Thermal diffusivity from Fourier’s inverse problem supervised by an optimization model: Theoretical analysis and experimental validation

Abstract

An original experimental device coupled with an optimization technique, for determining the thermal diffusivity (αdiff) of solid materials, has been devised and experimentally validated. The inverse problem of the classical Fourier heat equation in transient condition is numerically supervised by an optimization procedure for the initial and boundary conditions from measurements. Imperfect adiabaticity on the insulated lateral surfaces is explained by modeling heat loss correction functions with additional time dependent Robin conditions. The optimization model identifies the optimal values of the heat transfer coefficients and of αdiff by minimizing the residual function between the model predictions and the experimental data. Incorporating the heat loss corrections in the solution of the heat equation significantly improves the estimation of the αdiff. Indeed, the time profile of the surface temperatures measured for a specimen of PPMA material is well reflected by the simulated curves. The estimated αdiff is in good agreement with an experimental inter-comparison of eleven laboratories equipped with Laser Flash, hot disk, and hot bridge certified devices. Our results reveal a reliable capability of the model to identify the αdiff value that explains the functional dependence underlying the experimental observations. The error lies in the range 5% or 34%, depending on whether the heat losses are accounted or not.

Keywords

• Heat conduction
• Thermal diffusivity
• Inverse problem
• Optimization model