數(shù)據(jù) (300< Re<5500) 的圖 7 被清楚地表達, ih 和 i 的相互關(guān)系為： 如圖10,11,和12所示, 27 能在 15% ，里面描述 88.9% 的 jh 因素。 28 能使有相互關(guān)系 81.2% 的 j 在 20%以內(nèi)和里面的因素。 29 能使有相互關(guān)系 h 的 85.5% 在 20% 里面 4. 結(jié)論 這一項研究是調(diào)查管板換熱器的傳熱和傳質(zhì)特性，由以前的結(jié)論得出現(xiàn)在的結(jié)論： 1 分析管的Threlkeld方法在研究中去檢驗，對于空氣完全濕的情況下，它是為兩者的傳質(zhì)和傳熱性能發(fā)生改變，即外物對傳質(zhì)性能的影響。 2 在完全干燥情況下，板的傳熱能力是相對獨立的，這是因為外物改變空氣含量，即更適合換熱器的混合特性。 3傳熱和傳質(zhì)性能之比在0.6~1.0范圍內(nèi)，在版的雷諾數(shù)高時，很明顯影響傳熱比。 4 相關(guān)板的結(jié)構(gòu)為Chilton占89%，Colburnj傳熱因素在15%以內(nèi)，和Chilton.Colburn相關(guān)的81%傳質(zhì)因素在20%以內(nèi)。 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 42:1945-1956 ORIGINAL 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 coe?cients 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 su?cient 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 Mo?at [15], are tabulated in Table 2. 3 Data reduction 3.1 Heat transfer coe?cient (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: 27±0.5C176C 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: 7±0.5C176C Water velocity inside the tube: 1.5–1.7 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 ), e1T _ Q w ? _m w C p;w eT w;out C0 T w;in T; e2T _ Q avg ? _ Q a t _ Q w 2 : e3T The overall heat transfer coe?cient, U o,w , is based on the enthalpy potential and is given as follows: _ Q avg ? U o;w A o Di m F; e4T where Di m is the mean enthalpy di?erence for counter flow coil, Di m ? i a;m C0 i r;m : e5T According to Bump [4] and Myers [16], for the counter flow configuration, the mean enthalpy is i a;m ? i a;in t i a;in C0i a;out ln i a;in C0 i r;out C0C1C14 i a;out C0i r;in C0C1 C0 ei a;in C0 i a;out Tei a;in C0 i r;out T ei a;in C0 i r;out TC0(i a;out C0 i r;in T ; e6T i r;m ? i r;out t i r;out C0 i r;in ln i a;in C0i r;out C0C1C14 i a;out C0 i r;in C0C1 C0 ei r;out C0i r;in )(i a;in C0i r;out ) ei a;in C0 i r;out )C0ei a;out C0i r;in T ; e7T where F in Eq. 4 is the correction factor accounting for the present cross-flow unmixed/unmixed configuration. The overall heat transfer coe?cient 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 t b 0 p A o ln D c =D i eT 2pk p L p t 1 h o;w A p;o . b 0 w;p A o C16C17 t A f g f;wet . b 0 w;m A o C16C17; e8T where h o,w ? 1 C p;a . b 0 w;m h c;o C16C17 t y w =k w eT ; e9T 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 0.5–5% 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 coe?cient, 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 0.3–1% 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 ? ef i =2TeRe Di C01000TPr 1:07t12:7 ???????? f i =2 p ePr 2=3 C01T C1 k i D i ; e10T and the friction factor, f i is f i ? 1 e1:58ln Re Di C03:28T 2 : e11T 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 ; e12T b 0 p ? i s;p;o;m C0 i s;p;i;m T p;o;m C0 T p;i;m : e13T 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 e?ciency (g f,wet ) is based on the enthalpy di?erence proposed by Threlkeld [20]. i.e., g f,wet ? i C0 i s,fm i C0i s,fb ; e14T 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 e?ciency calculation as illustrated by Kandlikar [10]. However, the original formulation of the wet fin e?ciency by Threlkeld [20] was for straight fin configuration (Fig. 2a). For a circular fin (Fig. 2b), the wet fin e?ciency 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 )tK 0 (M T r i )I 1 (M T r o ) C20C21 ; e15T where M T ? ??????????? 2h o;w k f t r ; e16T The test heat exchangers are of Fig. 3c configura- tion. Hence, the corresponding fin e?ciency 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 t b 0 p ln D c =D i eT 2pk p L p "# ! C2ei a;m C0i r;m T: e17T An algorithm for solving the sensible heat transfer coe?cient 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 coe?cient 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 eT 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 3.5–3.13 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 3.3–3.15 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 coe?cient (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 ei a C0 i s;w T eW a C0 W s;w T tei g C02;501RT; e18T 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 : e19T 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 di?erent 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 ei a;m C0i s;p;o;m Tt h c;o C p;a dA f ei a;m C0 i s;w;m T: e20T 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 eW a;m C0 W s;p;o;m T t h d;o dA f eW a;m C0 W s;w;m T: e21T Dividing Eq. 20 by Eq. 21 yields di a dW a ? R C1ei a;m C0 i s;p;o;m TtR C1ee C01TC1ei a;m C0 i s;w;m T eW a;m C0 W s;p;o;m Ttee C01TC1eW a;m C0 W s;w;m T ; e22T where e ? A o A p;o : e23T 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 coe?cient can be obtained. Analogous procedures for obtaining the mass transfer coe?cients 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 ; e24T j m ? h d;o G max Sc 2=3 : e25T 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 di?erent 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 e?ect 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 e?ect 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 e?ect 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 coe?cient 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 E?ect of the fin pitch on j h between those derived by Threlkeld method and by present method Fig. 6 E?ect 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 di?usion 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: e26T 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