積耗散最小換熱器的優(yōu)化設(shè)計外文翻譯

1、<p><b>　　中文3430字</b></p><p><b>　　外 文 翻 譯</b></p><p>　　積耗散最小換熱器的優(yōu)化設(shè)計</p><p>　　Entransy dissipation minimization for optimization of heat</p><p

2、>　　exchanger design</p><p>　　性 質(zhì): ?畢業(yè)設(shè)計 □畢業(yè)論文</p><p>　　積耗散最小換熱器的優(yōu)化設(shè)計</p><p>　　李雪芳，郭江楓，徐明天&林城;程林學(xué)院熱科學(xué)與技術(shù)，山東大學(xué)，濟(jì)南250061，中國2010年7月16日收到；2011年3月15日接受</p><p>　　摘

3、要：本文以水平衡的逆流換熱器為例，耗散理論應(yīng)用于換熱器的優(yōu)化設(shè)計。在一定的條件下，分析確定最佳的管道縱橫比。當(dāng)傳熱面積或管道的容積是固定的，得到最優(yōu)的質(zhì)量速度和最小耗散率的解析表達(dá)式。結(jié)果表明，若降低換熱器的不可逆耗散，則熱交換面積必須盡可能加大，而質(zhì)量流速應(yīng)盡可能的減少。</p><p>　　關(guān)鍵詞：火積，換熱器，優(yōu)化設(shè)計</p><p>　　由于化石燃料的逐漸枯竭，燃料價格肯定會上漲。

4、因此，能源短缺是預(yù)見到制約經(jīng)濟(jì)和社會發(fā)展的不利因素。提高能源利用效率是解決能源危機(jī)的最有效的方法。換熱器廣泛應(yīng)用于化學(xué)工業(yè)，煉油廠，電力工程，食品工業(yè)，和許多其他領(lǐng)域。因此，通過優(yōu)化設(shè)計提高換熱器的性能，減少不必要的能源消耗是很有價值的。</p><p>　　換熱器優(yōu)化設(shè)計的目的可以分為兩類：一是盡量減少換熱器成本[1-5]；另一是減少基于熱力學(xué)第二定律不可逆而制造的換熱器[6-10]。第一種方法可以降低成本，但

5、可能是以犧牲為代價換熱器性能[11]。第二種方法表示的是最小熵的理論，就是所謂的“熵產(chǎn)悖論”[8,11]。</p><p>　　通過電傳導(dǎo)模擬，郭等人。定義一個新的物理概念，火積，它描述了傳熱性能[ 13 ]?；谶@樣的理念，換熱器的等效熱阻的定義確定換熱器的傳熱不可逆性[ 14 ]。陳等人。應(yīng)用耗散理論的傳導(dǎo)問題[ 15 ]。郭等人。定義一個耗散數(shù)評價換熱器性能，不僅避免了“熵產(chǎn)悖論”，但也可以表征換熱器整體性

6、能[ 12 ]徐等人，[ 16 ]開發(fā)了換熱器有限的壓降下的流摩擦耗散表達(dá)式。</p><p>　　目前，基于耗散的熱傳導(dǎo)有限溫度差和流動摩擦壓降下的問題[ 14，16 ]，郭等人提出的無量綱化方法[ 12 ]。定義了一個全面的耗散數(shù)?？偦鸱e耗散數(shù)為目標(biāo)函數(shù)。假設(shè)我們試圖證明，由于導(dǎo)管的縱橫比或質(zhì)量流速的變化，對兩種積耗散溫差下的熱傳導(dǎo)和流動阻力的影響下引起的有限的壓降，分別都有一個對應(yīng)的最佳管道的縱橫比或質(zhì)量流

7、速。我們還開發(fā)了有公式可循的優(yōu)化管的長徑比和熱交換器，用于優(yōu)化設(shè)計質(zhì)量速度。</p><p><b>　　1耗散數(shù)</b></p><p>　　積定義為一半產(chǎn)品的熱容量和溫度</p><p><b>　　(1)</b></p><p>　　其中T是溫度，qvh是定容熱容量，CP是在恒定壓力下的比熱。

