Improved transient plane source measurements of layer–substrate structures via a semi‑analytical temperature response model

Journal article, 2026

The Transient Plane Source (TPS) method is widely used to investigate the thermal properties of homogeneous bulk materials and has been further extended to layer–substrate structures. Conventional models on layer–substrate structures typically assume one-dimensional (1D) heat flux across the layer from the heating area into the backing substrate. This assumption imposes a series of constraints on the layer (thermal conductivity ' 2 Wm⁻¹K⁻¹ and thickness ' 600 μm) and on the heating area (radius ' 11 mm), which greatly limits the scope of the current method. In this study, we present a new semi-analytical model with consideration of non-1D heat flux within the layer, along with an iterative algorithm which automatically selects time range for data analysis. This new model substantially relaxes these constraints, expanding the applicable layer thermal conductivity by an order of magnitude (up to 20 Wm⁻¹K⁻¹) and thickness by about three times (up to 2000 μm). Moreover, the model enables the use of a new TPS probe for layer-substrate structures, which has a radius of only 6.6 mm. Experiments are described to validate the new model, showing that inaccuracies primarily stem from the thermal contact resistance. Finite element simulations further indicate that a measurement accuracy better than 10 % can be achieved provided that thermal contact resistance is mitigated.