3ω method in combination with a meander shaped heater: Theoretical and experimental investigation

Abstract The 3ω-method is usually applied to a line heater because it simplifies the analytical solution of the heat transfer equation. Other potentially beneficial heater geometries, such as meandering heater structures, have not yet been addressed in the literature to date. A meandering structure is advantageous when the available space is limited. This article presents the detailed investigation on meander shaped heater structures, in combination with the 3ω-method. A theoretical approach approximated the meandering structure as several parallel strips with a certain spacing. It investigates the influence of the spacing and compares it with the conventional line heater model. It was found that the conventional model is an accurate model when the thermal diffusivity of the surrounding area of the heater is high and the spacing between the heater lines is small. This finding was used in the experimental investigation. Due to the general expressions of the theoretical model, it can be used as a tool for future investigations. An experimental approach investigated the loss of invariance along the lateral axis, which is often assumed for a line heater where its length is much larger than its width and a two-dimensional description can be used. The boundary effect of the finite length is neglected. The basic idea of the experimental work is to fabricate several meandering structures with different length-width ratios, but with the same total path length of the structures, such that the structures with different length-width ratios can be compared. The results based on platinum thin film structures showed that the straight structure with a length-to-width ratio of 300 deviates from the prediction of the two-dimensional model by about 5%. The structures with a length-to-width ratio 50 match significantly poorer with the two-dimensional model. The deviation becomes larger than 10%. A strong signal helps regarding the resolution in the application. The theoretical findings showed that the signal is highest if the distance between the heater lines is as small as possible. Moreover, the experimental work showed highest performance if the length-width ratio is around 1.4.