8、現(xiàn)在，使用水平衡的逆流換熱器為例，討論在換熱器中的耗散。</p><p>　　假定冷熱流體的壓縮。進(jìn)氣溫度和熱、冷流體表示為T1和T2的壓力，P1，P2，分別。同樣，出口溫度和壓力是T1，T2和P1，P2。為平衡熱交換器，熱容量率比滿足條件（其中m是質(zhì)量流量）。對于一維換熱器在目前的工作中，通常假設(shè)如穩(wěn)定流動，與環(huán)境無熱交換，并忽略動能和勢能的變化以及縱向傳導(dǎo)了。</p><p>　　在換

9、熱器中，主要存在兩種不可逆性：一是有限的溫度差異下的熱傳導(dǎo)和第二流動摩擦壓降下有限。因熱傳導(dǎo)有限溫差下的耗散率寫為[ 14 ]</p><p><b>　　(2)</b></p><p>　　相應(yīng)的耗散數(shù)定義為[ 12 ]</p><p><b>　　(3)</b></p><p>　　其中Q是傳熱

10、速率，是換熱器效能?被定義為實際的熱傳遞率達(dá)到最大可能的傳熱速率的比值。由于有限的壓降下流動摩擦耗散表示為[ 16 ]</p><p><b>　　(4)</b></p><p>　　在P1和P2指在冷、熱水壓力下降，分別為1和2；有其相應(yīng)的密度。在無量綱形式導(dǎo)致</p><p><b>　　(5)</b></p&g

11、t;<p>　　這是由于水流的摩擦耗散數(shù)。假設(shè)換熱器表現(xiàn)為一個接近理想的換熱器，然后（1-ε）要比團(tuán)結(jié)[ 17 ]小。對于水-水換熱器在通常的操作條件下，熱水和冷水入口之間的溫差，ΔT=T1-T2，小于100 K，因此。因此，方程（5）可簡化為</p><p><b>　　(6)</b></p><p>　　因此，整體的耗散數(shù)變?yōu)?lt;/p>

12、<p><b>　?。?）</b></p><p>　　對于一個典型的水平衡的換熱器，傳熱單元數(shù)NTU可以推出，接近無窮大的效力趨于統(tǒng)一，那么c=1有效[ 17 ]</p><p><b>　?。?）</b></p><p><b>　　在傳熱單元數(shù)定義為</b></p>&l

13、t;p>　　U在這里是總傳熱系數(shù)，A是傳熱面積。假設(shè)固體壁的熱傳導(dǎo)阻力可以忽略，與對流換熱相比，那么它是適當(dāng)?shù)膶α鲹Q熱系數(shù)H.因此取代U。</p><p><b>　?。?a）</b></p><p>　　或者 （9b）</p><p>　　在H1和H2的熱、冷流體，對流換熱系數(shù)

14、是。在近乎理想的換熱器的限制，Ntu遠(yuǎn)大于1，即[ 17 ]</p><p><b>　?。?0）</b></p><p>　　從式（7）整體耗散數(shù)表示為</p><p><b>　?。?1）</b></p><p>　　公式右邊的兩個術(shù)語（11）對應(yīng)于傳熱表面兩側(cè)的火積耗散。每側(cè)，耗散數(shù)可以表示如

15、下</p><p><b>　?。?2）</b></p><p>　　很明顯，耗散熱傳導(dǎo)在有限溫差下，第二耗散流動摩擦壓降下是有限的。為簡單起見，我們使用E不是EI表示耗散數(shù)換熱器表面每一側(cè)。注意，在方程的推導(dǎo)過程中（2）和（4），沒有假設(shè)層流[14,16]；因此，上述結(jié)果的層流和湍流流動是適用的。</p><p><b>　　2參數(shù)

