Abstract This article intends to revisit the electro-diffusional theory for the wall shear stress measurement from mass transfer probes of rectangular shape by considering the existence of two components of the wall shear rate (i.e., axial and transversal). General analytical formulas for the effective transfer length and the dimensionless mass transport coefficient were derived as a function of two parameters: a dimensionless angle of the flow direction, relative to the leading edge of the probe, and the aspect ratio between the width and the length of the strip probe. The correctness of the analytical relations for arbitrary flow direction and the aspect ratio was confirmed by numerical solutions of the transport equation in the convective-diffusive regime. It has also been proved that the differences between the Leveque solution and the general analytical formula exhibit a significant deviation for a specific range of parameters. In the case of the three-dimensional boundary layers, in addition to the magnitude of the wall shear stress, the direction of the fluid flow in the vicinity of the probe’s surface is of paramount importance. Accordingly, a measurement methodology is proposed using two strip probes with different aspect ratios. The resulting equations required to quantify the magnitude of the wall shear rate vector and the dimensionless angle are also derived.

中文翻译：

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重新审视壁面剪应力测量的电扩散理论

摘要 本文考虑壁面剪切速率的两个分量（即轴向和横向）的存在，旨在重新审视矩形传质探头壁面剪切应力测量的电扩散理论。有效传输长度和无量纲传质系数的一般分析公式作为两个参数的函数导出：流动方向的无量纲角度，相对于探头的前缘，以及宽度和长度之间的纵横比条状探针。任意流向和纵横比的解析关系的正确性通过对流扩散状态下的输运方程的数值解得到证实。也证明了 Leveque 解与一般解析公式之间的差异对于特定的参数范围表现出显着的偏差。在三维边界层的情况下，除了壁面剪切应力的大小外，探头表面附近的流体流动方向也至关重要。因此，提出了使用具有不同纵横比的两个条形探针的测量方法。还导出了量化壁面剪切速率矢量大小和无量纲角所需的所得方程。探头表面附近的流体流动方向至关重要。因此，提出了使用具有不同纵横比的两个条形探针的测量方法。还导出了量化壁面剪切速率矢量大小和无量纲角所需的所得方程。探头表面附近的流体流动方向至关重要。因此，提出了使用具有不同纵横比的两个条形探针的测量方法。还导出了量化壁面剪切速率矢量大小和无量纲角所需的所得方程。