- 學位論文
定熱通量加熱下完全展開層流管流之熵產生分析
Entropy Generation in a Fully Developed Laminar Flow through Ducts with Constant Heat Flux
摘要
本研究之目的在於利用熱力學第一、第二定律，在定壁面熱通量邊界條件下，探討高寬比( )、角度( )、熱通量( )和截面積( )這四個參數對完全展開層流六角形和梯形截面管路之熵產生的影響，並以熵產生最小的方法，分析在不同的參數下，使熱力系統之熵產生最小的最佳雷諾數，以達到最少的可用能損失。 結果得到：隨著雷諾數 增加，熱傳熵產生 逐漸減少，而摩擦熵產生 逐漸增加。由於Re對 和 為相反的效應，因此，存在一最佳的 值( )使得總熵產生最小。當雷諾數 較小時，流場中熵產生主要來自於有限溫差熱傳所引起的熱力學不可逆；而當雷諾數 較大時，流場中熵產生主要來源則為黏滯摩擦所引起的熱力學不可逆。隨著 逐漸增加，總熵產生(Overall Entropy Generation)先逐漸減少，到達熵產生最低值後，又逐漸增加。 不管六角形管或梯形管，在雷諾數 較大時，熵產生和泵巨滫怬㊣H截面積( )或高寬比( )的遞增而遞減；然而，熵產生卻隨著夾角( )或熱通量( )的增大而增大，且泵母H著 增大或 降低而增大。因此，隨著 或 越大，熵產生最小值(Nsmin)就越小，而其對應之最佳雷諾數 越大。隨著 越大， Nsmin越大，且其對應之 也越大。有趣的是不管六角形管或梯形管，由 到 時，熵產生的最小值Nsmin會先降到最低點，之後，從 到 時，會再漸漸的上升，亦即，當 時，Nsmin值最小。此外，六角形管在夾角 和 的情況下，當 <1時，總熵產生隨 值的增加而減少，並在 =1附近達到最低的總熵產生；之後，當 >1時，總熵產生就轉變為隨 值的增加而增加。
並列摘要
Second law analysis of heat transfer in a fully developed laminar flow through hexagonal and trapezoidal cross-sectional ducts with constant heat flux was studied analytically. The influences of four parameters including aspect ratio ( ), included angle ( ), heat flux ( ), and cross-sectional area ( ) on entropy generation were considered based on entropy generation minimization method. The results show that as Re increases, the entropy generation due to heat transfer irreversibility decreases; the entropy generation due to friction irreversibility increases; the overall entropy generation first decreases, then increases after it achieves the minimum entropy generation. In addition, the optimum Reynolds number ( ) with the minimum entropy generation were reported and discussed. Regardless of hexagonal or trapezoidal cross-sectional ducts, for high Re, both entropy generation and pumping power decrease with the increase of cross-sectional area ( ) or aspect ratio ( ). However, both entropy generation and pumping power increase with included angle ( ). Also, entropy generation increases but pumping power decreases with increasing heat flux ( ). Increase in or results in the decrease of the minimum entropy generation (Nsmin) and the increase of its corresponding . A larger amount of heat flux ( ) leads to greater values of Nsmin and . It is of interest to note that irrespective of hexagonal or trapezoidal cross-sectional ducts, when included angle ranges from to , Nsmin decreases gradually, and then increases form to . In other words, at , the value of Nsmin is the lowest. Furthermore, for hexagonal cross-sectional ducts, as <1, the overall entropy generation decreases with increasing . After Nsmin is obtained at =1, as >1, conversely, the overall entropy generation increases with increasing .