Two-dimensional angstrom two-point inversion method for measuring the in-plane dynamic thermal diffusivity of flat-plate devices

Abstract

This paper proposes a two-dimensional Angstrom two-point inversion method for measuring the in-plane dynamic thermal diffusivity of flat-plate devices such as vapor chambers under periodic thermal excitation. The method overcomes the limitations of steady-state thermal resistance tests in characterizing dynamic diffusion responses and those of conventional one-dimensional Angstrom models in describing radial thermal-wave propagation in plates. Based on the two-dimensional unsteady heat conduction equation and the far-field approximation of cylindrical thermal waves, a two-point inversion model incorporating geometric spreading correction is established. Temperature-wave amplitudes and phases are extracted via Levenberg-Marquardt nonlinear sinusoidal fitting, enabling calculation of the apparent directional equivalent thermal diffusivity. The method was validated using pure copper, 6063 aluminum alloy, and 304 stainless steel thin plates; measured diffusivities agreed with theoretical values in order of magnitude and exhibited good directional consistency. The method was subsequently applied to an Al6063-R1233zd vapor chamber. Results show that the excitation period strongly affects far-point signal quality and inversion stability. As the period increases from 60 s to above 150 s, the far-point fitting goodness R 2 improves from approximately 0.68 to above 0.88 and stabilizes near 0.95 at longer periods. The apparent directional equivalent thermal diffusivity of the vapor chamber first increases and then stabilizes with increasing period, indicating that the proposed method can capture its dynamic in-plane thermal diffusion response with limited measurement points and low experimental complexity.

The authors' abstract, as published at the source. Applied Thermal Engineering, 2026 · DOI ↗