A revisit of the electro-diffusional theory for the wall shear stress measurement

•The electro-diffusional theory is revisited for strip mass transfer probes.•The arbitrary 2D flow direction and the probe aspect ratio are considered.•Analytical formulas for the dimensionless mass transport coefficient are derived.•The correctness of the analytical equations is confirmed by numeri...

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Bibliographic Details
Published in:International journal of heat and mass transfer 2021-02, Vol.165, p.120610, Article 120610
Main Authors: Havlica, Jaromir, Kramolis, David, Huchet, Florian
Format: Article
Language:English
Subjects:
Aspect ratio
Boundary layer
Computational fluid dynamics
Electrochemical method
Fluid flow
Lévêque
Mass transfer
Parameters
Shear rate
Shear stress
Stress measurement
Strip
Three dimensional boundary layer
Transport equations
Transport properties
Wall shear rate
Wall shear stresses
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Summary:•The electro-diffusional theory is revisited for strip mass transfer probes.•The arbitrary 2D flow direction and the probe aspect ratio are considered.•Analytical formulas for the dimensionless mass transport coefficient are derived.•The correctness of the analytical equations is confirmed by numerical solutions.•A measurement methodology for strip probe is proposed. [Display omitted] 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 Lévêque 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.
ISSN:0017-9310
1879-2189
DOI:10.1016/j.ijheatmasstransfer.2020.120610