Abstract The effect of the tangential conduction contribution in a thermally anisotropic heated-thin-foil heat flux sensor is examined. A parameter to assess the degree of importance of tangential conduction in the sensor is defined and evaluated in order to justify the need of tangential conduction corrections. Printed circuit boards (PCBs) are typical examples of sensors with anisotropic thermal conduction properties, due to the different conductance values in the directions either parallel or orthogonal to the copper tracks which are placed onto a fiberglass substrate. A parametric study on PCBs with different tracks coverage fraction and copper-to-fiberglass heat conductance ratio is carried out. A revised heated-thin-foil formulation, including a correction for anisotropic thermal properties of the PCB, is experimentally tested. The selected thermo-fluid-dynamic test case is the convective heat transfer of a normally impinging round jet for which axisymmetric maps of the Nusselt number are expected. The anisotropic tangential conduction results in non-axisymmetric temperature distributions. Consequently, if anisotropy is not properly accounted for, non-axisymmetric Nusselt number maps are obtained. The anisotropic conduction effects are shown to be weakly sensitive to the copper tracks coverage fraction while strongly dependent on a parameter called degree of anisotropy, which accounts for the copper-to-fiberglass heat-conductance ratio. Anisotropic conduction effects are found to be almost negligible in PCBs with low values of the degree of anisotropy and/or low values of the tangential conduction degree of importance. Accounting for the anisotropic tangential conduction in the heated-thin-foil formulation allows minimizing the differences between the Nusselt number profiles measured in the directions parallel and orthogonal to the copper tracks. For all the considered PCBs, differences after correction are found to be below the measurement uncertainty expected for an equivalent thermally-isotropic sensor. The proposed approach also allows reducing below the measurement uncertainty the spread between the Nusselt number values measured with all the considered printed circuit boards, providing measurements practically independent of the sensor characteristics.

中文翻译：

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印刷电路板加热薄箔热通量传感器中各向异性切向传导的评估

摘要 研究了热各向异性加热薄箔热通量传感器中切向传导贡献的影响。定义和评估用于评估传感器中切向传导的重要性程度的参数以证明切向传导校正的需要是合理的。印刷电路板 (PCB) 是具有各向异性热传导特性的传感器的典型示例，因为在与放置在玻璃纤维基板上的铜迹线平行或正交的方向上的电导值不同。对具有不同轨道覆盖率和铜与玻璃纤维热导比的 PCB 进行了参数研究。修改后的加热薄箔配方，包括对 PCB 各向异性热特性的修正，进行了实验测试。选定的热流体动力学测试案例是正常撞击圆形射流的对流热传递，预计会有 Nusselt 数的轴对称图。各向异性切向传导导致非轴对称温度分布。因此，如果没有正确考虑各向异性，将获得非轴对称 Nusselt 数图。各向异性传导效应显示出对铜轨道覆盖率的敏感性较弱，而强烈依赖于称为各向异性程度的参数，该参数解释了铜与玻璃纤维的热导比。发现各向异性传导效应在具有低各向异性程度值和/或低值切向传导重要程度值的 PCB 中几乎可以忽略不计。考虑到加热薄箔配方中的各向异性切向传导，可以最大限度地减少在平行和正交于铜迹线的方向上测量的努塞尔数分布之间的差异。对于所有考虑的 PCB，发现校正后的差异低于等效热各向同性传感器预期的测量不确定度。所提出的方法还允许将使用所有考虑的印刷电路板测量的 Nusselt 数值之间的差降低到测量不确定度以下，从而提供实际上独立于传感器特性的测量。发现校正后的差异低于等效热各向同性传感器预期的测量不确定度。所提出的方法还允许将使用所有考虑的印刷电路板测量的 Nusselt 数值之间的差降低到测量不确定度以下，从而提供实际上独立于传感器特性的测量。发现校正后的差异低于等效热各向同性传感器预期的测量不确定度。所提出的方法还允许将使用所有考虑的印刷电路板测量的 Nusselt 数值之间的差降低到测量不确定度以下，从而提供实际上独立于传感器特性的测量。