16、優(yōu)化</b></p><p>　　從理論上講，換熱器的有效性增加時，在熱交換器降低不可逆耗散。由于耗散可以用來描述這些不可逆耗散[ 18,19 ]，因此我們尋求管道長徑比與質(zhì)量流速優(yōu)化最小耗散數(shù)E例如方程（12）。</p><p><b>　　2.1最佳長寬比</b></p><p>　　雖然在傳熱表面的一側(cè)耗散數(shù)的總和可以表示為熱

17、傳導(dǎo)的貢獻(xiàn)有限的溫度差和流動摩擦壓降下有限的情況下，這兩個因素對換熱器的不可逆性的影響是強(qiáng)耦合的熱交換器管居住在那邊幾何參數(shù)。因此，基于耗散最小化，可以得到換熱器的最佳管徑比等幾何參數(shù)優(yōu)化。</p><p>　　回憶中的斯坦頓數(shù)St的定義St（（Re）D，pr）和摩擦系數(shù)f（（Re）D）：</p><p><b>　?。?3）</b></p><p

18、><b>　?。?4）</b></p><p>　　其中質(zhì)量速度是G=m/a，L是流動路徑的長度和D是管道的水力直徑。引入無量綱的質(zhì)量流速，，讓</p><p>　　替代式。（13）和（14）代入式（12），我們得到</p><p><b>　?。?5）</b></p><p>　　顯然，導(dǎo)管

19、的縱橫比4L／D有兩個方面對等式的右邊的作用相反例如（15）。因此，存在一個最佳的管道縱橫比減少積數(shù)。當(dāng)雷諾茲數(shù)和質(zhì)量速度是固定的，最大限度地減少耗散數(shù)導(dǎo)致以下表達(dá)式優(yōu)化：</p><p><b>　?。?6）</b></p><p><b>　　相應(yīng)的最小耗散數(shù)</b></p><p><b>　?。?7）&l

20、t;/b></p><p>　　從（16）和（17）可以發(fā)現(xiàn)，最佳管道的縱橫比的降低和質(zhì)量流速G增加，最小耗散數(shù)和無量綱質(zhì)量速度成正比。注意，最小耗散數(shù)也依賴于雷諾茲數(shù)通過F和ST，的雷諾茲數(shù)的最小耗散數(shù)影響很弱，使許多傳熱表面的磨擦系數(shù)斯坦頓數(shù)的比例沒有顯著的變化隨著雷諾茲數(shù)的變化[17 ]。因此，最小耗散數(shù)主要由選定的無量綱質(zhì)量流速確定。顯然，其質(zhì)量速度較小，工作流體較長的存留在傳熱表面和熱交換器存在較

21、低的不可逆耗散。</p><p>　　2.2固定換熱面積下的參數(shù)優(yōu)化</p><p>　　在換熱器設(shè)計，換熱面積是一個重要的考慮因素時，它占了一個換熱器的總成本。因此在這一部分，我們討論的一個固定的傳熱面積和換熱器的優(yōu)化設(shè)計。</p><p>　　從水力直徑的定義，一個側(cè)的傳熱面積是</p><p>　　AC是管道截面。這種表達(dá)可以放在無量綱

22、形式</p><p><b>　?。?8）</b></p><p>　　其中一個是無量綱傳熱面積。替代式（18）代入式（15）的收益率</p><p><b>　?。?9）</b></p><p>　　顯然，無量綱流速有相反的效果兩個方面對等，等式為（19）；因此，存在一個最佳的無量綱流速使熵耗散數(shù)

23、達(dá)到最小值時，A和雷諾茲數(shù)（Re）D。求解該優(yōu)化問題的產(chǎn)生</p><p><b>　?。?0）</b></p><p><b>　?。?1）</b></p><p>　　由上可得（20）和（21）給出最優(yōu)無量綱質(zhì)量速度和最小耗散數(shù)，分別在固定A和雷諾茲數(shù)（Re）D.從這兩方程，較大的傳熱面積明顯對應(yīng)較小的質(zhì)量速度和低的耗

