Estimation of Thermal Diffusivity in the Inverse Heat Transfer Problem for a Polymer Plate

This study investigates the inverse estimation of the effective thermal diffusivity of a polytetrafluoroethylene (PTFE) plate subjected to oscillatory heating from a hot plate with on–off control. Transient temperature measurements at four internal positions were used to evaluate three modeling strategies: a constant-diffusivity formulation with a prescribed Dirichlet boundary condition, a position-dependent effective diffusivity formulation, (x), and a constant-diffusivity model with a Robin boundary condition to account for thermal contact resistance. The constant-diffusivity Dirichlet model, when fitted to all data simultaneously, was unable to reproduce the experimental thermal response satisfactorily. When fitted separately at each thermocouple position, the estimated effective diffusivity increased systematically with position change, indicating that the experimental response could not be represented by a single scalar parameter under the adopted Dirichlet formulation. Variable-(x) models improved the fit, especially the exponential and rational expressions, which reproduced the apparent saturating spatial trend more effectively. However, these functions should be interpreted as empirical effective representations rather than intrinsic constitutive laws for PTFE. The Robin-boundary model with constant diffusivity also provided a comparable fit, suggesting that interfacial thermal resistance at the PTFE–hot plate contact may explain part of the apparent spatial variation inferred by the Dirichlet models. These results indicate that internal temperature measurements under realistic transient heating are not sufficient to uniquely distinguish between distributed effective diffusivity and boundary-contact resistance effects. Therefore, the estimated diffusivity values should be interpreted as model-dependent effective parameters rather than direct measurements of intrinsic PTFE thermal diffusivity.