Internal Temperature Field Reconstruction in Solids Using Ultrasonic Upper Envelope Area

The nondestructive estimation of transient heat flux and internal temperature fields in solids is crucial for the thermal management and safety evaluation of high-end equipment and is particularly valuable for applications involving demanding thermal conditions. However, the ill-posed nature of inverse heat transfer problems, coupled with the severe scattering interference faced by conventional ultrasonic parameters such as time-of-flight in heterogeneous materials, makes accurate estimation highly challenging. This study proposes a novel inverse estimation method based on the upper envelope area of ultrasonic echoes, treating it as an energy-based, temperature-sensitive macroscopic parameter. A sequentially coupled thermo-acoustic forward model is established, transforming the temperature measurement into an optimization inverse problem solved by the conjugate gradient method. Systematic numerical experiments demonstrate that this method achieves high-precision tracking and reconstruction of various boundary heat fluxes as well as transient temperature fields, with the relative error strictly controlled within 1%. Furthermore, the algorithm exhibits good robustness against initial guess errors, thermophysical property uncertainties up to ±10%, and measurement noise up to 1 × 10−7 V·μs. This study establishes the upper envelope area as a robust observation input for inverse heat transfer problems, providing a new solution for the nondestructive estimation of heat flux and temperature fields inside complex heterogeneous materials.