24、散率。因此，需要減少不可逆耗散在熱交換器的傳熱面積，但是必須應(yīng)在條件允許的情況下采用。</p><p>　　假設(shè)E和（Re）D是該換熱器的最小傳熱面積</p><p><b>　　(22)</b></p><p>　　和 （23）</p><p&

25、gt;　　由（22）和（23）可得，我們可以看到一個低的耗散率對應(yīng)于傳熱面積大或?qū)Ч艿目v橫比。得到（21）和（22）是相同的，提供的產(chǎn)品為在給定的雷諾茲數(shù)達(dá)到最小值的表達(dá)式。</p><p>　　2.3參數(shù)優(yōu)化固定導(dǎo)管的體積</p><p>　　在一些空間有限的情況下，如在海洋和航空航天應(yīng)用，通過換熱器占用的空間，在換熱器設(shè)計的一個重要約束。因此，在這一部分，我們討論了換熱器的優(yōu)化設(shè)計固定

26、管體積下的約束</p><p>　　管道體積V=LA可以寫為</p><p><b>　?。?4）</b></p><p>　　其中V是無量綱的體積，是運(yùn)動粘度。替代式（24）代入式（15）整理所得的方程，我們得到</p><p><b>　?。?5）</b></p><p>

27、;　　類似于公式（19），無量綱流速有兩個方面相反的效果對等式（25）。因此，存在一個最佳的無量綱流速允許耗散數(shù)達(dá)到最小值時，V和雷諾茲數(shù)（Re）D。求解該優(yōu)化問題的產(chǎn)生</p><p><b>　?。?6）</b></p><p><b>　?。?7）</b></p><p>　　由上（26）和（27）公式的最優(yōu)無量綱質(zhì)

28、量速度和最小耗散數(shù)，分別在固定V和雷諾茲數(shù)（Re）D.由上（26）和（27）可以看到，管體最大可能導(dǎo)致最低的耗散率和最小質(zhì)量流速。顯然，限制管的體積限制是最可能限制最小耗散率的。</p><p>　　當(dāng)E和（Re）D是固定的，最小管體積</p><p><b>　?。?8）</b></p><p>　　由上（27）和（28）是等價的，產(chǎn)量為產(chǎn)品

29、固定雷諾茲數(shù)下的最小可能值的表達(dá)式。</p><p><b>　　3結(jié)語</b></p><p>　　由水逆流換熱器為例，目前的工作表明，熱交換器的最佳管道縱橫比所決定的雷諾茲數(shù)和流速下，當(dāng)耗散數(shù)作為性能評價標(biāo)準(zhǔn)，分析得到了最優(yōu)的管道縱橫比的公式。固定的傳熱面積的限制下（或管體積）和雷諾茲數(shù)，它表明，存在一個最佳的無量綱流速的解析表達(dá)式；并給出了結(jié)果，如果采用降低換熱

30、器的不可逆耗散，最大可能的傳熱面積和最低的質(zhì)量速度。這一結(jié)論如果是由殼體和耗散數(shù)為目標(biāo)函數(shù)[20]，則可得到管式換熱器優(yōu)化設(shè)計得到的數(shù)值結(jié)果相吻合。</p><p>　　從本研究中得到的結(jié)果，可以看出，傳統(tǒng)換熱器的設(shè)計優(yōu)化，以總費(fèi)用為目標(biāo)函數(shù)通常犧牲換熱器換熱性能。此問題已通過數(shù)值結(jié)果表明[ 11 ]。在本文中[ 11 ]的分析可以看到，換熱器性能的一個小的改進(jìn)可以導(dǎo)致在節(jié)能和環(huán)保方面大的收益。因此，在換熱器設(shè)計

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45、 Han G Z, Guo Z Y. Physical mechanism of heat conduction ability dissipation and its analytical expression (in Chinese). Proc CSEE, 2007, 27: 98–102</p><p>　　20 Guo J F, Li M X, Xu M T, et al. The applicatio

46、n of entransy dissipation theory in optimization design of heat exchanger. In: Proceedings of the 14th International Heat Transfer Conference, Washington, 2010</p><p>　　Entransy dissipation minimization for

