| 摘要: | .對於一組兩端具有迴流效應的平行板逆流熱交換器而言,可將其視為一共軛格拉茲系統, 為尋求其解析解, 吾人使用理論性的方法與性質對系統作一解析, 可望藉此得到合理的解釋與結果。本文的方法, 導致吾人必須求解一共軛邊界問題, 也就是將一般性的單一股流流動問題擴展為多相流動
或多股流流動問題, 因為這些問題的統制方程式(governing
equation)在邊界上呈現聯結的共軛情況, 不似一般的邊界情況可逐一求解。吾人將伴隨於兩股流在邊界及入口處之能量方程式, 以變數分離法使之成為司徒姆 - 呂維爾 (Sturm-Liouville)方程式, 再以數值方式求取特徵值及對應之特徵函數, 利用高斯消去法獲得展開式的係數後, 即可
求得板中之溫度分佈。其結論是:較大格拉茲數之系統, 迴流效應可加強熱傳效果; 以及,較小格拉茲數之系統, 迴流效應對熱傳效果並不顯著。
A theoretical method is described for obtainingion to a conjugated graetz system with the effects of recycle at the ends of a parallel plate counter-flow heat exchanger. The present method leads to necessity of solving conjugated boundary value problems,i.e. extending the single stream problems mentioned above to multiphase or multistream problem.
Since the governing equation in these problems are
coupled throuth conjugated conditions at the boundaries. We do with the system described by the energy eguation associated with the boundary and inlet conditions for the two streams, using the separation of variables leads to a special case of the Sturm-Liouville problem; the eigen-values and the corresponding eigen-functions of the Sturm-Liouville system has been calculated by completely numerical methods. After obtaining the coefficients of expansion by means of Gauss-Elimination , we can get
the temperature profiles in plates. Coming to the
conclusion that the introduction of recycle can enhance the effect of heat transfer for large Graetz number, and that the introduction of recycle will reduce the effect of heat transfer for small Graetz number。 |
