Generally, the 3ω method for the measurement of fluid thermal properties is based on an approximate solution to heat conduction model assuming vanishing heater-thickness, no dielectric layer and infinite heater-length. In this study, a novel three-dimensional model and partial differential equations of the dimensionless heating conduction in frequency domain were established, which took into account the finite thicknesses of the heater and dielectric layer as well as a finite heater length to investigate thermal conductivity and diffusivity of fluid. Through the numerical studies, it was found that we could reduce the ratio of thickness to width of heater or the thickness and thermal conductivity of the dielectric layer to minimize discrepancy between the numerical results and the approximate solutions. Additionally, the edge effects of a finite heater length can be ignored at low measurement frequencies and high ratio of length to width of the heater.
Huang, X., Hebibul, R., Zhao, L., Xu, T., Zhao, Y., & Jiang, Z. (2016). Analysis of the 3ω method for the measurement of fluid thermal properties. In 2016 IEEE 11th Annual International Conference on Nano/Micro Engineered and Molecular Systems, NEMS 2016 (pp. 196–199). Institute of Electrical and Electronics Engineers Inc. https://doi.org/10.1109/NEMS.2016.7758231