47、optimization of heatexchanger design</p><p>　　LI XueFang, GUO JiangFeng, XU MingTian& CHENG LinInstitute of Thermal Science and Technology, Shandong University, Jinan 250061, ChinaReceived July 16, 2010;

48、 accepted March 15, 2011</p><p>　　In this paper, by taking the water-water balanced counterflow heat exchanger as an example, the entransy dissipation theory isapplied to optimizing the design of heat exchan

49、gers. Under certain conditions, the optimal duct aspect ratio is determined analytically.When the heat transfer area or the duct volume is fixed, analytical expressions of the optimal mass velocity and the minimalentrans

50、y dissipation rate are obtained. These results show that to reduce the irreversible dissipation in heat exc</p><p>　　entransy, heat exchanger, optimization design</p><p>　　As fossil fuels are gr

51、adually depleted, fuel prices will surelyrise. As a result, energy shortages are foreseen as a detrimentalfactor that could restrict economic and social development.Improving energy use efficiency is one of the mosteffec

52、tive ways to address an energy crisis. Heat exchangersare widely applied in the chemical industries, petroleumrefineries, power engineering, food industries, and manyother areas. Therefore, it will be of great value to r

53、educeneedless energy dissipation and i</p><p>　　The objectives in heat exchanger design optimization canbe classified into two groups: one is minimizing costs ofheat exchangers [1–5]; the other is minimizing

54、 irreversibilitybased on the second law of thermodynamics that occursin heat exchangers [6–10]. The first approach can reducecosts, but possibly at the expense of sacrificing heat exchangerperformance [11]. As representa

55、tive of the secondapproach, entropy generation minimization suffers fromso-called “entropy generation paradox” [8,12].</p><p>　　By analogy with electrical conduction, Guo et al. defineda new physical concept

56、, entransy, which describes heattransfer capability [13]. Based on this concept, the equivalentthermal resistance of a heat exchanger was defined toquantify heat transfer irreversibility in heat exchangers[14].Chen et al

57、. applied entransy dissipation theory to thevolume-to-pointconduction problem[15]. Guo et al. defined anentransy dissipation number to evaluate heatexchangerperformance that not only avoids the “entrop</p><p&g

58、t;　　The present work, based on expressions of entransy dissipationfrom heat conduction under finite temperature differencesand flow friction under finite pressure drops [14,16], and on the dimensionless method proposed b

59、y Guo etal. [12], defines an overall entransy dissipation numbers.The minimum overall entransy dissipation number is thentaken as an objective function. Under certain assumptionswe attempt to prove that since the variati

60、on in the duct aspectratio or mass velocity has opposing effects</p><p>　　1 Entransy dissipation number</p><p>　　The entransy is defined as one-half the product of heat capacity and temperature

61、[13]:</p><p><b>　　(1)</b></p><p>　　where T is the temperature, Qvh is the heat capacity at constant volume, and cp is the specific heat at constant pressure.Now, using the water-wate

62、r balanced counter-flow heatexchanger as an example, we attempt to discuss the entransydissipation in heat exchangers.</p><p>　　Assume that both the hot and cold fluids are incompressible.The inlet temperatu

63、re and pressure of the hot andcold fluids are denoted as T1, P1 and T2, P2, respectively.Similarly the outlet temperature and pressure are T1,out, P1,outand T2,out, P2,out. For the balanced heat exchanger, the heatcapaci

64、ty rate ratio satisfies condition(where m is the mass flow rate). For the one-dimensionalheat exchanger considered in the present work, the usualassumptions such as steady flow, no heat exchange withen</p><p&g

65、t;　　In the heat exchanger, there mainly exist two kinds of irreversibility:the first is heat conduction under finite temperaturedifferences and the second is flow friction under finite pressure drops. The entransy dissip

66、ation rate caused by heat conduction under a finite temperature difference iswritten as [14]</p><p><b>　　(2)</b></p><p>　　The corresponding entransy dissipation number is defined as

