本研究運用冪次流體作為工作流體，設計一可忽略熱阻之鋁板於兩平行板間並加入迴流裝置，使之成為一邊為固定壁溫度，另一邊為固定熱通量之二行程平板型熱交換器。此系統所推導之統制方程式屬於共軛格拉茲問題 (conjugated Graetz problem)，並運用分離變數法、重疊原理(superposition)及正交展開法(orthogonal expansion technique)，求得於一邊固定壁溫與另一邊固定熱通量混合型邊界條件下之解析解。此外，在理論推導過程中，另定義一包含兩端邊界條件之無因次數（β），其可明顯的影響熱交換器之出口溫度，其值主要決定於一端壁加熱功率以及進口流體溫度與另一邊壁溫差之比值。本研究探討流體冪次指數、迴流比大小、β值、隔板位置等參數對熱傳之影響。結果顯示實驗與理論計算值相符合，並且兩端邊界條件β值越大或流體冪次指數越小時，具有較高的熱傳效率。 The heat-transfer Graetz problem of a double-pass parallel-plate heat exchanger for the power-law flow subject to the hybrid boundary condition, was investigated theoretically. An impermeable barrier without thermal resistance was placed between two parallel plates, whose thermal boundaries were preset at constant temperature at one side, and constant heat flux at the other; it is called the hybrid boundary condition. In order to enhance the device performance, the recycle operation was designed between the flows in the two subchannels. The mathematical model was solved analytically using the separation of variables, together with the superposition principle and an orthogonal expansion in the power series. A dimensionless number (β) is defined as the ratio of the temperature difference between the inlet-flow and the wall at one side over the heat flux at the other side. Both theβvalue and the recycle ratio can render significant influences on the heat transfer efficiency and thus the outlet temperature from the heat exchanger. The experiments were conducted to justified the theoretical simulations. Both the theoretical and experimental results showed that the power law indices play little effect on the heat transfer of the double-pass heat exchanger in this study.
