竖直圆柱常物性层流自然对流的半解析解

The semi-analytic solution of natural convecttion for vertical cylinder with constant physical properties

本文给出了竖圆柱定壁温自然对流问题相似解存在的条件，并用加权残数法得到了半解析解．此解适用于任意Ｄ／Ｌ（圆柱长径比）的情况，且表明：当半径Ｒ→０时，由于自然对流流量的增加，导致了放热系数的增加，以及在足够长的Ｌ处，边界层不仅相似，而且相同，该处的等壁温解与等热流解亦相同．

The conditions of existence of an analogous solution of vertical cylinder's natural convection with constant wall temperature is presented in the paper. A semi-analytic solution has been obtained with the method of weighted residuals, which is suitable for any D/L ratio. The study illustrates: when cylinder radius R →0, the convective heat transfer coefficient increases, accompanying with the increase of natural convation flow and at the position of long L, the boundary layer is similar and equal, leading to an unique solution of both the constant wall tempetature case and the constant heat flow case.