67、[12]</p><p><b>　　(3)</b></p><p>　　where Q is the heat transfer rate, is the heat exchangereffectiveness which is defined as the ratio of the actual heattransfer rate to the maximum p

68、ossible heat transfer rate. The entransy dissipation due to flow friction under a finite pressuredrop is expressed as [16]</p><p><b>　　(4)</b></p><p>　　where P1 and P2 refer to the p

69、ressure drops in the hot and cold water, respectively; 1 and 2 are their corresponding densities. Putting in dimensionless form leads to</p><p><b>　　(5)</b></p><p>　　which is called

70、the entransy dissipation number due to flow friction. Assuming that the heat exchanger behaves as a nearly ideal heat exchanger, then (1-ε) is considerably smaller than unity [17]. For a water-water heat exchanger under

71、usual operating conditions, the inlet temperature difference between hot and cold water，ΔT=T1-T2，小于100 K, is less than 100 K,hence There fore, eq. (5) can be simplified to</p><p><b>　　(6)</b><

72、/p><p>　　Accordingly, the overall entransy dissipation number becomes</p><p><b>　　(7)</b></p><p>　　For a typical water-water balanced heat exchanger, the number of heat tra

73、nsfer units Ntu can be introduced, which approaches infinity as the effectiveness tends to unity. Since c=1, the effectiveness is [17]</p><p><b>　　(8)</b></p><p>　　where the number o

74、f heat transfer units is defined as</p><p>　　Here U is the overall heat transfer coefficient, and A is the heat transfer area. Assuming that the heat conduction resistance of the solid wall can be neglected,

75、 compared with the convective heat transfer, then it is appropriate to replace U with the convective heat transfer coefficient h. Therefore</p><p><b>　　(9a)</b></p><p>　　or

76、 (9b)</p><p>　　where h1 and h2 are the convective heat transfer coefficients of the hot and cold fluids, respectively, andNtu hA mc i i ii . In the nearly ideal heat exchangerlimit, Ntu＞1,

77、 that is [17]</p><p><b>　　(10)</b></p><p>　　from eq. (7) the overall entransy dissipation number is expressed as</p><p><b>　　(11)</b></p><p>　　T

78、he two terms on the right of eq. (11) correspond to the entransy dissipations of two sides of heat transfer surfaces. For each side, the entransy dissipation number can be expressed as follows:</p><p><b&

79、gt;　　(12)</b></p><p>　　It is evident that the first term accounts for the entransy dissipationfrom the heat conduction under finite temperaturedifference and the second for the entransy dissipation fro

80、m flow friction under finite pressure drop. For simplicity, we now use E instead of Ei to denote the entransy dissipation number for each side of the heat exchanger surface. Note that in the derivations of eqs. (2) and (

81、4), there is no assumption that the flow is laminar [14,16]; therefore, the above results are applicab</p><p>　　2 Parameter optimization</p><p>　　Theoretically, the exchanger effectiveness incre

82、ases when the irreversible dissipation in the heat exchanger decreases. Since the entransy dissipation can be used to describe these irreversible dissipations [18,19], therefore we seek optimums in duct aspect ratio and

83、mass velocity by minimizing the entransy dissipation number E based on eq. (12).</p><p>　　2.1 The optimum aspect ratio</p><p>　　Although the entransy dissipation number on one side of a heat tr

84、ansfer surface can be expressed as the sum of the contributions of the heat conduction under the finite temperature difference and flow friction under the finite pressure drop, the effects of these two factors on heat ex

85、changer irreversibility are strongly coupled through the geometric parameters of the heat exchanger tube residing on that side. Therefore, based on entransy dissipation minimization, it is possible to obtain optimal</

86、p><p>　　Recall the definition of the Stanton number St((Re)D,Pr) and friction factor f((Re)D):</p><p><b>　　(13)</b></p><p><b>　　(14)</b></p><p>　　w

