An accurate low-frequency model for the 3 omega method

An analytical solution of the 3D heat diffusion problem, in the two-pad and four-pad 3 omega experimental technique configurations, is achieved using integral transforms. It leads to rapid calculation of the average temperature on the heated area without any numerical problems whatever the dimensions of the narrow strip. Such an analytical resolution is of great interest in the low-frequency range, which is generally concerned by the method, where the finite thickness of the material plays a crucial role. In particular, we demonstrate that the 3D method is required to correctly calculate the heat diffusion along a narrow strip, when its length is particularly short, as it is the case in the two-pad configuration.