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Convection dimensional analysis

机译：对流尺寸分析

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A modification of the method of inspectional analysis is presented for convective heat transfer applications. Inspectional analysis is used to derive the appropriate non-dimensional groups by non-dimensionalising the governing equations. In the past, this was always achieved by the introduction of boundary conditions into the governing equations and, consequently, it was never clear whether the groups were derived from the equations or the boundary conditions. In the new method presented here, the goveming equations are used to derive the minimum number of groups whitout reference to boundary conditions and to define the non-dimensional dependant and independent variables. These variables are then used to define boundary and initial conditions which in turn generate boundary condition specific groups. The sum of the two grups give the total number of non-dimensional groups. By this means, the method is put on a clearer and more rational footing. Examples are presented for free and forced flows, for a wide range of boundary conditions. These show, for the first time, both the scaling of common convective problems and mathemnatical proof of the derivation of sets of well-known dimensional groups.
机译：提出了对对流传热应用的检验分析方法的修改。检查分析用于通过非维度传播控制方程来导出适当的非尺寸组。在过去，通过将边界条件引入控制方程来始终实现这一点，因此，从不清楚这些组是否源自等式或边界条件。在此处呈现的新方法中，GoVeming方程用于导出最小数量的WHitout参考边界条件，并定义非维度相关和独立变量。然后使用这些变量来定义边界和初始条件，又会生成边界条件特定组。两个GRUPS的总和给出了非维数组的总数。通过这种方式，该方法被置于更清晰，更合理的基础上。用于自由和强制流动的实例，用于各种边界条件。这些节目是，首次进行共同对流问题的缩放和众所周知的尺寸组集的推导的马术证明。

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