87、here G=m/a is the mass velocity, L is the flow path length and D is the duct hydraulic diameter. Introducing the dimensionless mass velocity, , letting</p><p>　　and substituting eqs. (13) and (14) into eq. (

88、12), we obtain</p><p><b>　　(15)</b></p><p>　　Clearly, the duct aspect ratio 4L/D has opposing effects onthe two terms of the right side of eq. (15). Therefore, there exists an optima

89、l duct aspect ratio to minimize the entransynumber. When the Reynolds number and mass velocity are fixed, minimizing the entransy dissipation number leads to the following expression for this optimum:</p><p>

90、;<b>　　(16)</b></p><p>　　The corresponding minimum entransy dissipation number is</p><p><b>　　(17)</b></p><p>　　From eqs. (16) and (17), one can see that the

91、optimal duct aspect ratio decreases as the mass velocity G* increases, and the minimum entransy dissipation number is directly proportional to the dimensionless mass velocity. Note that the minimum entransy dissipation n

92、umber is also dependent on the Reynolds number via f and St. However, the impact of the Reynolds number on the minimum entransy dissipation number is very weak since for many heat transfer surfaces the ratio of the frict

93、ion factor to </p><p>　　2.2 Parameter optimization under fixed heat transfer area</p><p>　　In designing a heat exchanger, the heat transfer area is anim portant consideration when it accounts fo

94、r most of the total cost of a heat exchanger. Thus in this subsection, we discuss design optimization of the heat exchanger with a fixed heat transfer area.</p><p>　　From the definition of the hydraulic diam

95、eter, the heattransfer area for one side is</p><p>　　where Ac is the duct cross-section. This expression can be put in dimensionless form as</p><p><b>　　(18)</b></p><p>

96、　　where A is the dimensionless heat transfer areaSubstituting eq. (18) into eq. (15) yields</p><p><b>　　(19)</b></p><p>　　Obviously, the dimensionless mass velocity has an opposing e

97、ffect on the two terms of the right side of eq.(19); thus, there exists an optimal dimensionless mass velocity which allows the entropy dissipation number to reach a minimum value when A* and Reynolds number (Re)D are gi

98、ven. Solving this optimization problem yields</p><p><b>　　(20)</b></p><p><b>　　(21)</b></p><p>　　Eqs. (20) and (21) give the optimal dimensionless mass veloc

99、ity and the minimum entransy dissipation number, respectively, under fixed A* and Reynolds number (Re)D. From these two equations, the larger heat transfer area clearly corresponds to the smaller mass velocity and lower

100、entransy dissipation rates. Hence, to reduce the irreversible dissipation occurring in a heat exchanger, the largestpossible heat transfer area should be adopted under the allowable conditions.</p><p>　　If

101、E and (Re)D are given, the minimum heat transfer area is</p><p><b>　　(22)</b></p><p>　　Or (23)</p><p>　　From eqs. (22) and (23),

102、one can see that a low entransy dissipation rate corresponds to large heat transfer area or duct aspect ratio. Eqs. (21) and (22) are identical, providing an expression for the minimum attainable value for the productund

103、er the given Reynolds number.</p><p>　　2.3 Parameter optimization under fixed duct volume</p><p>　　In some space-limited situations, such as in marine and aerospace applications, space occupied

104、by a heat exchanger is an important constraint on the heat exchanger design. Therefore, in this subsection, we discuss design optimization of heat exchangers under the fixed duct volume constraint.</p><p>　　

105、The duct volume V=LA can be written as</p><p><b>　　(24)</b></p><p>　　where V* is the dimensionless volume,,is the kinematic viscosity. Substituting eq. (24) into eq. (15) and rearran

106、ging the resulting equation, we obtain</p><p><b>　　(25)</b></p><p>　　Similar to eq. (19), the dimensionless mass velocity has an opposing effect on the two terms of the right side of

107、 Eq. (25). Therefore, there exists an optimal dimensionless mass velocity that allows the entransy dissipation number to obtain a minimum value when V* and Reynolds number (Re)D are given. Solving this optimization probl