A compulsory element of all textbooks on natural convection has been a detailed similarity analysis for laminar natural convection on a heated semi-infinite vertical plate and a routinely used boundary condition for such analysis is u = 0 at x = 0. The same boundary condition continues to be assumed in related theoretical analyses, even in recent publications. The present work examines the consequence of this long-held assumption, which appears to have never been questioned in the literature, on the fluid dynamics and heat transfer characteristics. The assessment has been made here by solving the Navier-Stokes equations numerically with two boundary conditions—one with constrained velocity at x = 0 to mimic the similarity analysis and the other with no such constraints simulating the case of a heated vertical plate in an infinite expanse of the quiescent fluid medium. It is found that the fluid flow field given by the similarity theory is drastically different from that given by the computational fluid dy...

中文翻译：

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加热垂直板周围自然对流的热流体动力学与标准相似理论的批判性评估

所有自然对流教科书的必修元素是对加热的半无限垂直板上的层流自然对流进行详细的相似性分析，此类分析的常规边界条件是 u = 0 at x = 0。相同的边界条件继续在相关的理论分析中，即使是在最近的出版物中。目前的工作检验了这一长期存在的假设对流体动力学和传热特性的影响，该假设在文献中似乎从未受到质疑。此处的评估是通过使用两个边界条件对 Navier-Stokes 方程进行数值求解来进行的——一个在 x = 0 处具有约束速度以模拟相似性分析，另一个没有此类约束来模拟无限加热垂直板的情况静止流体介质的膨胀。发现相似理论给出的流体流场与计算流体力学给出的流场有很大的不同...