Evaluation of anisotropic tangential conduction in printed-circuit-board heated-thin-foil heat flux sensors

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. (C) 2018 Elsevier Ltd. All rights reserved.