【正文】 ication, which amounts w10% of the electrical energy consumed worldwide (Malo and Silva, 2021). 2. Mathematical formulation In general, condensers and evaporators for refrigeration applications are designed considering the coil ?ooded with twophase refrigerant, and also a wall temperature equal to the refrigerant temperature (Barbarossa and Hermes, 2021), in such a way as the temperature pro?les along the streams are those represented in Fig. 1. In addition, the outer (., air,water, brine) side heat transfer coef?cient and the physical properties are assumed to be constant. Therefore, the heat transfer rate if calculated from: （ 1） where is the mass ?ow rate, Ti, To and Ts are the inlet, outlet and surface temperatures, respectively, Q 188。 Achaean and Wongwises, 2021。industry 1. Introduction Condensers and evaporators are heat exchangers with fairly uniformwall temperature employed in a wide range of HVACR products, spanning from household to industrial applications. In general, they are designed aiming at acplishing a certain heat transfer duty at the penalty of pumping are two wellestablished methods available for the thermal heat exchanger design, the logmean temperature difference (LMTD) and the effectiveness/number of transfer units (εNTU) approach (Kakac184。附錄 B：參考英文文獻(xiàn)及譯文 Thermodynamic design of condensers and evaporators:Formulation and applications Christian . Hermes a b s t r a c t This paper assesses the thermhydraulic design approach introduced in a previous publication (Hermes, 2021) for condensers and evaporators aimed at minimum entropy generation. An algebraic model which expresses the dimensionless rate of entropy generation as a function of the number of transfer units, the ?uid properties, the thermalhydraulic characteristics, and the operating conditions is derived. Case studies are carried out with different heat exchanger con?gurgitations for smallcapacity refrigeration applications. The theoretical analysis led to the conclusion that a high effectiveness heat exchanger does not necessarily provide the best thermalhydraulic design for condenser and evaporator coils, when the rates of entropy generation due to heat transfer and ?uid friction are of the same order of magnitude. The analysis also indicated that a high aspect ratio heat exchanger produces a lower amount of entropy than a low aspect ratio thermodynamic condenser et desse 180。design。 Leprous et al., 2021。 Pussoli et al., 2021。 To)/2, and the entropy variation, soesi,is calculated from the 2ndlaw of Thermodynamics, （ 5） where the ?rst term in the righthand side accounts for the reversible entropy transport with heat ( _Q=Ts), whereas _Sg is the irreversible entropy generation due to both the heat transfer with ?nite temperature difference and the viscous ow. Substituting Eqs. (1), (3) and (5) into Eq. (4), it follows that: NS 188。 eln(1eε), which is used in Eq. (8) with j 188。 1000 m3h1Ti 188。 $ f 188。 rucDh/m. Fig. 5 pares the dimensionless entropy generation Observed for both surfaces as a function of NTU. A curve ofε 188。 4s/Dh (see Fig. 9b) where St 188。理論分析得出的結(jié)論為高效率換熱器并不一定提供冷凝器和蒸發(fā)器的線圈，最佳的熱工水力設(shè)計時的熱轉(zhuǎn)移和 液體 摩擦的熵產(chǎn)生率的數(shù)量級相同。如今有兩種有效的方法可用于熱換熱器設(shè)計、 溫度平均對數(shù)比和效能 /傳質(zhì)單元數(shù)的辦法，第二個一直是首選，前者主要用于板式換熱器的設(shè)計，為了緊湊式換熱器設(shè)計的有效性，定義為實際的熱傳遞率之間的比率，可以傳輸?shù)淖畲蠼痤~。 在最近的一份出版物中，愛馬仕（ 2021 年）提出一個明確的，代數(shù)的配方，它表示的無量綱熵產(chǎn)率的函數(shù)的傳質(zhì)單元數(shù)流體性質(zhì)水力特性（ j 和 f 曲線），和熱交換器的運(yùn)行條件具有均勻壁溫。兩側(cè)的通道有向下 流的熱流體，然而中間通道有向上流動的冷流體。應(yīng)該指出的，在換熱器的不同區(qū)域，三角形分布器的存在會使熱交換部位每一單元長度都是有區(qū)別的。 數(shù)學(xué)模型基于以下假設(shè)條件可通過能量平衡方程建立： ⑴ 軸向流傳導(dǎo)在流動通道和板上表現(xiàn)不顯著 。 ⑸ 忽略熱損失 。 ⑼ 通過子通道的溫度變化忽略不計。其中一邊通道的控制體的能量平衡方程是： 將方程（ 3）和（ 4）組成方程組，通過方程組來控制換熱器相鄰?fù)ǖ懒黧w的溫度分布。對于這個增加的表面積，冷熱流體的溫度分別是 和 ，我們可以假設(shè)總傳熱系數(shù)可以作為這些溫度的函數(shù)而表示出來。像密度、熱導(dǎo)率等一些其他的流體性質(zhì)與溫度無關(guān)。他們注意到，常數(shù) C 取決于 換熱板 的類型和換熱器的幾何形狀，而常數(shù) n 取決于流體的流態(tài)。 Mehrabian(1996 年 )進(jìn)行了廣泛的研究，從實 驗和理論觀點(diǎn)探究流體動力學(xué)和板式換熱器的熱性能。 結(jié)果和討論 為了得到獨(dú)立網(wǎng)格數(shù)據(jù)結(jié)果 ，程序運(yùn)行時將軸向分為幾個不同的部分。通過實驗結(jié)果表明，軸向部分的數(shù)目為 17。當(dāng)?shù)玫匠隹跍囟葧r，每種流體的性質(zhì)可以由其本身的平均溫度來估算。這種誤差在 范圍內(nèi)，這樣才表明這種數(shù)值法的準(zhǔn)確性。水 苯與水 苯的溫度分布相似，因此，并沒有在圖 2 和 3 中。這種現(xiàn)象的原因是甘油和異辛烷的對流傳熱系數(shù)小于水之間的對流傳熱系數(shù)，因此，它們控制了總傳熱系數(shù)。 U與 T 之間的線性關(guān)系和液體粘度與溫度的關(guān)系都在圖 6 中體現(xiàn)。 換熱器恒定粘度和多變粘度的 關(guān)系圖在圖 9 中。 當(dāng)粘度只受溫度限制時，對于不同的工作流體圖 10 描繪了 圖形